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Wikipedia:Malwina Luczak#0 | Malwina J. Luczak is a mathematician specializing in probability theory and the theory of random graphs. She is Professor of Applied Probability and Leverhulme International Professor at the Department of Mathematics at the University of Manchester. == Education and research == Luczak grew up in Poland, and began her university studies at age 16 at the Nicolaus Copernicus University in Toruń, where she took philology of the English language. However, after her second year studying philology at Keele University in the UK, she decided to switch to mathematics, and enrolled at St Catherine's College, Oxford. After her first year's examinations, she was able to obtain scholarship support, continue her studies and remain at Oxford for doctoral work. She completed her D.Phil. in 2001 with a dissertation, Probability, algorithms and telecommunication systems, supervised by Colin McDiarmid and Dominic Welsh. She became an assistant lecturer at the Statistical Laboratory at the University of Cambridge and then a reader in mathematics at the London School of Economics. However, in 2010, after failing to receive an expected promotion to professor, she took a professorial chair position at the University of Sheffield and a five-year Engineering and Physical Sciences Research Council Leadership Fellowship. She moved again to Queen Mary University of London before taking a Professorship in Melbourne in 2017. Most recently, in 2023 she joined the University of Manchester. == Research == Luczak's publications include research on the supermarket model in queueing theory,[a] cores of random graphs,[b] the giant component in random graphs with specified degree distributions,[c] and the Glauber dynamics of the Ising model.[d] They include: == References == == External links == Department of Mathematics, University of Manchester Malwina Luczak publications indexed by Google Scholar |
Wikipedia:Mamokgethi Phakeng#0 | Rosina Mamokgethi Phakeng (née Mmutlana, born 1 November 1966) is a South African professor of mathematics education who in 2018 became a vice-chancellor of the University of Cape Town (UCT). She has been the vice principal of research and innovation, at the University of South Africa and acting executive dean of the College of Science, Engineering and Technology at UNISA. In 2018 she was an invited speaker at the International Congresses of Mathematicians. In February 2023 it was announced that she would leave her position as vice-chancellor of UCT and take early retirement. She was succeeded by Professor Daya Reddy on 13 March 2023. == Early life == Phakeng was born in Eastwood, Pretoria, to Frank and Wendy Mmutlana (née Thipe). Her mother went back to school after having her three children to complete Form 3 as entry to gaining a Primary Teachers Certificate to practice as a teacher. Her father was one of the first black radio announcers at the South African Broadcasting Corporation (SABC). Phakeng started school in 1972 at Ikageleng Primary in Marapyane village and then Ikageng Primary in Ga-Rankuwa. She attended Tsela-tshweu higher primary; Tswelelang Higher Primary; Thuto-Thebe Middle School; Odi High School and Hebron. She completed her matric with University Exemption in 1983 (Grade 12) in the village of Hebron's College of Education. == Higher education == Phakeng achieved a Bachelor of Education in mathematics education at the University of North-West, and a M.Ed in mathematics education at the University of the Witwatersrand, and in 2002 became the first black female South African to obtain a PhD in mathematics education. In September 2022, Phakeng won the first Africa Education Medal for her commitment to promoting education in Africa, particularly for her research on language practices in multilingual mathematics classrooms. === Career accomplishments === Phakeng has won awards for excellence in service. These honors include: Doctor of Science, honoris causa, University of Bristol The Order of the Baobab (Silver) for her excellent contribution in the field of science and representing South Africa on the international stage through her outstanding research work presented to her by former president of South Africa Jacob Zuma (April 2016) Order of Ikhamanga in gold CEO Magazine award for being the most influential woman in education and training in South Africa (August 2013) NSTF award for being the most outstanding Senior Black Female Researcher over the last 5 to 10 years in recognition of her innovative, quality research on teaching and learning mathematics in multilingual classrooms (May 2011) Golden key International Society Honorary life membership (May 2009) Association of Mathematics Education of South Africa (AMESA) honorary life membership (July 2009) Amstel Salute to Success finalist (2005) Dr. T. W. Khambule Research Award for being the most outstanding young female black researcher for 2003 – conferred by the NSTF (May 2004) Outstanding Service Award (Education category) – conferred by the Sunday Sun and Christ Centred Church (2004) Finalist for SA Woman of the Year in the Science and Technology Category (2003) Prestige National Award South Africa's Inspirational Women Achievers Award – conferred by RCP Media, (June 2003) NRF Thuthuka Award (2003–2008) National Research Foundation/National Science Foundation USA/SA fellowship (2001, 2003) Mellon Award (1998–2000) SAB Women in Rural Areas Award (1997) === Positions held === Vice-Chancellor of the University of Cape Town (2018–2023) Deputy Vice-Chancellor of the University of Cape Town (2016) Vice-Principal of Research and Innovation at the University of South Africa Executive Dean of College of Science Engineering and Technology of University of South Africa Honorary Professor of University of the Witwatersrand Professor extraordinaire of Tshwane University of Technology Deputy Chairperson of National Committee for the International Mathematics Union Trustee of FirstRand Foundation Trustee of Telkom SA Foundation Board Member of South Africa, International Council for Science (ICSU) Board Managing Director of Pythagoras Bristol Illustrious Visiting Professor == Personal life == Phakeng was married to Richard Setati for 19 years (1988–2007) and they had one son, Tsholofelo who was born in 1990. In 2012, she married Madimetja Lucky Phakeng, thereby adding the appendage "Phakeng" to her surname. Lucky Phakeng is an advocate currently heading the Takeover Regulation Panel. == Controversy == Shortly after being appointed to the position as vice-chancellor of UCT, allegations questioning Phakeng's academic credentials emerged which she characterised as being part of a smear campaign against her. On 22 February 2023 it was reported by News24 that Phakeng would take early retirement from her position as vice-chancellor of UCT following the appointment of an independent panel to investigate allegations of mismanagement and abuse of power. Phakeng was paid R12 million (US$ 667,000) for the leaving before her contract expired in 2028 whilst an investigation into allegations of mismanagement and abuse of power was conducted by an independent panel of retired judges. The report, published eight months later, concluded that Phakeng's conduct whilst vice-chancellor at UCT was problematic with notable and repeated instances of unprofessional conduct.: 174 === Twitter === During her time at UCT a number of controversial social media statements have been made via Phakeng's Twitter account. In 2018 Phakeng controversially congratulated a UCT student activist, Masixole Mlandu, who notably ended his undergraduate paper with the racially divisive slogan "One Settler, One Bullet." Phakeng later stated she regretted the divisive incident, did not see the statement before making the congratulatory statement, would never support calls for violence, and was instead trying to congratulate a student on a significant personal academic milestone. === Managerial style === Phakeng's tenure as vice-chancellor of UCT was controversial with accusations by university academics and the university's ombud that she allowed for the emergence of a culture of fear, secrecy, racialisation, unfair treatment and bullying within the university that resulted in the departure of numerous academics. The ombud and the university's former deputy council chair accused Phakeng of covering up accusations and findings against her whilst the university's former deputy vice-chancellor for teaching and learning accused her of having deliberately misled university's Senate. In a Senate vote on the matter Phakeng controversially cast a deciding vote against an independent investigation into her own conduct, thereby possibly breaching university conflict of interest rules. Phakeng's supporters, including the Economic Freedom Fighters, alleged that she was being targeted by groups resistant to racial transformation of the university. UCT stated that the accusations against Phakeng contained within a 2022 Daily Maverick article on the matter were "incorrect, misleading and unethical"; the Daily Maverick disputed UCT's criticisms of their article. == Independent investigation into UCT governance == === Introduction === An independent panel, chaired by retired judge Lex Mpati, featuring fellow retired judge Azhar Cachalia, public sector governance expert Trish Hanekom and Wits transformation head Bernadette Johnson investigated governance issues at the University of Cape Town (UCT), triggered by undisclosed events leading to Associate Professor Lis Lange's departure and a subsequent Non-Disclosure Agreement. The probe was initiated amid the extension of Vice-Chancellor (VC) Professor Mamokgethi Phakeng's term, highlighting concerns over executive committee stability and unexplained senior resignations. === Revised terms of reference === The Council revised the investigation's scope following VC Phakeng's agreed exit, broadening the inquiry to address broader governance failures and their impact on executive resignations from January 2018 to December 2022, with a view towards recommending future preventive strategies. === Breaches of law and policy === The Panel implicated former VC Phakeng in several breaches of law and policy, including unlawful contract terminations, defamatory behaviour, conflicts of interest, and unprofessional conduct. Additionally, she engaged in prohibited activities such as issuing threats, employing ethnic slurs, and sharing racially offensive content on social media. === Senior resignations === Investigations revealed that the actions of Mamokgethi Phakeng and the Chair of Council, Ms Babalwa Ngonyama, were central to the resignation of several senior UCT officials: Professor Loretta Feris, former Deputy Vice-Chancellor (DVC) for Transformation Dr Russel Ally, former Executive Director of Development and Alumni Associate Professor Lis Lange, former DVC for Teaching and Learning Ms Gerda Kruger, former Executive Director of Communication and Marketing Mr Royston Pillay, Registrar Dr Reno Morar, former Chief Operating Officer Professor Linda Ronnie, former Dean of Commerce (now returned as acting DVC for Teaching and Learning) Ms Miriam Hoosain, Executive Director of HR Ms Judith du Toit, Director in the Office of the VC. == References == == External links == Publications by Mamokgethi Phakeng at ResearchGate |
Wikipedia:Mandelbrot set#0 | The Mandelbrot set () is a two-dimensional set that is defined in the complex plane as the complex numbers c {\displaystyle c} for which the function f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} does not diverge to infinity when iterated starting at z = 0 {\displaystyle z=0} , i.e., for which the sequence f c ( 0 ) {\displaystyle f_{c}(0)} , f c ( f c ( 0 ) ) {\displaystyle f_{c}(f_{c}(0))} , etc., remains bounded in absolute value. This set was first defined and drawn by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian groups. Afterwards, in 1980, Benoit Mandelbrot obtained high-quality visualizations of the set while working at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York. Images of the Mandelbrot set exhibit an infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications; mathematically, the boundary of the Mandelbrot set is a fractal curve. The "style" of this recursive detail depends on the region of the set boundary being examined. Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point c {\displaystyle c} , whether the sequence f c ( 0 ) , f c ( f c ( 0 ) ) , … {\displaystyle f_{c}(0),f_{c}(f_{c}(0)),\dotsc } goes to infinity. Treating the real and imaginary parts of c {\displaystyle c} as image coordinates on the complex plane, pixels may then be colored according to how soon the sequence | f c ( 0 ) | , | f c ( f c ( 0 ) ) | , … {\displaystyle |f_{c}(0)|,|f_{c}(f_{c}(0))|,\dotsc } crosses an arbitrarily chosen threshold (the threshold must be at least 2, as −2 is the complex number with the largest magnitude within the set, but otherwise the threshold is arbitrary). If c {\displaystyle c} is held constant and the initial value of z {\displaystyle z} is varied instead, the corresponding Julia set for the point c {\displaystyle c} is obtained. The Mandelbrot set is well-known, even outside mathematics, for how it exhibits complex fractal structures when visualized and magnified, despite having a relatively simple definition. == History == The Mandelbrot set has its origin in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The fractal was first defined and drawn in 1978 by Robert W. Brooks and Peter Matelski as part of a study of Kleinian groups. On 1 March 1980, at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York, Benoit Mandelbrot first visualized the set. Mandelbrot studied the parameter space of quadratic polynomials in an article that appeared in 1980. The mathematical study of the Mandelbrot set really began with work by the mathematicians Adrien Douady and John H. Hubbard (1985), who established many of its fundamental properties and named the set in honor of Mandelbrot for his influential work in fractal geometry. The mathematicians Heinz-Otto Peitgen and Peter Richter became well known for promoting the set with photographs, books (1986), and an internationally touring exhibit of the German Goethe-Institut (1985). The cover article of the August 1985 Scientific American introduced the algorithm for computing the Mandelbrot set. The cover was created by Peitgen, Richter and Saupe at the University of Bremen. The Mandelbrot set became prominent in the mid-1980s as a computer-graphics demo, when personal computers became powerful enough to plot and display the set in high resolution. The work of Douady and Hubbard occurred during an increase in interest in complex dynamics and abstract mathematics, and the topological and geometric study of the Mandelbrot set remains a key topic in the field of complex dynamics. == Formal definition == The Mandelbrot set is the uncountable set of values of c in the complex plane for which the orbit of the critical point z = 0 {\textstyle z=0} under iteration of the quadratic map z ↦ z 2 + c {\displaystyle z\mapsto z^{2}+c} remains bounded. Thus, a complex number c is a member of the Mandelbrot set if, when starting with z 0 = 0 {\displaystyle z_{0}=0} and applying the iteration repeatedly, the absolute value of z n {\displaystyle z_{n}} remains bounded for all n > 0 {\displaystyle n>0} . For example, for c = 1, the sequence is 0, 1, 2, 5, 26, ..., which tends to infinity, so 1 is not an element of the Mandelbrot set. On the other hand, for c = − 1 {\displaystyle c=-1} , the sequence is 0, −1, 0, −1, 0, ..., which is bounded, so −1 does belong to the set. The Mandelbrot set can also be defined as the connectedness locus of the family of quadratic polynomials f ( z ) = z 2 + c {\displaystyle f(z)=z^{2}+c} , the subset of the space of parameters c {\displaystyle c} for which the Julia set of the corresponding polynomial forms a connected set. In the same way, the boundary of the Mandelbrot set can be defined as the bifurcation locus of this quadratic family, the subset of parameters near which the dynamic behavior of the polynomial (when it is iterated repeatedly) changes drastically. == Basic properties == The Mandelbrot set is a compact set, since it is closed and contained in the closed disk of radius 2 centred on zero. A point c {\displaystyle c} belongs to the Mandelbrot set if and only if | z n | ≤ 2 {\displaystyle |z_{n}|\leq 2} for all n ≥ 0 {\displaystyle n\geq 0} . In other words, the absolute value of z n {\displaystyle z_{n}} must remain at or below 2 for c {\displaystyle c} to be in the Mandelbrot set, M {\displaystyle M} , and if that absolute value exceeds 2, the sequence will escape to infinity. Since c = z 1 {\displaystyle c=z_{1}} , it follows that | c | ≤ 2 {\displaystyle |c|\leq 2} , establishing that c {\displaystyle c} will always be in the closed disk of radius 2 around the origin. The intersection of M {\displaystyle M} with the real axis is the interval [ − 2 , 1 4 ] {\displaystyle \left[-2,{\frac {1}{4}}\right]} . The parameters along this interval can be put in one-to-one correspondence with those of the real logistic family, x n + 1 = r x n ( 1 − x n ) , r ∈ [ 1 , 4 ] . {\displaystyle x_{n+1}=rx_{n}(1-x_{n}),\quad r\in [1,4].} The correspondence is given by r = 1 + 1 − 4 c , c = r 2 ( 1 − r 2 ) , z n = r ( 1 2 − x n ) . {\displaystyle r=1+{\sqrt {1-4c}},\quad c={\frac {r}{2}}\left(1-{\frac {r}{2}}\right),\quad z_{n}=r\left({\frac {1}{2}}-x_{n}\right).} This gives a correspondence between the entire parameter space of the logistic family and that of the Mandelbrot set. Douady and Hubbard showed that the Mandelbrot set is connected. They constructed an explicit conformal isomorphism between the complement of the Mandelbrot set and the complement of the closed unit disk. Mandelbrot had originally conjectured that the Mandelbrot set is disconnected. This conjecture was based on computer pictures generated by programs that are unable to detect the thin filaments connecting different parts of M {\displaystyle M} . Upon further experiments, he revised his conjecture, deciding that M {\displaystyle M} should be connected. A topological proof of the connectedness was discovered in 2001 by Jeremy Kahn. The dynamical formula for the uniformisation of the complement of the Mandelbrot set, arising from Douady and Hubbard's proof of the connectedness of M {\displaystyle M} , gives rise to external rays of the Mandelbrot set. These rays can be used to study the Mandelbrot set in combinatorial terms and form the backbone of the Yoccoz parapuzzle. The boundary of the Mandelbrot set is the bifurcation locus of the family of quadratic polynomials. In other words, the boundary of the Mandelbrot set is the set of all parameters c {\displaystyle c} for which the dynamics of the quadratic map z n = z n − 1 2 + c {\displaystyle z_{n}=z_{n-1}^{2}+c} exhibits sensitive dependence on c , {\displaystyle c,} i.e. changes abruptly under arbitrarily small changes of c . {\displaystyle c.} It can be constructed as the limit set of a sequence of plane algebraic curves, the Mandelbrot curves, of the general type known as polynomial lemniscates. The Mandelbrot curves are defined by setting p 0 = z , p n + 1 = p n 2 + z {\displaystyle p_{0}=z,\ p_{n+1}=p_{n}^{2}+z} , and then interpreting the set of points | p n ( z ) | = 2 {\displaystyle |p_{n}(z)|=2} in the complex plane as a curve in the real Cartesian plane of degree 2 n + 1 {\displaystyle 2^{n+1}} in x and y. Each curve n > 0 {\displaystyle n>0} is the mapping of an initial circle of radius 2 under p n {\displaystyle p_{n}} . These algebraic curves appear in images of the Mandelbrot set computed using the "escape time algorithm" mentioned below. == Other properties == === Main cardioid and period bulbs === The main cardioid is the period 1 continent. It is the region of parameters c {\displaystyle c} for which the map f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} has an attracting fixed point. It consists of all parameters of the form c ( μ ) := μ 2 ( 1 − μ 2 ) {\displaystyle c(\mu ):={\frac {\mu }{2}}\left(1-{\frac {\mu }{2}}\right)} for some μ {\displaystyle \mu } in the open unit disk. To the left of the main cardioid, attached to it at the point c = − 3 / 4 {\displaystyle c=-3/4} , a circular bulb, the period-2 bulb is visible. The bulb consists of c {\displaystyle c} for which f c {\displaystyle f_{c}} has an attracting cycle of period 2. It is the filled circle of radius 1/4 centered around −1. More generally, for every positive integer q > 2 {\displaystyle q>2} , there are ϕ ( q ) {\displaystyle \phi (q)} circular bulbs tangent to the main cardioid called period-q bulbs (where ϕ {\displaystyle \phi } denotes the Euler phi function), which consist of parameters c {\displaystyle c} for which f c {\displaystyle f_{c}} has an attracting cycle of period q {\displaystyle q} . More specifically, for each primitive q {\displaystyle q} th root of unity r = e 2 π i p q {\displaystyle r=e^{2\pi i{\frac {p}{q}}}} (where 0 < p q < 1 {\displaystyle 0<{\frac {p}{q}}<1} ), there is one period-q bulb called the p q {\displaystyle {\frac {p}{q}}} bulb, which is tangent to the main cardioid at the parameter c p q := c ( r ) = r 2 ( 1 − r 2 ) , {\displaystyle c_{\frac {p}{q}}:=c(r)={\frac {r}{2}}\left(1-{\frac {r}{2}}\right),} and which contains parameters with q {\displaystyle q} -cycles having combinatorial rotation number p q {\displaystyle {\frac {p}{q}}} . More precisely, the q {\displaystyle q} periodic Fatou components containing the attracting cycle all touch at a common point (commonly called the α {\displaystyle \alpha } -fixed point). If we label these components U 0 , … , U q − 1 {\displaystyle U_{0},\dots ,U_{q-1}} in counterclockwise orientation, then f c {\displaystyle f_{c}} maps the component U j {\displaystyle U_{j}} to the component U j + p ( mod q ) {\displaystyle U_{j+p\,(\operatorname {mod} q)}} . The change of behavior occurring at c p q {\displaystyle c_{\frac {p}{q}}} is known as a bifurcation: the attracting fixed point "collides" with a repelling period-q cycle. As we pass through the bifurcation parameter into the p q {\displaystyle {\tfrac {p}{q}}} -bulb, the attracting fixed point turns into a repelling fixed point (the α {\displaystyle \alpha } -fixed point), and the period-q cycle becomes attracting. === Hyperbolic components === Bulbs that are interior components of the Mandelbrot set in which the maps f c {\displaystyle f_{c}} have an attracting periodic cycle are called hyperbolic components. It is conjectured that these are the only interior regions of M {\displaystyle M} and that they are dense in M {\displaystyle M} . This problem, known as density of hyperbolicity, is one of the most important open problems in complex dynamics. Hypothetical non-hyperbolic components of the Mandelbrot set are often referred to as "queer" or ghost components. For real quadratic polynomials, this question was proved in the 1990s independently by Lyubich and by Graczyk and Świątek. (Note that hyperbolic components intersecting the real axis correspond exactly to periodic windows in the Feigenbaum diagram. So this result states that such windows exist near every parameter in the diagram.) Not every hyperbolic component can be reached by a sequence of direct bifurcations from the main cardioid of the Mandelbrot set. Such a component can be reached by a sequence of direct bifurcations from the main cardioid of a little Mandelbrot copy (see below). Each of the hyperbolic components has a center, which is a point c such that the inner Fatou domain for f c ( z ) {\displaystyle f_{c}(z)} has a super-attracting cycle—that is, that the attraction is infinite. This means that the cycle contains the critical point 0, so that 0 is iterated back to itself after some iterations. Therefore, f c n ( 0 ) = 0 {\displaystyle f_{c}^{n}(0)=0} for some n. If we call this polynomial Q n ( c ) {\displaystyle Q^{n}(c)} (letting it depend on c instead of z), we have that Q n + 1 ( c ) = Q n ( c ) 2 + c {\displaystyle Q^{n+1}(c)=Q^{n}(c)^{2}+c} and that the degree of Q n ( c ) {\displaystyle Q^{n}(c)} is 2 n − 1 {\displaystyle 2^{n-1}} . Therefore, constructing the centers of the hyperbolic components is possible by successively solving the equations Q n ( c ) = 0 , n = 1 , 2 , 3 , . . . {\displaystyle Q^{n}(c)=0,n=1,2,3,...} . The number of new centers produced in each step is given by Sloane's OEIS: A000740. === Local connectivity === It is conjectured that the Mandelbrot set is locally connected. This conjecture is known as MLC (for Mandelbrot locally connected). By the work of Adrien Douady and John H. Hubbard, this conjecture would result in a simple abstract "pinched disk" model of the Mandelbrot set. In particular, it would imply the important hyperbolicity conjecture mentioned above. The work of Jean-Christophe Yoccoz established local connectivity of the Mandelbrot set at all finitely renormalizable parameters; that is, roughly speaking those contained only in finitely many small Mandelbrot copies. Since then, local connectivity has been proved at many other points of M {\displaystyle M} , but the full conjecture is still open. === Self-similarity === The Mandelbrot set is self-similar under magnification in the neighborhoods of the Misiurewicz points. It is also conjectured to be self-similar around generalized Feigenbaum points (e.g., −1.401155 or −0.1528 + 1.0397i), in the sense of converging to a limit set. The Mandelbrot set in general is quasi-self-similar, as small slightly different versions of itself can be found at arbitrarily small scales. These copies of the Mandelbrot set are all slightly different, mostly because of the thin threads connecting them to the main body of the set. === Further results === The Hausdorff dimension of the boundary of the Mandelbrot set equals 2 as determined by a result of Mitsuhiro Shishikura. The fact that this is greater by a whole integer than its topological dimension, which is 1, reflects the extreme fractal nature of the Mandelbrot set boundary. Roughly speaking, Shishikura's result states that the Mandelbrot set boundary is so "wiggly" that it locally fills space as efficiently as a two-dimensional planar region. Curves with Hausdorff dimension 2, despite being (topologically) 1-dimensional, are oftentimes capable of having nonzero area (more formally, a nonzero planar Lebesgue measure). Whether this is the case for the Mandelbrot set boundary is an unsolved problem. It has been shown that the generalized Mandelbrot set in higher-dimensional hypercomplex number spaces (i.e. when the power α {\displaystyle \alpha } of the iterated variable z {\displaystyle z} tends to infinity) is convergent to the unit ( α {\displaystyle \alpha } −1)-sphere. In the Blum–Shub–Smale model of real computation, the Mandelbrot set is not computable, but its complement is computably enumerable. Many simple objects (e.g., the graph of exponentiation) are also not computable in the BSS model. At present, it is unknown whether the Mandelbrot set is computable in models of real computation based on computable analysis, which correspond more closely to the intuitive notion of "plotting the set by a computer". Hertling has shown that the Mandelbrot set is computable in this model if the hyperbolicity conjecture is true. === Relationship with Julia sets === As a consequence of the definition of the Mandelbrot set, there is a close correspondence between the geometry of the Mandelbrot set at a given point and the structure of the corresponding Julia set. For instance, a value of c belongs to the Mandelbrot set if and only if the corresponding Julia set is connected. Thus, the Mandelbrot set may be seen as a map of the connected Julia sets. This principle is exploited in virtually all deep results on the Mandelbrot set. For example, Shishikura proved that, for a dense set of parameters in the boundary of the Mandelbrot set, the Julia set has Hausdorff dimension two, and then transfers this information to the parameter plane. Similarly, Yoccoz first proved the local connectivity of Julia sets, before establishing it for the Mandelbrot set at the corresponding parameters. == Geometry == For every rational number p q {\displaystyle {\tfrac {p}{q}}} , where p and q are coprime, a hyperbolic component of period q bifurcates from the main cardioid at a point on the edge of the cardioid corresponding to an internal angle of 2 π p q {\displaystyle {\tfrac {2\pi p}{q}}} . The part of the Mandelbrot set connected to the main cardioid at this bifurcation point is called the p/q-limb. Computer experiments suggest that the diameter of the limb tends to zero like 1 q 2 {\displaystyle {\tfrac {1}{q^{2}}}} . The best current estimate known is the Yoccoz-inequality, which states that the size tends to zero like 1 q {\displaystyle {\tfrac {1}{q}}} . A period-q limb will have q − 1 {\displaystyle q-1} "antennae" at the top of its limb. The period of a given bulb is determined by counting these antennas. The numerator of the rotation number, p, is found by numbering each antenna counterclockwise from the limb from 1 to q − 1 {\displaystyle q-1} and finding which antenna is the shortest. === Pi in the Mandelbrot set === There are intriguing experiments in the Mandelbrot set that lead to the occurrence of the number pi. For a parameter c = − 3 4 + i ε {\displaystyle c=-{\tfrac {3}{4}}+i\varepsilon } with ε > 0 {\displaystyle \varepsilon >0} , verifying that c {\displaystyle c} means iterating the sequence z ↦ z 2 + c {\displaystyle z\mapsto z^{2}+c} starting with z = 0 {\displaystyle z=0} , until the sequence leaves the disk around 0 {\displaystyle 0} of any radius R > 2 {\displaystyle R>2} . This is motivated by the (still open) question whether the vertical line at real part 3 / 4 {\displaystyle 3/4} intersects the Mandelbrot set at points away from the real line. It turns out that the necessary number of iterations, multiplied by ε {\displaystyle \varepsilon } , converges to pi. For example, for ε {\displaystyle \varepsilon } = 0.0000001, and R = 2 {\displaystyle R=2} , the number of iterations is 31415928 and the product is 3.1415928. This experiment was performed independently by many people in the early 1990's, if not before; for instance by David Boll. Analogous observations have also been made at the parameters c = − 5 / 4 {\displaystyle c=-5/4} and c = 1 / 4 {\displaystyle c=1/4} (with a necessary modification in the latter case). In 2001, Aaron Klebanoff published a (non-conceptual) proof for this phenomenon at c = 1 / 4 {\displaystyle c=1/4} In 2023, Paul Siewert developed, in his Bachelor thesis, a conceptual proof also for the value c = 1 / 4 {\displaystyle c=1/4} , explaining why the number pi occurs (geometrically as half the circumference of a unit circle). In 2025, the three high school students Thies Brockmöller, Oscar Scherz, and Nedim Srkalovic extended the theory and the conceptual proof to all the infinitely bifurcation points in the Mandelbrot set. === Fibonacci sequence in the Mandelbrot set === The Mandelbrot Set features a fundamental cardioid shape adorned with numerous bulbs directly attached to it. Understanding the arrangement of these bulbs requires a detailed examination of the Mandelbrot Set's boundary. As one zooms into specific portions with a geometric perspective, precise deducible information about the location within the boundary and the corresponding dynamical behavior for parameters drawn from associated bulbs emerges. The iteration of the quadratic polynomial f c ( z ) = z 2 + c {\displaystyle f_{c}(z)=z^{2}+c} , where c {\displaystyle c} is a parameter drawn from one of the bulbs attached to the main cardioid within the Mandelbrot Set, gives rise to maps featuring attracting cycles of a specified period q {\displaystyle q} and a rotation number p / q {\displaystyle p/q} . In this context, the attracting cycle of exhibits rotational motion around a central fixed point, completing an average of p / q {\displaystyle p/q} revolutions at each iteration. The bulbs within the Mandelbrot Set are distinguishable by both their attracting cycles and the geometric features of their structure. Each bulb is characterized by an antenna attached to it, emanating from a junction point and displaying a certain number of spokes indicative of its period. For instance, the 2 / 5 {\displaystyle 2/5} bulb is identified by its attracting cycle with a rotation number of 2 / 5 {\displaystyle 2/5} . Its distinctive antenna-like structure comprises a junction point from which five spokes emanate. Among these spokes, called the principal spoke is directly attached to the 2 / 5 {\displaystyle 2/5} bulb, and the 'smallest' non-principal spoke is positioned approximately 2 / 5 {\displaystyle 2/5} of a turn counterclockwise from the principal spoke, providing a distinctive identification as a 2 / 5 {\displaystyle 2/5} -bulb. This raises the question: how does one discern which among these spokes is the 'smallest'? In the theory of external rays developed by Douady and Hubbard, there are precisely two external rays landing at the root point of a satellite hyperbolic component of the Mandelbrot Set. Each of these rays possesses an external angle that undergoes doubling under the angle doubling map θ ↦ {\displaystyle \theta \mapsto } 2 θ {\displaystyle 2\theta } . According to this theorem, when two rays land at the same point, no other rays between them can intersect. Thus, the 'size' of this region is measured by determining the length of the arc between the two angles. If the root point of the main cardioid is the cusp at c = 1 / 4 {\displaystyle c=1/4} , then the main cardioid is the 0 / 1 {\displaystyle 0/1} -bulb. The root point of any other bulb is just the point where this bulb is attached to the main cardioid. This prompts the inquiry: which is the largest bulb between the root points of the 0 / 1 {\displaystyle 0/1} and 1 / 2 {\displaystyle 1/2} -bulbs? It is clearly the 1 / 3 {\displaystyle 1/3} -bulb. And note that 1 / 3 {\displaystyle 1/3} is obtained from the previous two fractions by Farey addition, i.e., adding the numerators and adding the denominators 0 1 {\displaystyle {\frac {0}{1}}} ⊕ {\displaystyle \oplus } 1 2 {\displaystyle {\frac {1}{2}}} = {\displaystyle =} 1 3 {\displaystyle {\frac {1}{3}}} Similarly, the largest bulb between the 1 / 3 {\displaystyle 1/3} and 1 / 2 {\displaystyle 1/2} -bulbs is the 2 / 5 {\displaystyle 2/5} -bulb, again given by Farey addition. 1 3 {\displaystyle {\frac {1}{3}}} ⊕ {\displaystyle \oplus } 1 2 {\displaystyle {\frac {1}{2}}} = {\displaystyle =} 2 5 {\displaystyle {\frac {2}{5}}} The largest bulb between the 2 / 5 {\displaystyle 2/5} and 1 / 2 {\displaystyle 1/2} -bulb is the 3 / 7 {\displaystyle 3/7} -bulb, while the largest bulb between the 2 / 5 {\displaystyle 2/5} and 1 / 3 {\displaystyle 1/3} -bulbs is the 3 / 8 {\displaystyle 3/8} -bulb, and so on. The arrangement of bulbs within the Mandelbrot set follows a remarkable pattern governed by the Farey tree, a structure encompassing all rationals between 0 {\displaystyle 0} and 1 {\displaystyle 1} . This ordering positions the bulbs along the boundary of the main cardioid precisely according to the rational numbers in the unit interval. Starting with the 1 / 3 {\displaystyle 1/3} bulb at the top and progressing towards the 1 / 2 {\displaystyle 1/2} circle, the sequence unfolds systematically: the largest bulb between 1 / 2 {\displaystyle 1/2} and 1 / 3 {\displaystyle 1/3} is 2 / 5 {\displaystyle 2/5} , between 1 / 3 {\displaystyle 1/3} and 2 / 5 {\displaystyle 2/5} is 3 / 8 {\displaystyle 3/8} , and so forth. Intriguingly, the denominators of the periods of circular bulbs at sequential scales in the Mandelbrot Set conform to the Fibonacci number sequence, the sequence that is made by adding the previous two terms – 1, 2, 3, 5, 8, 13, 21... The Fibonacci sequence manifests in the number of spiral arms at a unique spot on the Mandelbrot set, mirrored both at the top and bottom. This distinctive location demands the highest number of iterations of for a detailed fractal visual, with intricate details repeating as one zooms in. === Image gallery of a zoom sequence === The boundary of the Mandelbrot set shows more intricate detail the closer one looks or magnifies the image. The following is an example of an image sequence zooming to a selected c value. The magnification of the last image relative to the first one is about 1010 to 1. Relating to an ordinary computer monitor, it represents a section of a Mandelbrot set with a diameter of 4 million kilometers. The seahorse "body" is composed by 25 "spokes" consisting of two groups of 12 "spokes" each and one "spoke" connecting to the main cardioid. These two groups can be attributed by some metamorphosis to the two "fingers" of the "upper hand" of the Mandelbrot set; therefore, the number of "spokes" increases from one "seahorse" to the next by 2; the "hub" is a Misiurewicz point. Between the "upper part of the body" and the "tail", there is a distorted copy of the Mandelbrot set, called a "satellite". The islands in the third-to-last step seem to consist of infinitely many parts, as is the case for the corresponding Julia set J c {\displaystyle J_{c}} . They are connected by tiny structures, so that the whole represents a simply connected set. The tiny structures meet each other at a satellite in the center that is too small to be recognized at this magnification. The value of c {\displaystyle c} for the corresponding J c {\displaystyle J_{c}} is not the image center but, relative to the main body of the Mandelbrot set, has the same position as the center of this image relative to the satellite shown in the 6th step. === Inner structure === While the Mandelbrot set is typically rendered showing outside boundary detail, structure within the bounded set can also be revealed. For example, while calculating whether or not a given c value is bound or unbound, while it remains bound, the maximum value that this number reaches can be compared to the c value at that location. If the sum of squares method is used, the calculated number would be max:(real^2 + imaginary^2) − c:(real^2 + imaginary^2). The magnitude of this calculation can be rendered as a value on a gradient. This produces results like the following, gradients with distinct edges and contours as the boundaries are approached. The animations serve to highlight the gradient boundaries. == Generalizations == === Multibrot sets === Multibrot sets are bounded sets found in the complex plane for members of the general monic univariate polynomial family of recursions z ↦ z d + c {\displaystyle z\mapsto z^{d}+c} . For an integer d, these sets are connectedness loci for the Julia sets built from the same formula. The full cubic connectedness locus has also been studied; here one considers the two-parameter recursion z ↦ z 3 + 3 k z + c {\displaystyle z\mapsto z^{3}+3kz+c} , whose two critical points are the complex square roots of the parameter k. A parameter is in the cubic connectedness locus if both critical points are stable. For general families of holomorphic functions, the boundary of the Mandelbrot set generalizes to the bifurcation locus. The Multibrot set is obtained by varying the value of the exponent d. The article has a video that shows the development from d = 0 to 7, at which point there are 6 i.e. ( d − 1 ) {\displaystyle (d-1)} lobes around the perimeter. In general, when d is a positive integer, the central region in each of these sets is always an epicycloid of ( d − 1 ) {\displaystyle (d-1)} cusps. A similar development with negative integral exponents results in ( 1 − d ) {\displaystyle (1-d)} clefts on the inside of a ring, where the main central region of the set is a hypocycloid of ( 1 − d ) {\displaystyle (1-d)} cusps. === Higher dimensions === There is no perfect extension of the Mandelbrot set into 3D, because there is no 3D analogue of the complex numbers for it to iterate on. There is an extension of the complex numbers into 4 dimensions, the quaternions, that creates a perfect extension of the Mandelbrot set and the Julia sets into 4 dimensions. These can then be either cross-sectioned or projected into a 3D structure. The quaternion (4-dimensional) Mandelbrot set is simply a solid of revolution of the 2-dimensional Mandelbrot set (in the j-k plane), and is therefore uninteresting to look at. Taking a 3-dimensional cross section at d = 0 ( q = a + b i + c j + d k ) {\displaystyle d=0\ (q=a+bi+cj+dk)} results in a solid of revolution of the 2-dimensional Mandelbrot set around the real axis. === Other non-analytic mappings === The tricorn fractal, also called the Mandelbar set, is the connectedness locus of the anti-holomorphic family z ↦ z ¯ 2 + c {\displaystyle z\mapsto {\bar {z}}^{2}+c} . It was encountered by Milnor in his study of parameter slices of real cubic polynomials. It is not locally connected. This property is inherited by the connectedness locus of real cubic polynomials. Another non-analytic generalization is the Burning Ship fractal, which is obtained by iterating the following: z ↦ ( | ℜ ( z ) | + i | ℑ ( z ) | ) 2 + c {\displaystyle z\mapsto (|\Re \left(z\right)|+i|\Im \left(z\right)|)^{2}+c} . == Computer drawings == There exist a multitude of various algorithms for plotting the Mandelbrot set via a computing device. Here, the naïve "escape time algorithm" will be shown, since it is the most popular and one of the simplest algorithms. In the escape time algorithm, a repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel. The x and y locations of each point are used as starting values in a repeating, or iterating calculation (described in detail below). The result of each iteration is used as the starting values for the next. The values are checked during each iteration to see whether they have reached a critical "escape" condition, or "bailout". If that condition is reached, the calculation is stopped, the pixel is drawn, and the next x, y point is examined. The color of each point represents how quickly the values reached the escape point. Often black is used to show values that fail to escape before the iteration limit, and gradually brighter colors are used for points that escape. This gives a visual representation of how many cycles were required before reaching the escape condition. To render such an image, the region of the complex plane we are considering is subdivided into a certain number of pixels. To color any such pixel, let c {\displaystyle c} be the midpoint of that pixel. Iterate the critical point 0 under f c {\displaystyle f_{c}} , checking at each step whether the orbit point has a radius larger than 2. When this is the case, c {\displaystyle c} does not belong to the Mandelbrot set, and color the pixel according to the number of iterations used to find out. Otherwise, keep iterating up to a fixed number of steps, after which we decide that our parameter is "probably" in the Mandelbrot set, or at least very close to it, and color the pixel black. In pseudocode, this algorithm would look as follows. The algorithm does not use complex numbers and manually simulates complex-number operations using two real numbers, for those who do not have a complex data type. The program may be simplified if the programming language includes complex-data-type operations. for each pixel (Px, Py) on the screen do x0 := scaled x coordinate of pixel (scaled to lie in the Mandelbrot X scale (-2.00, 0.47)) y0 := scaled y coordinate of pixel (scaled to lie in the Mandelbrot Y scale (-1.12, 1.12)) x := 0.0 y := 0.0 iteration := 0 max_iteration := 1000 while (x^2 + y^2 ≤ 2^2 AND iteration < max_iteration) do xtemp := x^2 - y^2 + x0 y := 2*x*y + y0 x := xtemp iteration := iteration + 1 color := palette[iteration] plot(Px, Py, color) Here, relating the pseudocode to c {\displaystyle c} , z {\displaystyle z} and f c {\displaystyle f_{c}} : z = x + i y {\displaystyle z=x+iy} z 2 = x 2 + i 2 x y − y 2 {\displaystyle z^{2}=x^{2}+i2xy-y^{2}} c = x 0 + i y 0 {\displaystyle c=x_{0}+iy_{0}} and so, as can be seen in the pseudocode in the computation of x and y: x = R e ( z 2 + c ) = x 2 − y 2 + x 0 {\displaystyle x=\mathop {\mathrm {Re} } \left(z^{2}+c\right)=x^{2}-y^{2}+x_{0}} and y = I m ( z 2 + c ) = 2 x y + y 0 {\displaystyle y=\mathop {\mathrm {Im} } \left(z^{2}+c\right)=2xy+y_{0}} . To get colorful images of the set, the assignment of a color to each value of the number of executed iterations can be made using one of a variety of functions (linear, exponential, etc.). === Python code === Here is the code implementing the above algorithm in Python: The value of power variable can be modified to generate an image of equivalent multibrot set ( z = z power + c {\displaystyle z=z^{\text{power}}+c} ). For example, setting p = 2 produces the associated image. == References in popular culture == The Mandelbrot set is widely considered the most popular fractal, and has been referenced several times in popular culture. The Jonathan Coulton song "Mandelbrot Set" is a tribute to both the fractal itself and to the man it is named after, Benoit Mandelbrot. Blue Man Group's 1999 debut album Audio references the Mandelbrot set in the titles of the songs "Opening Mandelbrot", "Mandelgroove", and "Klein Mandelbrot". Their second album, The Complex (2003), closes with a hidden track titled "Mandelbrot IV". The second book of the Mode series by Piers Anthony, Fractal Mode, describes a world that is a perfect 3D model of the set. The Arthur C. Clarke novel The Ghost from the Grand Banks features an artificial lake made to replicate the shape of the Mandelbrot set. Benoit Mandelbrot and the eponymous set were the subjects of the Google Doodle on 20 November 2020 (the late Benoit Mandelbrot's 96th birthday). The American rock band Heart has an image of a Mandelbrot set on the cover of their 2004 album, Jupiters Darling. The British black metal band Anaal Nathrakh uses an image resembling the Mandelbrot set on their Eschaton album cover art. The television series Dirk Gently's Holistic Detective Agency (2016) prominently features the Mandelbrot set in connection with the visions of the character Amanda. In the second season, her jacket has a large image of the fractal on the back. In Ian Stewart's 2001 book Flatterland, there is a character called the Mandelblot, who helps explain fractals to the characters and reader. The unfinished Alan Moore 1990 comic book series Big Numbers used Mandelbrot's work on fractal geometry and chaos theory to underpin the structure of that work. Moore at one point was going to name the comic book series The Mandelbrot Set. In the manga The Summer Hikaru Died, Yoshiki hallucinates the Mandelbrot set when he reaches into the body of the false Hikaru. == See also == == References == == Further reading == Milnor, John W. (2006). Dynamics in One Complex Variable. Annals of Mathematics Studies. Vol. 160 (Third ed.). Princeton University Press. ISBN 0-691-12488-4. (First appeared in 1990 as a Stony Brook IMS Preprint, available as arXiV:math.DS/9201272 ) Lesmoir-Gordon, Nigel (2004). The Colours of Infinity: The Beauty, The Power and the Sense of Fractals. Clear Press. ISBN 1-904555-05-5. (includes a DVD featuring Arthur C. Clarke and David Gilmour) Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar (2004) [1992]. Chaos and Fractals: New Frontiers of Science. New York: Springer. ISBN 0-387-20229-3. == External links == Video: Mandelbrot fractal zoom to 6.066 e228 Relatively simple explanation of the mathematical process, by Dr Holly Krieger, MIT Mandelbrot Set Explorer: Browser based Mandelbrot set viewer with a map-like interface Various algorithms for calculating the Mandelbrot set (on Rosetta Code) Fractal calculator written in Lua by Deyan Dobromiroiv, Sofia, Bulgaria |
Wikipedia:Mandelbulb#0 | The Mandelbulb is a three-dimensional fractal, constructed for the first time in 1997 by Jules Ruis and further developed in 2009 by Daniel White and Paul Nylander using spherical coordinates. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers. It is possible to construct Mandelbrot sets in 4 dimensions using quaternions and bicomplex numbers. White and Nylander's formula for the "nth power" of the vector v = ⟨ x , y , z ⟩ {\displaystyle \mathbf {v} =\langle x,y,z\rangle } in ℝ3 is v n := r n ⟨ sin ( n θ ) cos ( n ϕ ) , sin ( n θ ) sin ( n ϕ ) , cos ( n θ ) ⟩ , {\displaystyle \mathbf {v} ^{n}:=r^{n}\langle \sin(n\theta )\cos(n\phi ),\sin(n\theta )\sin(n\phi ),\cos(n\theta )\rangle ,} where r = x 2 + y 2 + z 2 , {\displaystyle r={\sqrt {x^{2}+y^{2}+z^{2}}},} ϕ = arctan y x = arg ( x + y i ) , {\displaystyle \phi =\arctan {\frac {y}{x}}=\arg(x+yi),} θ = arctan x 2 + y 2 z = arccos z r . {\displaystyle \theta =\arctan {\frac {\sqrt {x^{2}+y^{2}}}{z}}=\arccos {\frac {z}{r}}.} The Mandelbulb is then defined as the set of those c {\displaystyle \mathbf {c} } in ℝ3 for which the orbit of ⟨ 0 , 0 , 0 ⟩ {\displaystyle \langle 0,0,0\rangle } under the iteration v ↦ v n + c {\displaystyle \mathbf {v} \mapsto \mathbf {v} ^{n}+\mathbf {c} } is bounded. For n > 3, the result is a 3-dimensional bulb-like structure with fractal surface detail and a number of "lobes" depending on n. Many of their graphic renderings use n = 8. However, the equations can be simplified into rational polynomials when n is odd. For example, in the case n = 3, the third power can be simplified into the more elegant form: ⟨ x , y , z ⟩ 3 = ⟨ ( 3 z 2 − x 2 − y 2 ) x ( x 2 − 3 y 2 ) x 2 + y 2 , ( 3 z 2 − x 2 − y 2 ) y ( 3 x 2 − y 2 ) x 2 + y 2 , z ( z 2 − 3 x 2 − 3 y 2 ) ⟩ . {\displaystyle \langle x,y,z\rangle ^{3}=\left\langle {\frac {(3z^{2}-x^{2}-y^{2})x(x^{2}-3y^{2})}{x^{2}+y^{2}}},{\frac {(3z^{2}-x^{2}-y^{2})y(3x^{2}-y^{2})}{x^{2}+y^{2}}},z(z^{2}-3x^{2}-3y^{2})\right\rangle .} The Mandelbulb given by the formula above is actually one in a family of fractals given by parameters (p, q) given by v n := r n ⟨ sin ( p θ ) cos ( q ϕ ) , sin ( p θ ) sin ( q ϕ ) , cos ( p θ ) ⟩ . {\displaystyle \mathbf {v} ^{n}:=r^{n}\langle \sin(p\theta )\cos(q\phi ),\sin(p\theta )\sin(q\phi ),\cos(p\theta )\rangle .} Since p and q do not necessarily have to equal n for the identity |vn| = |v|n to hold, more general fractals can be found by setting v n := r n ⟨ sin ( f ( θ , ϕ ) ) cos ( g ( θ , ϕ ) ) , sin ( f ( θ , ϕ ) ) sin ( g ( θ , ϕ ) ) , cos ( f ( θ , ϕ ) ) ⟩ {\displaystyle \mathbf {v} ^{n}:=r^{n}{\big \langle }\sin {\big (}f(\theta ,\phi ){\big )}\cos {\big (}g(\theta ,\phi ){\big )},\sin {\big (}f(\theta ,\phi ){\big )}\sin {\big (}g(\theta ,\phi ){\big )},\cos {\big (}f(\theta ,\phi ){\big )}{\big \rangle }} for functions f and g. == Cubic formula == Other formula come from identities parametrising the sum of squares to give a power of the sum of squares, such as ( x 3 − 3 x y 2 − 3 x z 2 ) 2 + ( y 3 − 3 y x 2 + y z 2 ) 2 + ( z 3 − 3 z x 2 + z y 2 ) 2 = ( x 2 + y 2 + z 2 ) 3 , {\displaystyle (x^{3}-3xy^{2}-3xz^{2})^{2}+(y^{3}-3yx^{2}+yz^{2})^{2}+(z^{3}-3zx^{2}+zy^{2})^{2}=(x^{2}+y^{2}+z^{2})^{3},} which we can think of as a way to cube a triplet of numbers so that the modulus is cubed. So this gives, for example, x → x 3 − 3 x ( y 2 + z 2 ) + x 0 {\displaystyle x\to x^{3}-3x(y^{2}+z^{2})+x_{0}} y → − y 3 + 3 y x 2 − y z 2 + y 0 {\displaystyle y\to -y^{3}+3yx^{2}-yz^{2}+y_{0}} z → z 3 − 3 z x 2 + z y 2 + z 0 {\displaystyle z\to z^{3}-3zx^{2}+zy^{2}+z_{0}} or other permutations. This reduces to the complex fractal w → w 3 + w 0 {\displaystyle w\to w^{3}+w_{0}} when z = 0 and w → w ¯ 3 + w 0 {\displaystyle w\to {\overline {w}}^{3}+w_{0}} when y = 0. There are several ways to combine two such "cubic" transforms to get a power-9 transform, which has slightly more structure. == Quintic formula == Another way to create Mandelbulbs with cubic symmetry is by taking the complex iteration formula z → z 4 m + 1 + z 0 {\displaystyle z\to z^{4m+1}+z_{0}} for some integer m and adding terms to make it symmetrical in 3 dimensions but keeping the cross-sections to be the same 2-dimensional fractal. (The 4 comes from the fact that i 4 = 1 {\displaystyle i^{4}=1} .) For example, take the case of z → z 5 + z 0 {\displaystyle z\to z^{5}+z_{0}} . In two dimensions, where z = x + i y {\displaystyle z=x+iy} , this is x → x 5 − 10 x 3 y 2 + 5 x y 4 + x 0 , {\displaystyle x\to x^{5}-10x^{3}y^{2}+5xy^{4}+x_{0},} y → y 5 − 10 y 3 x 2 + 5 y x 4 + y 0 . {\displaystyle y\to y^{5}-10y^{3}x^{2}+5yx^{4}+y_{0}.} This can be then extended to three dimensions to give x → x 5 − 10 x 3 ( y 2 + A y z + z 2 ) + 5 x ( y 4 + B y 3 z + C y 2 z 2 + B y z 3 + z 4 ) + D x 2 y z ( y + z ) + x 0 , {\displaystyle x\to x^{5}-10x^{3}(y^{2}+Ayz+z^{2})+5x(y^{4}+By^{3}z+Cy^{2}z^{2}+Byz^{3}+z^{4})+Dx^{2}yz(y+z)+x_{0},} y → y 5 − 10 y 3 ( z 2 + A x z + x 2 ) + 5 y ( z 4 + B z 3 x + C z 2 x 2 + B z x 3 + x 4 ) + D y 2 z x ( z + x ) + y 0 , {\displaystyle y\to y^{5}-10y^{3}(z^{2}+Axz+x^{2})+5y(z^{4}+Bz^{3}x+Cz^{2}x^{2}+Bzx^{3}+x^{4})+Dy^{2}zx(z+x)+y_{0},} z → z 5 − 10 z 3 ( x 2 + A x y + y 2 ) + 5 z ( x 4 + B x 3 y + C x 2 y 2 + B x y 3 + y 4 ) + D z 2 x y ( x + y ) + z 0 {\displaystyle z\to z^{5}-10z^{3}(x^{2}+Axy+y^{2})+5z(x^{4}+Bx^{3}y+Cx^{2}y^{2}+Bxy^{3}+y^{4})+Dz^{2}xy(x+y)+z_{0}} for arbitrary constants A, B, C and D, which give different Mandelbulbs (usually set to 0). The case z → z 9 {\displaystyle z\to z^{9}} gives a Mandelbulb most similar to the first example, where n = 9. A more pleasing result for the fifth power is obtained by basing it on the formula z → − z 5 + z 0 {\displaystyle z\to -z^{5}+z_{0}} . == Power-nine formula == This fractal has cross-sections of the power-9 Mandelbrot fractal. It has 32 small bulbs sprouting from the main sphere. It is defined by, for example, x → x 9 − 36 x 7 ( y 2 + z 2 ) + 126 x 5 ( y 2 + z 2 ) 2 − 84 x 3 ( y 2 + z 2 ) 3 + 9 x ( y 2 + z 2 ) 4 + x 0 , {\displaystyle x\to x^{9}-36x^{7}(y^{2}+z^{2})+126x^{5}(y^{2}+z^{2})^{2}-84x^{3}(y^{2}+z^{2})^{3}+9x(y^{2}+z^{2})^{4}+x_{0},} y → y 9 − 36 y 7 ( z 2 + x 2 ) + 126 y 5 ( z 2 + x 2 ) 2 − 84 y 3 ( z 2 + x 2 ) 3 + 9 y ( z 2 + x 2 ) 4 + y 0 , {\displaystyle y\to y^{9}-36y^{7}(z^{2}+x^{2})+126y^{5}(z^{2}+x^{2})^{2}-84y^{3}(z^{2}+x^{2})^{3}+9y(z^{2}+x^{2})^{4}+y_{0},} z → z 9 − 36 z 7 ( x 2 + y 2 ) + 126 z 5 ( x 2 + y 2 ) 2 − 84 z 3 ( x 2 + y 2 ) 3 + 9 z ( x 2 + y 2 ) 4 + z 0 . {\displaystyle z\to z^{9}-36z^{7}(x^{2}+y^{2})+126z^{5}(x^{2}+y^{2})^{2}-84z^{3}(x^{2}+y^{2})^{3}+9z(x^{2}+y^{2})^{4}+z_{0}.} These formula can be written in a shorter way: x → 1 2 ( x + i y 2 + z 2 ) 9 + 1 2 ( x − i y 2 + z 2 ) 9 + x 0 {\displaystyle x\to {\frac {1}{2}}\left(x+i{\sqrt {y^{2}+z^{2}}}\right)^{9}+{\frac {1}{2}}\left(x-i{\sqrt {y^{2}+z^{2}}}\right)^{9}+x_{0}} and equivalently for the other coordinates. == Spherical formula == A perfect spherical formula can be defined as a formula ( x , y , z ) → ( f ( x , y , z ) + x 0 , g ( x , y , z ) + y 0 , h ( x , y , z ) + z 0 ) , {\displaystyle (x,y,z)\to {\big (}f(x,y,z)+x_{0},g(x,y,z)+y_{0},h(x,y,z)+z_{0}{\big )},} where ( x 2 + y 2 + z 2 ) n = f ( x , y , z ) 2 + g ( x , y , z ) 2 + h ( x , y , z ) 2 , {\displaystyle (x^{2}+y^{2}+z^{2})^{n}=f(x,y,z)^{2}+g(x,y,z)^{2}+h(x,y,z)^{2},} where f, g and h are nth-power rational trinomials and n is an integer. The cubic fractal above is an example. == Uses in media == In the 2014 animated film Big Hero 6, the climax takes place in the middle of a wormhole, which is represented by the stylized interior of a Mandelbulb. In the 2018 science fiction horror film Annihilation, an extraterrestrial being appears in the form of a partial Mandelbulb. In the webcomic Unsounded the spirit realm of the khert is represented by a stylized golden mandelbulb. In the 2013-2020 drama show Marvel's Agents of S.H.I.E.L.D, season 7, episode 13, "What We're Fighting For", the beginning shows the S.H.I.E.L.D. team travel through the Quantum Realm whose opening appearance from the outside resembles the end of an internally rotating mandelbulb. In the 2016 film Marvel's Doctor Strange, one of the dimensions Strange is shown by the Ancient One depicts the top end of an expanding mandelbulb. In the 2020 film 2067, as the main character is arriving in the future, the distorted land he descends upon resembles a distorted and morphing mandelbulb. == See also == Mandelbox List of fractals by Hausdorff dimension == References == 6. http://www.fractal.org the Fractal Navigator by Jules Ruis == External links == for the first use of the Mandelbulb formula on www.fractal.org website Jules Ruis Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal, on Daniel White's website Several variants of the Mandelbulb, on Paul Nylander's website An opensource fractal renderer that can be used to create images of the Mandelbulb Formula for Mandelbulb/Juliabulb/Juliusbulb by Jules Ruis Mandelbulb/Juliabulb/Juliusbulb with examples of real 3D objects Video : View of the Mandelbulb The discussion thread in Fractalforums.com that led to the Mandelbulb Video fly through of an animated Mandelbulb world Open-source Mandelbulber v2 software - Explore trigonometric, hyper-complex, Mandelbox, IFS, and many other 3D fractals. Silent video: Explore the Mandelbulb (2024 rendering) |
Wikipedia:Manjul Bhargava#0 | Manjul Bhargava (born 8 August 1974) is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He is known primarily for his contributions to number theory. Bhargava was awarded the Fields Medal in 2014. According to the International Mathematical Union citation, he was awarded the prize "for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves". He was also a member of the Padma Award committee in 2023. == Education and career == Bhargava was born to an Indian Hindu Brahmin family in Hamilton, Ontario, Canada, but grew up and attended school primarily on Long Island, New York. His mother Mira Bhargava, a mathematician at Hofstra University, was his first mathematics teacher. He completed all of his high school math and computer science courses by age 14. He attended Plainedge High School in North Massapequa, and graduated in 1992 as the class valedictorian. He obtained his AB from Harvard University in 1996. For his research as an undergraduate, he was awarded the 1996 Morgan Prize. Bhargava went on to pursue graduate studies at Princeton University, where he completed a doctoral dissertation titled "Higher composition laws" under the supervision of Andrew Wiles and received his PhD in 2001, with the support of a Hertz Fellowship. He was a visiting scholar at the Institute for Advanced Study in 2001–02, and at Harvard University in 2002–03. Princeton appointed him as a tenured Full Professor in 2003. He was appointed to the Stieltjes Chair in Leiden University in 2010. Bhargava has also studied the tabla under gurus such as Zakir Hussain. He also studied Sanskrit from his grandfather Purushottam Lal Bhargava, a scholar of Sanskrit and ancient Indian history. He is an admirer of Sanskrit poetry. == Career and research == Bhargava’s PhD thesis generalized Gauss's classical law for composition of binary quadratic forms to many other situations. One major use of his results is the parametrization of quartic and quintic orders in number fields, thus allowing the study of the asymptotic behavior of the arithmetic properties of these orders and fields. His research also includes fundamental contributions to the representation theory of quadratic forms, to interpolation problems and p-adic analysis, to the study of ideal class groups of algebraic number fields, and to the arithmetic theory of elliptic curves. A short list of his specific mathematical contributions are: Fourteen new Gauss-style composition laws. Determination of the asymptotic density of discriminants of quartic and quintic number fields. Proofs of the first-known cases of the Cohen-Lenstra-Martinet heuristics for class groups. Proof of the 15 theorem, including an extension of the theorem to other number sets such as the odd numbers and the prime numbers. Proof (with Jonathan Hanke) of the 290 theorem. A novel generalization of the factorial function, Bhargava factorial, providing an answer to a decades-old question of George Pólya. Proof (with Arul Shankar) that the average rank of all elliptic curves over Q (when ordered by height) is bounded. Proof that most hyperelliptic curves over Q have no rational points. In 2015, Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves. == Awards and honours == Bhargava has won several awards for his research, the most prestigious being the Fields Medal, the highest award in the field of mathematics, which he won in 2014. He received the Morgan Prize in 1996. and Hertz Fellowship He was named one of Popular Science magazine's "Brilliant 10" in November 2002. He then received a Clay 5-year Research Fellowship and the Merten M. Hasse Prize from the MAA in 2003, the Clay Research Award, the SASTRA Ramanujan Prize, and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics in 2005. Peter Sarnak of Princeton University has said of Bhargava: At mathematics he's at the very top end. For a guy so young I can't remember anybody so decorated at his age. He certainly started out with a bang and has not let it get to his head, which is unusual. Of course he couldn't do what he does if he wasn't brilliant. It's his exceptional talent that's so striking In 2008, Bhargava was awarded the American Mathematical Society's Cole Prize. The citation reads: Bhargava's original and surprising contribution is the discovery of laws of composition on forms of higher degree. His techniques and insights into this question are dazzling; even in the case considered by Gauss, they lead to a new and clearer presentation of that theory. In 2009, he was awarded the Face of the Future award at the India Abroad Person of the Year ceremony in New York City. In 2014, the same publication gave the India Abroad Publisher's Prize for Special Excellence. In 2011, he was awarded the Fermat Prize for "various generalizations of the Davenport-Heilbronn estimates and for his startling recent results (with Arul Shankar) on the average rank of elliptic curves". In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award, and became a fellow of the American Mathematical Society in its inaugural class of fellows. He was awarded the 2012 Infosys Prize in mathematics for his "extraordinarily original work in algebraic number theory, which has revolutionized the way in which number fields and elliptic curves are counted". In 2013, he was elected to the National Academy of Sciences. In 2014, Bhargava was awarded the Fields Medal at the International Congress of Mathematicians in Seoul for "developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves". In 2015, he was awarded the Padma Bhushan, the third-highest civilian award of India. In 2017, Bhargava was elected as a member of the American Academy of Arts and Sciences. In 2018, Bhargava was named as the inaugural occupant of The Distinguished Chair for the Public Dissemination of Mathematics at The National Museum of Mathematics (MoMath). This is the first visiting professorship in the United States dedicated exclusively to raising public awareness of mathematics. Bhargava was conferred a Fellowship at the Royal Society in 2019. == Selected publications == Bhargava, Manjul (2000). "The Factorial Function and Generalizations" (PDF). The American Mathematical Monthly. 107 (9): 783–799. CiteSeerX 10.1.1.585.2265. doi:10.2307/2695734. JSTOR 2695734. Archived from the original (PDF) on 3 March 2016. Bhargava, Manjul (2004). "Higher Composition Laws I: A New View on Gauss Composition, and Quadratic Generalizations" (PDF). Annals of Mathematics. 159: 217–250. doi:10.4007/annals.2004.159.217. Bhargava, Manjul (2004). "Higher Composition Laws II: On Cubic Analogues of Gauss Composition" (PDF). Annals of Mathematics. 159 (2): 865–886. doi:10.4007/annals.2004.159.865. Bhargava, Manjul (2004). "Higher Composition Laws III: The Parametrization of Quartic Rings" (PDF). Annals of Mathematics. 159 (3): 1329–1360. doi:10.4007/annals.2004.159.1329. Bhargava, Manjul (2005). "The density of discriminants of quartic rings and fields" (PDF). Annals of Mathematics. 162 (2): 1031–1063. doi:10.4007/annals.2005.162.1031. S2CID 53482033. Bhargava, Manjul (2008). "Higher composition laws IV: The parametrization of quintic rings" (PDF). Annals of Mathematics. 167: 53–94. doi:10.4007/annals.2008.167.53. Bhargava, Manjul (2010). "The density of discriminants of quintic rings and fields" (PDF). Annals of Mathematics. 172 (3): 1559–1591. arXiv:1005.5578. Bibcode:2010arXiv1005.5578B. doi:10.4007/annals.2010.172.1559. Bhargava, Manjul; Satriano, Matthew (2014). "On a notion of "Galois closure" for extensions of rings". Journal of the European Mathematical Society. 16 (9): 1881–1913. arXiv:1006.2562. doi:10.4171/JEMS/478. MR 3273311. S2CID 18493502. Bhargava, Manjul; Shankar, Arul (2015). "Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves". Annals of Mathematics. 181 (1): 191–242. arXiv:1006.1002. doi:10.4007/annals.2015.181.1.3. MR 3272925. S2CID 111383310. Bhargava, Manjul; Shankar, Arul (2015). "Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0". Annals of Mathematics. 181 (2): 587–621. arXiv:1007.0052. doi:10.4007/annals.2015.181.2.4. S2CID 1456959. == See also == Indians in the New York City metropolitan area == References == == External links == Manjul Bhargava at NPR Manjul Bhargava at ICTS Article in The Hindu on Bhargava winning the SASTRA prize Princeton University article by Steven Schultz |
Wikipedia:Manuel Sadosky#0 | Manuel Sadosky (April 13, 1914 – June 18, 2005) was an Argentine mathematician, civil servant and author who was born in Buenos Aires to Jewish Russian immigrants who had fled the pogroms in Europe. == Biography == Son of a shoemaker, Natalio Sadosky and his wife Maria Steingart of Ekaterinoslav (currently Dnipro), Ukraine, the family had arrived in Argentina in 1905. Sadosky studied at the Mariano Acosta teachers school. Noted novelist Julio Cortázar was his classmate there, and remained a longtime friend. Since his childhood he was an ardent supporter of San Lorenzo de Almagro. He married fellow mathematician and activist Cora Ratto de Sadosky (1912–1981) in 1937. Biographer Pablo Jacovkis has said that Cora, had a "powerful personality [that] was not overshadowed by her husband's." The couple had one child, mathematician Cora Sadosky (1940–2010). === Education === Sadosky graduated as a Doctor in Physics and Mathematics at the University of Buenos Aires in 1940, under supervision of Esteban Terradas. He then moved to the Henri Poincaré Institute in Paris to pursue postdoctoral studies on a scholarship granted by the French Government. After another year in Italy, he returned to Argentina, where he faced complicated employment options because of his opposition to the Peronist regime. After a coup d'état of 1955 removed President Juan Perón from office, Sadosky took up a position as professor at the University of Buenos Aires, where he was vice-dean of the Faculty of Exact and Natural Sciences from 1957 to 1966. === Computational Institute === In 1960 he was commissioned to develop the Computational Institute (Instituto de Cálculo) of the university, home of Clementina, a new Ferranti Mercury computer and the first one installed in Argentina for research and education. His staff there included several excellent mathematicians including Cecilia Berdichevsky and Rebeca Cherep de Guber, and both would work closely with him for many years to come. He directed the institute until another coup d'état installed a military dictatorship in 1966, causing him to resign with the rest of the faculty in opposition to government intervention in the hitherto autonomous state universities (the Night of the Long Batons) and flee the country. === In exile === He was later able to return to Argentina, but the Argentine Anticommunist Alliance death squad threatened to kill him so he fled with his family in 1974. He moved to Uruguay, finding employment in Montevideo at the Universidad de la República, where he continued publishing, helped to initiate computer studies and introduced the first research computer in that country. In 1974, due to political persecution, Sadosky left Argentina with his family, relocating to Caracas to join the Science faculty of the Central University of Venezuela. With the eventual return of democracy to Argentina in 1983, president Raúl Alfonsín appointed him as Secretary of State of Science and Technology (until 1989). One of his major contributions to computer science during this period, was the creation of the ESLAI (Latin American School of Higher Informatics). === Later years === Dr. Manuel Sadosky died in Buenos Aires on June 18, 2005. He was named an Illustrious Citizen of the City of Buenos Aires. The Computer Science Department of the Faculty of Exact and Natural Sciences at the University of Buenos Aires is named after him. == Selected publications == Sadosky, Manuel, Cálculo numérico y gráfico, Buenos Aires: Ediciones Libreria del Colegio, 1952 Sadosky, Manuel, Marx, hombre y revolucionario, Montevideo Libros de la pupila, 1969 Sadosky, Manuel, Catalogo colectivo de publicaciones periodicas en las bibliotecas universitarias del Uruguay, Montevideo : Universidad de la Republica, 1972. Sadosky, Manuel; Sadosky, Cora, Complementos teóricos de los Elementos de calculo diferencial e integral de Manuel Sadosky, Rebeca Ch. de Guber, Buenos Aires: Alsina, 1974. Sadosky, Manuel; Guber, Rebeca Ch de, Elementos de cálculo diferencial e integral, Buenos Aires: Alsina, 1982. == References == == External links == Fundación Sadosky Obituary Pagina/12 Obituary Clarín Secretaria de Ciencia y Tecnica Computer Science Department (FCEN-UBA) (in Spanish) |
Wikipedia:Manuela Garín#0 | Manuela (Mane) Garín Pinillos de Álvarez (1 January 1914 – 30 April 2019) was a Spanish-born and Cuban-raised mathematician who became one of the first women to study mathematics at the National Autonomous University of Mexico (UNAM). She has been named as a pioneer of mathematics in Mexico. == Personal life == Garín was born on 1 January 1914 in Asturias, Spain. Her mother and step-father escaped World War I by moving to Cuba, where she was home-taught by her step-father, an engineer for a mining company. After several years, they moved to Pinar del Río in Cuba, where she first entered formal schooling. In the economic and political crisis in Cuba under the reign of Gerardo Machado, the family began working for the political opposition but in 1932, in fear for their lives, moved to Mexico, using counterfeit Spanish passports. In Mexico, she became an activist in the Communist Party. She married Raúl Álvarez, an engineer. Their son, Raúl Álvarez Garín (1914–2014), was also a prominent activist, one of the leaders in the Mexican Movement of 1968 and later a professor of economics at UNAM. Although initially studying mathematics, their daughter Tania Álvarez Garín became a ballerina and choreographer. == Academic career == Once in Mexico, Garín caught up on the Mexican school curriculum through the Colegio Motolinía. But, because her Cuban education had omitted singing and sports, she was blocked from entering the Escuela Nacional Preparatoria until her family obtained an exception with the assistance of the Cuban ambassador to Mexico. She studied chemistry there, encouraged by her mother to aim for career as a pharmacist, as engineering work was not open to women at that time. However, she was encouraged to study mathematics by one of her teachers, Alfonso Nápoles Gándara. There was at that time an arrangement that ENP chemistry students could enter the science program at UNAM, but Garín had to overcome bureaucratic opposition to her entry, which she did in 1937 with the intervention of geophysicist Ricardo Monges López, entering alongside Enriqueta González Baz, and becoming the first women in the UNAM Faculty of Sciences. After graduating, marrying, living with her husband in Sinaloa and Ensenada, and then teaching at the Monterrey Institute of Technology and Higher Education for several years, she joined the UNAM Faculty of Engineering in 1951, and in 1952 began teaching as well in the Faculty of Sciences. She also worked as a researcher in the UNAM Institute of Geophysics, led by Monges. In this time, she also completed a master's thesis in probability theory, supervised by Remigio Valdés. As a professional mathematician, Garín specialized in applied mathematics involving the mathematical modeling of the Earth's magnetic field; she also worked on secondary-school mathematics education. In her later work, she helped found the Institute of Geophysics in the Universidad Autónoma de Yucatán and in 1964 became the founding director of the School of Advanced Studies of the Universidad de Sonora. She retired as a professor emerita of the Faculty of Engineering of UNAM in 1989. == Recognition == In 2020, a science contest for primary and secondary school girls was named in honor of Garín by the government of Mexico City. == References == == External links == Manuela Garín Pinillos de Álvarez, Matemáticos en México |
Wikipedia:Maor Farid#0 | Dr. Maor Farid (Hebrew: מאור פריד; born April 20, 1992) is an Israeli scientist, engineer and artificial intelligence researcher at Massachusetts Institute of Technology, social activist, and author. He is the founder and CEO of Learn to Succeed (Hebrew: ללמוד להצליח) for empowering of youths from the Israeli socio-economic periphery and youths at risk, a regional manager of the Israeli center of ScienceAbroad at MIT, and an activist in the American Technion Society. He is an alumnus of Unit 8200, and a fellow of Fulbright Program and the Israel Scholarship Educational Foundation. Dr. Farid was elected to the Forbes 30 Under 30 list of 2019, and won the Moskowitz Prize for Zionism. == Early life == Maor was born in Ness Ziona, a city in central Israel, as the eldest son for parents from immigrating families of Mizrahi Jews from Iraq and Libya. Maor suffered from Attention deficit hyperactivity disorder (ADHD) from a young age, and was classified as a problematic and violent student. His ADHD issues were diagnosed only after he began his university studies. However, inspired by his parents' background, he aspired to excel at school for a better future for his family. During elementary school, Maor attended local quizzes about Jewish history and Zionism, which significantly shaped his identity and national perspective. Farid graduated high school with the highest GPA in school. Later he was recruited to the Israel Defense Forces and drafted to the Brakim Program – an excellence program of the Israeli Intelligence Corps for training leading R&D officers for the Israeli military and defense industry. Maor graduated the program with honors and was elected by the Israeli Prime Minister's Office and Unit 8200, where he served as an artificial intelligence researcher, officer, and commander. During his Military service, he received various honors and awards, such as the Excellent Scientist Award, given to the top three academics serving in the Israel Defense Forces. In 2019, Farid completed his military service in the rank of a Captain. == Education and academic career == As part of the (4 years) Brakim Program, Maor completed his Bachelor's and Master's degrees at the Technion in Mechanical Engineering with honors. Then, he initiated his Ph.D. research as a collaboration with the Israel Atomic Energy Commission (IAEC) in parallel to his duty military service. The main goals of his Ph.D. research were predicting irreversible effects of major earthquakes on Israel's nuclear facilities, and improving their seismic resistance using energy absorption technologies. The mathematical models developed by Farid were able to forecast earthquake effects on facilities with major hazard potential, and predicted the failure of liquid storage tanks due to earthquakes took place in Italy (2012) and Mexico (2017). The energy absorption technologies used, increased in up to 90% the seismic resistance abilities of those sensitive facilities. The research results were published in multiple papers in peer-reviewed academic journals and presented in international academic conferences. Later, this research expanded to an official collaboration between the Technion and the Shimon Peres Negev Nuclear Research Center, which aims to implement the findings obtained on existing sensitive systems, and won funding of 1.5 million NIS from the Pazy foundation of the Israel Atomic Energy Commission and the Council for Higher Education. In 2017, Farid completed his Ph.D. and as the youngest graduate at the Technion for that year, at the age of 24. In the graduation ceremonies, he honored his parents to receive the diplomas on his behalf. At the same year, he served as a lecturer at Ben-Gurion University in an original course he developed as a solution for knowledge gaps he identified in the Israeli defense industry. In 2018, Dr. Farid served as an artificial intelligence researcher at a Data Science team of Unit 8200, where he developed machine learning-based solutions for military and operational needs. In 2019, Farid won the Fulbright and the Israel Scholarship Educational Foundation scholarships, and was accepted to post-doctoral position at Massachusetts Institute of Technology where he develops real-time methods for predicting earthquake effects using machine learning techniques. In 2020, Farid was accepted to the Emerging Leaders Program at Harvard Kennedy School in Cambridge, Massachusetts. At the same year, he received the excellence research grant of the Israel Academy of Sciences and Humanities for leading his research in collaboration between MIT and the Technion. == Social activism == Influenced by childhood experience, Dr. Farid focused on empowering youths from disadvantaged backgrounds from an early age. Between the years 2010–2015, he served as a mentor of a robotics team from Dimona in FIRST Robotics Competition, a mathematics tutor in "Aharai!" program for high-school students at risk in Dimona and Be'er Sheva, and a mentor and private tutor of adolescence and reserve duty soldiers from disadvantaged backgrounds. In 2010, he initiated "Learn to Succeed" (Hebrew: ללמוד להצליח) project, for mitigating the social gaps in the Israeli society by empowering youths from the social, economical, and geographical periphery for excellence, self-fulfillment and gaining formal education. In 2018, Learn to Succeed became an official non-profit organization. At the same year, Farid led a crowdfunding project of 150,000 NIS in order to expand the organization to a national scale. In 2019, he published the book "Learn to Succeed", in which he describes his struggle with ADHD, the violent environment in which he grew up, and the changing process he went through from being a violent teenager to becoming the youngest Ph.D. graduate at the Technion. The book was given to more than two thousand youths at risk and became a top seller in Israel shortly after its publication. Maor dedicated the book to his parents and to the memorial of his friend Captain Tal Nachman who was killed in operational activity during his military service in 2014. The organization consists of hundreds of volunteers, gives full scholarships to STEM students from the periphery who serve as mentors of youths, both Jews and Arabs, from disadvantaged backgrounds, runs a hotline which gives online practical and mental support to hundreds of youths, parents and educators, initiates inspirational activities with military orientation to increase the motivation of its teen-age members for significant military service, and gives inspirational lectures to more than 5,000 youths each year. In 2019, Maor initiated a collaboration with Unit 8200 in which tens of the program's members are being interviewed to the unit. This opportunity is usually given to students with the highest grades in the matriculate exams in each class. In 2020, Dr. Farid established the ScienceAbroad center at MIT, aiming to strengthen the connections between Israeli researchers in the institute and the state of Israel. Moreover, he serves as a volunteer in the American Technion Society. == Honors and awards == Fulbright Scholarship for post-doctoral studies. Given by the US State Department for distinguished scientific excellence and leadership skills (among 8 winners from all disciplines) (2019). Israel Scholarship Education Foundation (ISEF) postdoctoral fellowship for academic and personal excellence (among two winners from all disciplines) (2019). Moskowitz Prize for Zionism, leadership and social entrepreneurship for the establishment of Learn to Succeed association for empowering of youth at risk from the social, economical and geographical periphery, and mitigating social gaps in the Israeli society (among 2 winners) (2019). Elected on the 30 Under 30 list of Forbes magazine. The list members are considered as game-changers in their field, and expected to be key figures in the future (among 30 winners from all disciplines) (2019). Elected as Brakim Excellent Officer, received the Excellent Commander Award of Unit 8200, and other military honors, for excellence, leadership and distinguished contribution (2019). B.Sc., M.Sc. and Ph.D. graduation at the Technion with honors (2010–2017). == Personal life == Farid is married to Michal. == Interviews and articles == Ilan Leserovich, "The sons of the poor ones", Israel Hayom national daily newspaper, 2018. Avr Gilad and Tali Metz, "Without proper assistance, youths from the periphery have no chance to succeed", TV interview at Ha'Olam Ha'Boker morning show, 2018. Yael Dan, "They don't need your mercy, but only your guidance" radio interview at Galei Tzahal (Army Radio), 2018. Nadav Abekasis, "From a violent youth to the establishment of Learn to Succeed" at Tel-Aviv Radio, 2018. Ofer Noiman, "Giving youths at risk essential tools for success" radio interview at Tel-Aviv Radio, 2019. Yakov Sitruk Dahan, "Learning critical financial skills" at Sheva Journal, 2019. "Empowering the periphery in the Zionism of the 21st century", YouTube video, the Moskowitz Prize for Zionism 2019. "I wish you to change the world" YouTube video Speech on behalf of the Forbes 30 Under 30 list of 2019. Hadas Bashan, Forbes 30 Under 30 – Maor Farid, Forbes magazine, 2019. Hadas Bashan, "The economic periphery has a tremendous advantage in the world of research", Forbes magazine, 2019. Fulbright Program, "Meet a Fulbrighter", an interview for Fulbright magazine, 2019. == References == == External links == Maor Farid at Facebook The professional profile of Maor Farid at LinkedIn Scientific papers published by Maor Farid at Google Scholar Learn to Succeed - the official website |
Wikipedia:Map (mathematics)#0 | In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term transformation can be used interchangeably, but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory. == Maps as functions == In many branches of mathematics, the term map is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a "continuous function" in topology, a "linear transformation" in linear algebra, etc. Some authors, such as Serge Lang, use "function" only to refer to maps in which the codomain is a set of numbers (i.e. a subset of R or C), and reserve the term mapping for more general functions. Maps of certain kinds have been given specific names. These include homomorphisms in algebra, isometries in geometry, operators in analysis and representations in group theory. In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. A partial map is a partial function. Related terminology such as domain, codomain, injective, and continuous can be applied equally to maps and functions, with the same meaning. All these usages can be applied to "maps" as general functions or as functions with special properties. == As morphisms == In category theory, "map" is often used as a synonym for "morphism" or "arrow", which is a structure-respecting function and thus may imply more structure than "function" does. For example, a morphism f : X → Y {\displaystyle f:\,X\to Y} in a concrete category (i.e. a morphism that can be viewed as a function) carries with it the information of its domain (the source X {\displaystyle X} of the morphism) and its codomain (the target Y {\displaystyle Y} ). In the widely used definition of a function f : X → Y {\displaystyle f:X\to Y} , f {\displaystyle f} is a subset of X × Y {\displaystyle X\times Y} consisting of all the pairs ( x , f ( x ) ) {\displaystyle (x,f(x))} for x ∈ X {\displaystyle x\in X} . In this sense, the function does not capture the set Y {\displaystyle Y} that is used as the codomain; only the range f ( X ) {\displaystyle f(X)} is determined by the function. == See also == Apply function – Function that maps a function and its arguments to the function value Arrow notation – e.g., x ↦ x + 1 {\displaystyle x\mapsto x+1} , also known as map Bijection, injection and surjection – Properties of mathematical functions Homeomorphism – Mapping which preserves all topological properties of a given space List of chaotic maps Maplet arrow (↦) – commonly pronounced "maps to" Mapping class group – Group of isotopy classes of a topological automorphism group Permutation group – Group whose operation is composition of permutations Regular map (algebraic geometry) – Morphism of algebraic varieties == References == === Works cited === Halmos, Paul R. (1970). Naive Set Theory. Springer-Verlag. ISBN 978-0-387-90092-6. == External links == |
Wikipedia:Map algebra#0 | Map algebra is an algebra for manipulating geographic data, primarily fields. Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of primitive operations in a geographic information system (GIS) which allows one or more raster layers ("maps") of similar dimensions to produce a new raster layer (map) using mathematical or other operations such as addition, subtraction etc. == History == Prior to the advent of GIS, the overlay principle had developed as a method of literally superimposing different thematic maps (typically an isarithmic map or a chorochromatic map) drawn on transparent film (e.g., cellulose acetate) to see the interactions and find locations with specific combinations of characteristics. The technique was largely developed by landscape architects and city planners, starting with Warren Manning and further refined and popularized by Jaqueline Tyrwhitt, Ian McHarg and others during the 1950s and 1960s. In the mid-1970s, landscape architecture student C. Dana Tomlin developed some of the first tools for overlay analysis in raster as part of the IMGRID project at the Harvard Laboratory for Computer Graphics and Spatial Analysis, which he eventually transformed into the Map Analysis Package (MAP), a popular raster GIS during the 1980s. While a graduate student at Yale University, Tomlin and Joseph K. Berry re-conceptualized these tools as a mathematical model, which by 1983 they were calling "map algebra." This effort was part of Tomlin's development of cartographic modeling, a technique for using these raster operations to implement the manual overlay procedures of McHarg. Although the basic operations were defined in his 1983 PhD dissertation, Tomlin had refined the principles of map algebra and cartographic modeling into their current form by 1990. Although the term cartographic modeling has not gained as wide an acceptance as synonyms such as suitability analysis, suitability modeling and multi-criteria decision making, "map algebra" became a core part of GIS. Because Tomlin released the source code to MAP, its algorithms were implemented (with varying degrees of modification) as the analysis toolkit of almost every raster GIS software package starting in the 1980s, including GRASS, IDRISI (now TerrSet), and the GRID module of ARC/INFO (later incorporated into the Spatial Analyst module of ArcGIS). This widespread implementation further led to the development of many extensions to map algebra, following efforts to extend the raster data model, such as adding new functionality for analyzing spatiotemporal and three-dimensional grids. == Map algebra operations == Like other algebraic structures, map algebra consists of a set of objects (the domain) and a set of operations that manipulate those objects with closure (i.e., the result of an operation is itself in the domain, not something completely different). In this case, the domain is the set of all possible "maps," which are generally implemented as raster grids. A raster grid is a two-dimensional array of cells (Tomlin called them locations or points), each cell occupying a square area of geographic space and being coded with a value representing the measured property of a given geographic phenomenon (usually a field) at that location. Each operation 1) takes one or more raster grids as inputs, 2) creates an output grid with matching cell geometry, 3) scans through each cell of the input grid (or spatially matching cells of multiple inputs), 4) performs the operation on the cell value(s), and writes the result to the corresponding cell in the output grid. Originally, the inputs and the output grids were required to have the identical cell geometry (i.e., covering the same spatial extent with the same cell arrangement, so that each cell corresponds between inputs and outputs), but many modern GIS implementations do not require this, performing interpolation as needed to derive values at corresponding locations. Tomlin classified the many possible map algebra operations into three types, to which some systems add a fourth: Local Operators Operations that operate on one cell location at a time during the scan phase. A simple example would be an arithmetic operator such as addition: to compute MAP3 = MAP1 + MAP2, the software scans through each matching cell of the input grids, adds the numeric values in each using normal arithmetic, and puts the result in the matching cell of the output grid. Due to this decomposition of operations on maps into operations on individual cell values, any operation that can be performed on numbers (e.g., arithmetic, statistics, trigonometry, logic) can be performed in map algebra. For example, a LocalMean operator would take in two or more grids and compute the arithmetic mean of each set of spatially corresponding cells. In addition, a range of GIS-specific operations has been defined, such as reclassifying a large range of values to a smaller range of values (e.g., 45 land cover categories to 3 levels of habitat suitability), which dates to the original IMGRID implementation of 1975. A common use of local functions is for implementing mathematical models, such as an index, that are designed to compute a resultant value at a location from a set of input variables. Focal Operators Functions that operate on a geometric neighborhood around each cell. A common example is calculating slope from a grid of elevation values. Looking at a single cell, with a single elevation, it is impossible to judge a trend such as slope. Thus, the slope of each cell is computed from the value of the corresponding cell in the input elevation grid and the values of its immediate neighbors. Other functions allow for the size and shape of the neighborhood (e.g. a circle or square of arbitrary size) to be specified. For example, a FocalMean operator could be used to compute the mean value of all the cells within 1000 meters (a circle) of each cell. Zonal Operators Functions that operate on regions of identical value. These are commonly used with discrete fields (also known as categorical coverages), where space is partitioned into regions of homogeneous nominal or categorical value of a property such as land cover, land use, soil type, or surface geologic formation. Unlike local and focal operators, zonal operators do not operate on each cell individually; instead, all of the cells of a given value are taken as input to a single computation, with identical output being written to all of the corresponding cells. For example, a ZonalMean operator would take in two layers, one with values representing the regions (e.g., dominant vegetation species) and another of a related quantitative property (e.g., percent canopy cover). For each unique value found in the former grid, the software collects all of the corresponding cells in the latter grid, computes the arithmetic mean, and writes this value to all of the corresponding cells in the output grid. Global Operators Functions that summarize the entire grid. These were not included in Tomlin's work, and are not technically part of map algebra, because the result of the operation is not a raster grid (i.e., it is not closed), but a single value or summary table. However, they are useful to include in the general toolkit of operations. For example, a GlobalMean operator would compute the arithmetic mean of all of the cells in the input grid and return a single mean value. Some also consider operators that generate a new grid by evaluating patterns across the entire input grid as global, which could be considered part of the algebra. An example of these are the operators for evaluating cost distance. == Implementation == Several GIS software packages implement map algebra concepts, including PostGIS, ERDAS Imagine, QGIS, GRASS GIS, TerrSet, PCRaster, and ArcGIS. In Tomlin's original formulation of cartographic modeling in the Map Analysis Package, he designed a simple procedural language around the algebra operators to allow them to be combined into a complete procedure with additional structures such as conditional branching and looping. However, in most modern implementations, map algebra operations are typically one component of a general procedural processing system, such as a visual modeling tool or a scripting language. For example, ArcGIS implements Map Algebra in both its visual ModelBuilder tool and in Python. Here, Python's overloading capability allows simple operators and functions to be used for raster grids. For example, rasters can be multiplied using the same "*" arithmetic operator used for multiplying numbers. Here a modern MapAlgebra implementation, embedding map algebra expressions into SQL (of PostGIS and others), see function ST_MapAlgebra() guide: Here are some examples in MapBasic, the scripting language for MapInfo Professional: # demo for Brown's Pond data set # Give layers # altitude # development – 0: vacant, 1: major, 2: minor, 3: houses, 4: buildings, 5 cement # water – 0: dry, 2: wet, 3: pond # calculate the slope at each location based on altitude slope = IncrementalGradient of altitude # identify the areas that are too steep toosteep = LocalRating of slope where 1 replaces 4 5 6 where VOID replaces ... # create layer unifying water and development occupied = LocalRating of development where water replaces VOID notbad = LocalRating of occupied and toosteep where 1 replaces VOID and VOID where VOID replaces ... and ... roads = LocalRating of development where 1 replaces 1 2 where VOID replaces ... nearread = FocalNeighbor of roads at 0 ... 10 aspect = IncrementalAspect of altitude southface = LocalRating of aspect where 1 replaces 135 ... 225 where VOID replaces ... sites = LocalMinimum of nearroad and southface and notbad sitenums = FocalInsularity of sites at 0 ... 1 sitesize = ZonalSum of 1 within sitenums bestsites = LocalRating of sitesize where sitesize replaces 100 ... 300 where VOID replaces ... == See also == Mathematical morphology Field (geography) == External links == osGeo-RFC-39 about Layer Algebra == References == B. E. Davis GIS: A Visual Approach (2001 Cengage Learning) pp. 249ff. |
Wikipedia:Maple (software)#0 | Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation. Maple's capacity for symbolic computing include those of a general-purpose computer algebra system. For instance, it can manipulate mathematical expressions and find symbolic solutions to certain problems, such as those arising from ordinary and partial differential equations. Maple is developed commercially by the Canadian software company Maplesoft. The name 'Maple' is a reference to the software's Canadian heritage. == Overview == === Core functionality === Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbolic computation and visualization. Examples of symbolic computations are given below. Maple incorporates a dynamically typed imperative-style programming language (resembling Pascal), which permits variables of lexical scope. There are also interfaces to other languages (C, C#, Fortran, Java, MATLAB, and Visual Basic), as well as to Microsoft Excel. Maple supports MathML 2.0, which is a W3C format for representing and interpreting mathematical expressions, including their display in web pages. There is also functionality for converting expressions from traditional mathematical notation to markup suitable for the typesetting system LaTeX. === Architecture === Maple is based on a small kernel, written in C, which provides the Maple language. Most functionality is provided by libraries, which come from a variety of sources. Most of the libraries are written in the Maple language; these have viewable source code. Many numerical computations are performed by the NAG Numerical Libraries, ATLAS libraries, or GMP libraries. Different functionality in Maple requires numerical data in different formats. Symbolic expressions are stored in memory as directed acyclic graphs. The standard interface and calculator interface are written in Java. == History == The first concept of Maple arose from a meeting in late 1980 at the University of Waterloo. Researchers at the university wished to purchase a computer powerful enough to run the Lisp-based computer algebra system Macsyma. Instead, they opted to develop their own computer algebra system, named Maple, that would run on lower cost computers. Aiming for portability, they began writing Maple in programming languages from the BCPL family (initially using a subset of B and C, and later on only C). A first limited version appeared after three weeks, and fuller versions entered mainstream use beginning in 1982. By the end of 1983, over 50 universities had copies of Maple installed on their machines. In 1984, the research group arranged with Watcom Products Inc to license and distribute the first commercially available version, Maple 3.3. In 1988 Waterloo Maple Inc. (Maplesoft) was founded. The company's original goal was to manage the distribution of the software, but eventually it grew to have its own R&D department, where most of Maple's development takes place today (the remainder being done at various university laboratories). In 1989, the first graphical user interface for Maple was developed and included with version 4.3 for the Macintosh. X11 and Windows versions of the new interface followed in 1990 with Maple V. In 1992, Maple V Release 2 introduced the Maple "worksheet" that combined text, graphics, and input and typeset output. In 1994 a special issue of a newsletter created by Maple developers called MapleTech was published. In 1999, with the release of Maple 6, Maple included some of the NAG Numerical Libraries. In 2003, the current "standard" interface was introduced with Maple 9. This interface is primarily written in Java (although portions, such as the rules for typesetting mathematical formulae, are written in the Maple language). The Java interface was criticized for being slow; improvements have been made in later versions, although the Maple 11 documentation recommends the previous ("classic") interface for users with less than 500 MB of physical memory. Between 1995 and 2005 Maple lost significant market share to competitors due to a weaker user interface. With Maple 10 in 2005, Maple introduced a new "document mode" interface, which has since been further developed across several releases. In September 2009 Maple and Maplesoft were acquired by the Japanese software retailer Cybernet Systems. == Version history == == Features == Features of Maple include: Support for symbolic and numeric computation with arbitrary precision Elementary and special mathematical function libraries Complex numbers and interval arithmetic Arithmetic, greatest common divisors and factorization for multivariate polynomials over the rationals, finite fields, algebraic number fields, and algebraic function fields Limits, series and asymptotic expansions Gröbner basis Differential Algebra Matrix manipulation tools including support for sparse arrays Mathematical function graphing and animation tools Solvers for systems of equations, diophantine equations, ODEs, PDEs, DAEs, DDEs and recurrence relations Numeric and symbolic tools for discrete and continuous calculus including definite and indefinite integration, definite and indefinite summation, automatic differentiation and continuous and discrete integral transforms Constrained and unconstrained local and global optimization Statistics including model fitting, hypothesis testing, and probability distributions Tools for data manipulation, visualization and analysis Tools for probability and combinatoric problems Support for time-series and unit based data Connection to online collection of financial and economic data Tools for financial calculations including bonds, annuities, derivatives, options etc. Calculations and simulations on random processes Tools for text mining including regular expressions Tools for signal processing and linear and non-linear control systems Discrete math tools including number theory Tools for visualizing and analysing directed and undirected graphs Group theory including permutation and finitely presented groups Symbolic tensor functions Import and export filters for data, image, sound, CAD, and document formats Technical word processing including formula editing Programming language supporting procedural, functional and object-oriented constructs Tools for adding user interfaces to calculations and applications Tools for connecting to SQL, Java, .NET, C++, Fortran and http Tools for generating code for C, C#, Fortran, Java, JavaScript, Julia, Matlab, Perl, Python, R, and Visual Basic Tools for parallel programming == Examples of Maple code == The following code, which computes the factorial of a nonnegative integer, is an example of an imperative programming construct within Maple: Simple functions can also be defined using the "maps to" arrow notation: === Integration === Find ∫ cos ( x a ) d x {\displaystyle \int \cos \left({\frac {x}{a}}\right)dx} . Output: a sin ( x a ) {\displaystyle a\sin \left({\frac {x}{a}}\right)} === Determinant === Compute the determinant of a matrix. [ 1 2 3 a b c x y z ] {\displaystyle {\begin{bmatrix}1&2&3\\a&b&c\\x&y&z\end{bmatrix}}} LinearAlgebra:-Determinant(M); b z − c y + 3 a y − 2 a z + 2 x c − 3 x b {\displaystyle bz-cy+3ay-2az+2xc-3xb} === Series expansion === x − 1 3 x 3 + 2 15 x 5 − 17 315 x 7 {\displaystyle x-{\frac {1}{3}}\,x^{3}+{\frac {2}{15}}\,x^{5}-{\frac {17}{315}}\,x^{7}} + 62 2835 x 9 − 1382 155925 x 11 + 21844 6081075 x 13 + O ( x 15 ) {\displaystyle {}+{\frac {62}{2835}}\,x^{9}-{\frac {1382}{155925}}\,x^{11}+{\frac {21844}{6081075}}\,x^{13}+{\mathcal {O}}\left(x^{15}\right)} === Solve equations numerically === The following code numerically calculates the roots of a high-order polynomial: The same command can also solve systems of equations: === Plotting of function of single variable === Plot x sin ( x ) {\displaystyle x\sin(x)} with x ranging from -10 to 10: === Plotting of function of two variables === Plot x 2 + y 2 {\displaystyle x^{2}+y^{2}} with x and y ranging from -1 to 1: === Animation of functions === Animation of function of two variables f := 2 k 2 cosh 2 ( x k − 4 k 3 t ) {\displaystyle f:={\frac {2k^{2}}{\cosh ^{2}\left(xk-4k^{3}t\right)}}} Animation of functions of three variables Fly-through animation of 3-D plots. === Laplace transform === Laplace transform ( 1 + A t + B t 2 ) e c t {\displaystyle \left(1+A\,t+B\,t^{2}\right)e^{ct}} 1 s − c + A ( s − c ) 2 + 2 B ( s − c ) 3 {\displaystyle {\frac {1}{s-c}}+{\frac {A}{(s-c)^{2}}}+{\frac {2B}{(s-c)^{3}}}} inverse Laplace transform e a x {\displaystyle e^{ax}} === Fourier transform === Fourier transform I π ( D i r a c ( w + 1 ) − D i r a c ( w − 1 ) ) {\displaystyle \mathrm {I} \pi \,(\mathrm {Dirac} (w+1)-\mathrm {Dirac} (w-1))} === Integral equations === Find functions f that satisfy the integral equation f ( x ) − 3 ∫ − 1 1 ( x y + x 2 y 2 ) f ( y ) d y = h ( x ) {\displaystyle f(x)-3\int _{-1}^{1}(xy+x^{2}y^{2})f(y)dy=h(x)} . f ( x ) = ∫ − 1 1 ( − 15 x 2 y 2 − 3 x y ) h ( y ) d y + h ( x ) {\displaystyle f\left(x\right)=\int _{-1}^{1}\!\left(-15\,{x}^{2}{y}^{2}-3\,xy\right)h\left(y\right){dy}+h\left(x\right)} == Use of the Maple engine == The Maple engine is used within several other products from Maplesoft: MapleNet allows users to create JSP pages and Java Applets. MapleNet 12 and above also allow users to upload and work with Maple worksheets containing interactive components. MapleSim, an engineering simulation tool. Maple Quantum Chemistry Package from RDMChem computes and visualizes the electronic energies and properties of molecules. Listed below are third-party commercial products that no longer use the Maple engine: Versions of Mathcad released between 1994 and 2006 included a Maple-derived algebra engine (MKM, aka Mathsoft Kernel Maple), though subsequent versions use MuPAD. Symbolic Math Toolbox in MATLAB contained a portion of the Maple 10 engine, but now uses MuPAD (starting with MATLAB R2007b+ release). Older versions of the mathematical editor Scientific Workplace included Maple as a computational engine, though current versions include MuPAD. == See also == == References == == External links == Maplesoft, division of Waterloo Maple, Inc. – official website |
Wikipedia:Mara Alagic#0 | Mara Alagic is a Serbian mathematics educator and the editor-in-chief of the Journal of Mathematics and the Arts. She is an Associate Professor in the Department of Curriculum and Instruction and Graduate Coordinator at Wichita State University. == Education == Alagic obtained her Bachelor of Science in Mathematics, her Master's of Science in Mathematics and her PhD from the University of Belgrade in Yugoslavia. Her Master's thesis was on Category of Multivalued Mappings (Hypertopology). She completed her PhD in 1985 under the direction of Ðuro Kurepa; her dissertation title was Categorical Views of Some Relational Models. == Books == Alagic is the co-author of the book Locating Intercultures: Educating for Global Collaboration (2010). In addition, with Glyn M. Rimmington of Wichita State University, Alagic wrote the book Third place learning: Reflective inquiry into intercultural and global cage painting (Information Age Publishing, 2012). == References == == External links == Mara Alagic publications indexed by Google Scholar Mara Alagic ResearchGate Profile |
Wikipedia:Marc Thomas (computer scientist)#0 | Marc Phillip Thomas (1949–2017) was a professor of computer science and mathematics, retired chair and a system administrator of Computer Science department at CSU Bakersfield. He obtained a Ph.D. in mathematics from UC Berkeley in 1976. His successful research projects include the resolution of the commutative Singer–Wermer conjecture and construction of a non-standard closed ideal in a certain radical Banach algebra of power series and their quotients. == Exposition == The Relationship between C, ANSI C, and C++ "The Unix Operating System". Archived from the original on October 5, 2002. Retrieved February 17, 2006. (from Encyclopedia of Information Systems) "The PC Organism". Archived from the original on April 28, 1997. Retrieved February 17, 2006. "OS/2 FAQ". Archived from the original on April 28, 1997. Retrieved August 17, 2017. Remarks on Network Security Typical Hacking Attempts Typical Buffer Overflow Hack Attempts Moronic Hacking Efficient Hacking == Publications == Elements in the radical of a Banach algebra obeying the unbounded Kleinecke-Shirokov conjecture Marc P. Thomas (Jan 2003). "Local power series quotients of commutative Banach and Fréchet algebras". Trans. Amer. Math. Soc. 355 (5): 2139–2160. doi:10.1090/S0002-9947-03-03251-3. Prime-like Elements and Semi-direct Products in Commutative Banach Algebras Marc P. Thomas (1983). "Closed Ideals of l1({ωn}) when {ωn} is Star-Shaped". Pacific Journal of Mathematics. 105 (1): 237–255. doi:10.2140/pjm.1983.105.237. Principal Ideals and Semi-direct Products in Commutative Banach Algebras Single-Element Properties in Commutative Radical Banach Algebras:a Classification Scheme Reduction of discontinuity for derivations on Frechet algebras Radical Banach Algebrasand Quasinilpotent Weighted Shift Operators. The image of a derivation is contained in the radical (MR970607) Marc P. Thomas (1993). "Primitive Ideals and Derivations on Non-Commutative Banach Algebras". Pacific Journal of Mathematics. 159 (1): 139–152. doi:10.2140/pjm.1993.159.139. Marc P. Thomas (1978). "Algebra Homomorphisms and the Functional Calculus". Pacific Journal of Mathematics. 79 (1): 251–269. doi:10.2140/pjm.1978.79.251. == References == == External links == www.cs.csubak.edu/~marc/unix/unix_ap_copyr.html |
Wikipedia:Marc van Leeuwen#0 | Marc A. A. Van Leeuwen (born May 1, 1960) is a Dutch mathematician at the University of Poitiers. He is a project member of the atlas of Lie groups and representations. Van Leeuwen attended the Utrecht University, where he obtained his doctorate in 1989, under supervision of T. A. Springer. == External links == Website at University of Poitiers Marc van Leeuwen at the Mathematics Genealogy Project Marc van Leeuwen's results at International Mathematical Olympiad |
Wikipedia:Marcel F. Neuts#0 | Marcel Fernand Neuts (21 February 1935 – 9 March 2014) is a Belgian-American mathematician and probability theorist. He's known for contributions in algorithmic probability, stochastic processes, and queuing theory. == Education and career == Neuts was born in Ostend, Belgium and studied at the KU Leuven. He moved to the US in 1956 along with his wife Olga. He was admitted to graduate programs at Stanford University and received his MSc in 1959 and PhD at the same place in 1961, just two years after the MSc degree, under the supervision of Samuel Karlin. He held positions at Purdue University from 1962 to 1976, the University of Delaware from 1976 to 1985, and at the Department of Systems and Industrial Engineering at the University of Arizona from 1985 until his retirement in 1997. == Honors and awards == Neuts received the Lester R. Ford Award from the Mathematical Association of America in 1969. Neuts served as the chairman of the Applied Probability Society of the Institute for Operations Research and the Management Sciences between 1977 and 1978. He received the Alexander von Humboldt Fellowship in 1983 to conduct research at the University of Stuttgart. He was the founding editor of the journal Stochastic Models and a contributing editor for Journal of Applied Probability and Advances in Applied Probability. The journal Stochastic Models has established a prize after Neuts for best papers published in the journal. == Bibliography == Neuts, Marcel F. (1973). Probability. Boston, MA: Allyn and Bacon. Neuts, Marcel F., ed. (1977). Algorithmic methods in probability. TIMS Studies in the management sciences. Amsterdam: North-Holland Publ. ISBN 978-0-444-85049-2. Neuts, Marcel F. (1989). Structured stochastic matrices of M/G/1 type and their applications. Probability, pure and applied. New York, NY: Dekker. ISBN 978-0-8247-8283-2. Neuts, Marcel F. (1994). Matrix-geometric solutions in stochastic models: an algorithmic approach. Dover books on advanced mathematics. New York, NY: Dover Publications. ISBN 978-0-486-68342-3. Neuts, Marcel F. (1995). Algorithmic probability: a collection of problems. Stochastic modeling series (1st ed.). London Weinheim: Chapman & Hall. ISBN 978-0-412-99691-7. == References == |
Wikipedia:Marcel Guénin#0 | Marcel André Guénin (born 1937) is a theoretical physicist and mathematician, and Professor Emeritus of the University of Geneva. He obtained his PhD in 1962 at the University of Geneva under the supervision of Ernst Stueckelberg with a thesis titled "Opérateurs de champ antilinéaires, T- et CP-covariance". From 1983 to 1987 he was Rector of the University of Geneva. Jean-Pierre Eckmann was one of his PhD students. == References == |
Wikipedia:Marcel J. E. Golay#0 | Marcel Jules Edouard Golay (French: [gɔlɛ]; May 3, 1902 – April 27, 1989) was a Swiss mathematician, physicist, and information theorist, who applied mathematics to real-world military and industrial problems. He was born in Neuchâtel, Switzerland. == Career == Golay studied electrical engineering at the Eidgenössische Technische Hochschule (Swiss Federal Institute of Technology) in Zürich. He joined Bell laboratories in New York City in 1924, spending four years there. He received a Ph.D. in physics from the University of Chicago in 1931. Golay then joined the US Army Signal Corps, eventually rising to the post of Chief Scientist. He was based mostly in Fort Monmouth, New Jersey. He developed an IR "radar" based on its Golay Detector, the SCR-268T specifically designed to the detection of vessels (S/S Normandie was detected at its inaugural crossing). The SCR-268 (using Barkausen vacuum tubes) and the SCR-268T were to work together. However the 268T, only used in the Pacific theater was abandoned before the end of the war. Between 1955 and 1963, Golay was a consultant for Philco Corporation of Philadelphia, PA, and the Perkin-Elmer Corporation of Norwalk, Connecticut. In 1963, Golay joined the Perkin-Elmer company full-time as senior research scientist. Golay worked on many problems, including gas chromatography and optical spectroscopy. It was during this period when he patented an Analysis of Images, for two-dimensional parallel data processing, and worked to develop the idea, called Golay Logic for Optical Pattern Recognition along with Kendall Preston, Philip Norgren, David Dacava and Joseph Carvalko, Jr. He remained with Perkin-Elmer for the rest of his life. == Achievements == Discoverer of the famous binary and ternary Golay codes, which are perfect error-correcting codes that generalize the Hamming code. They were used in the Voyager probes, and led to advances in the theory of finite groups. Co-author with Abraham Savitzky of the Savitzky–Golay filter. Inventor of the Golay cell, a type of infrared detector. He introduced complementary sequences. Those are pairs of binary sequences whose autocorrelation functions add up to zero for all non-zero time shifts. Today they are used in various WiFi and 3G standards. He introduced the theory of dispersion in open tubular columns (capillary columns) and demonstrated their efficacy at the Second International Symposium on Gas Chromatography at Amsterdam in 1958. == Significant bibliography == Golay, M. (1949). "Notes on Digital Coding" (PDF). Proc. IRE. 37: 657. Archived from the original (PDF) on 2016-10-07. Golay, M. (January 1977). "Sieves for low autocorrelation binary sequences". IEEE Transactions on Information Theory. 23 (1): 43–51. doi:10.1109/TIT.1977.1055653. Golay, M. J. E. (January 1988). "Preparative capillary chromatography-a proposal". Journal of High Resolution Chromatography. 11 (1): 6–8. doi:10.1002/jhrc.1240110103. Golay, M. (April 1961). "Complementary series". IEEE Transactions on Information Theory. 7 (2): 82–87. doi:10.1109/TIT.1961.1057620. == References == == External links == Bibliography of writings by and about Marcel Golay, including awards. Compiled by his daughter, Nona Golay Bloomer (2007). Reprints of papers are in the Archives of the Science History Institute: "Finding Aid to Marcel J. E. Golay, 1931-2002 (bulk 1946-1989)". Science History Institute. Science History Institute. Click on 'Golay Box List' to go to full list. |
Wikipedia:Marcel Riesz#0 | Marcel Riesz (Hungarian: Riesz Marcell [ˈriːs ˈmɒrt͡sɛll]; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford algebras. He spent most of his career in Lund, Sweden. Marcel is the younger brother of Frigyes Riesz, who was also an important mathematician and at times they worked together (see F. and M. Riesz theorem). == Biography == Marcel Riesz was born in Győr, Austria-Hungary. He was the younger brother of the mathematician Frigyes Riesz. In 1904, he won the Loránd Eötvös competition. Upon entering the Budapest University, he also studied in Göttingen, and the academic year 1910-11 he spent in Paris. Earlier, in 1908, he attended the 1908 International Congress of Mathematicians in Rome. There he met Gösta Mittag-Leffler, in three years, Mittag-Leffler would offer Riesz to come to Sweden. Riesz obtained his PhD at Eötvös Loránd University under the supervision of Lipót Fejér. In 1911, he moved to Sweden, where from 1911 to 1925 he taught at Stockholm University. From 1926 to 1952, he was a professor at Lund University. According to Lars Gårding, Riesz arrived in Lund as a renowned star of mathematics, and for a time his appointment may have seemed like an exile. Indeed, there was no established school of mathematics in Lund at the time. However, Riesz managed to turn the tables around and make the academic atmosphere more active. Retired from the Lund University, he spent 10 years at universities in the United States. As a visiting research professor, he worked in Maryland, Chicago, etc. After ten years of intense work with little rest, he suffered a breakdown. Riesz returned to Lund in 1962. After a long illness, he died there in 1969. Riesz was elected a member of the Royal Swedish Academy of Sciences in 1936. == Mathematical work == === Classical analysis === The work of Riesz as a student of Fejér in Budapest was devoted to trigonometric series: a 0 2 + ∑ n = 1 ∞ { a n cos ( n x ) + b n sin ( n x ) } . {\displaystyle {\frac {a_{0}}{2}}+\sum _{n=1}^{\infty }\left\{a_{n}\cos(nx)+b_{n}\sin(nx)\right\}.\,} One of his results states that if ∑ n = 1 ∞ | a n | + | b n | n 2 < ∞ , {\displaystyle \sum _{n=1}^{\infty }{\frac {|a_{n}|+|b_{n}|}{n^{2}}}<\infty ,\,} and if the Fejer means of the series tend to zero, then all the coefficients an and bn are zero. His results on summability of trigonometric series include a generalisation of Fejér's theorem to Cesàro means of arbitrary order. He also studied the summability of power and Dirichlet series, and coauthored a book Hardy & Riesz (1915) on the latter with G.H. Hardy. In 1916, he introduced the Riesz interpolation formula for trigonometric polynomials, which allowed him to give a new proof of Bernstein's inequality. He also introduced the Riesz function Riesz(x), and showed that the Riemann hypothesis is equivalent to the bound {{{1}}} as x → ∞, for any ε > 0. Together with his brother Frigyes Riesz, he proved the F. and M. Riesz theorem, which implies, in particular, that if μ is a complex measure on the unit circle such that ∫ z n d μ ( z ) = 0 , n = 1 , 2 , 3 ⋯ , {\displaystyle \int z^{n}d\mu (z)=0,n=1,2,3\cdots ,\,} then the variation |μ| of μ and the Lebesgue measure on the circle are mutually absolutely continuous. === Functional-analytic methods === Part of the analytic work of Riesz in the 1920s used methods of functional analysis. In the early 1920s, he worked on the moment problem, to which he introduced the operator-theoretic approach by proving the Riesz extension theorem (which predated the closely related Hahn–Banach theorem). Later, he devised an interpolation theorem to show that the Hilbert transform is a bounded operator in Lp (1 < p < ∞). The generalisation of the interpolation theorem by his student Olaf Thorin is now known as the Riesz–Thorin theorem. Riesz also established, independently of Andrey Kolmogorov, what is now called the Kolmogorov–Riesz compactness criterion in Lp: a subset K ⊂Lp(Rn) is precompact if and only if the following three conditions hold: (a) K is bounded; (b) for every ε > 0 there exists R > 0 so that ∫ | x | > R | f ( x ) | p d x < ϵ p {\displaystyle \int _{|x|>R}|f(x)|^{p}dx<\epsilon ^{p}\,} for every f ∈ K; (c) for every ε > 0 there exists ρ > 0 so that ∫ R n | f ( x + y ) − f ( x ) | p d x < ϵ p {\displaystyle \int _{\mathbb {R} ^{n}}|f(x+y)-f(x)|^{p}dx<\epsilon ^{p}\,} for every y ∈ Rn with |y| < ρ, and every f ∈ K. === Potential theory, PDE, and Clifford algebras === After 1930, the interests of Riesz shifted to potential theory and partial differential equations. He made use of "generalised potentials", generalisations of the Riemann–Liouville integral. In particular, Riesz discovered the Riesz potential, a generalisation of the Riemann–Liouville integral to dimension higher than one. In the 1940s and 1950s, Riesz worked on Clifford algebras. His 1958 lecture notes, the complete version of which was only published in 1993 (Riesz (1993)), were dubbed by the physicist David Hestenes "the midwife of the rebirth" of Clifford algebras. === Students === Riesz's doctoral students in Stockholm include Harald Cramér and Einar Carl Hille. In Lund, Riesz supervised the theses of Otto Frostman, Lars Gårding, Lars Hörmander, and Olof Thorin. == Publications == Hardy, G. H.; Riesz, M. (1915). The general theory of Dirichlet's series. Cambridge University Press. JFM 45.0387.03. Riesz, Marcel (1988). Collected papers. Berlin, New York: Springer-Verlag. ISBN 978-3-540-18115-6. MR 0962287. Riesz, Marcel (1993) [1958]. Clifford numbers and spinors. Fundamental Theories of Physics. Vol. 54. Dordrecht: Kluwer Academic Publishers Group. ISBN 978-0-7923-2299-3. MR 1247961. == References == == External links == O'Connor, John J.; Robertson, Edmund F., "Marcel Riesz", MacTutor History of Mathematics Archive, University of St Andrews Marcel Riesz at the Mathematics Genealogy Project |
Wikipedia:Marcin Król z Żurawicy#0 | Marcin Król (c. 1422–1460), also Martinus Ruthenus, Marcin z Żurawica, Marcin Król z Przemyśla, Martinus Polonus, Martinus Rex de Premislia was a Ruthenian-born Polish mathematician, astronomer, and doctor. == Life == Marcin Król, son of Stanisław Król, was born around 1422 in Żurawica near Przemyśl. He joined the Cracow Academy to study the liberal arts in 1438. Six years later, he earned his baccalarius. In 1445 he gained the title magister and began to lecture on mathematics and astronomy. That same year, Zbigniew Oleśnicki, the academy's chancellor, arranged for him to study abroad. Król attended the universities in Prague (1445), Leipzig, Padua and Bologna, where he lectured on astronomy in 1448. In December 1449, he earned the title doctor of medicine. Shortly thereafter, Król left for Hungary, where he was the court physician to John Hunyadi. He probably also spent time at the court of John Vitéz w Oradea. Król returned to Cracow probably in the winter of 1450 through the intervention of Zbigniew Oleśnicki and Jan Długosz, and took up a position as professor at the Cracow Academy. He covered mathematics (geometry) and astronomy, founding the latter department. Sometime after 1450, he also established the department of astrology, which soon developed a European-wide reputation. He kept up close correspondence with other astronomers, including the Austrian Georg von Peuerbach and the German Regiomontanus. In this period Król also served as doctor to the bishop of Cracow. At his death in 1460, his substantial fortune went, in large part, to the University of Cracow, as was his wish. A small sum also went to his brother Florian, a peasant settled in the family village of Żurawica. == Works == Nova compilatio algorismi minutiarum. Algorismus minuciarum. 1445. Summa super Tabulas Alphonsi vel Correctiones Tabularum Alphonsi. 1450–1451(?). Treatise correcting the astronomical tables of 1251. Iudicia. Astrological almanacs for 1451 and 1452. Opus de geometria. c.1450. Canones super calendarium. 1456. Letters From Jan Długosz in Cracow, dated October 1449. From Zbigniew Oleśnicki, dated December(?) 1449. == Footnotes == Notes == Bibliography == Bibliografia Literatury Polskiej – Nowy Korbut, vol. 3 Piśmiennictwo Staropolskie, 461–62. Warsaw: Państwowy Instytut Wydawniczy, 1965 s. 461–462 Knoll, Paul W. “A Pearl of Powerful Learning”: The University of Cracow in the Fifteenth Century, 381ff. Leiden: Brill, 2016. Kuksiewicz, Zdzisław. "Marcin Król z Żurawicy alias z Przemyśla. Materiały i Studia Zakładu Historii Filozofii Starożytnej i Średniowiecznej 1 (1961): 118–40. Láng, Benedek. Unlocked Books: Manuscripts of Learned Magic in the Medieval Libraries of Central Europe, 247–49. University Park, PA: Penn State University Press, 2008. == External links == https://www.ipsb.nina.gov.pl/a/biografia/marcin-z-zurawicy |
Wikipedia:Marco Antonio Raupp#0 | Marco Antonio Raupp (9 July 1938 – 24 July 2021) was a Brazilian mathematician and politician. He served as Director of the National Institute for Space Research, President of the Sociedade Brasileira para o Progresso da Ciência, and Minister of Science, Technology and Innovation. == Biography == Raupp studied at the Federal University of Rio Grande do Sul and held a PhD in mathematics from the University of Chicago. He was a professor at the University of São Paulo's Institute of Mathematics and Statistics and the University of Brasília. He was also head researcher at the Laboratório Nacional de Computação Científica (LNCC). For his contributions as head of the LNCC and his various professorships, Raupp became a Commander of the Order of Rio Branco and of the National Order of Scientific Merit. He later served as President of the Sociedade Brasileira de Matemática Aplicada e Computacional. He was a member of the International Academy of Astronautics and was Director of the Parque Tecnológico de São José dos Campos. He also served as President of the Brazilian Space Agency. On 24 January 2012, Raupp was appointed by President Dilma Rousseff to be Minister of Science, Technology and Innovation, replacing Aloizio Mercadante. He left the position on 17 March 2014 following ministerial reforms led by President Rousseff. On 10 July 2016, Raupp was involved in a serious traffic collision which caused him to undergo surgery and enter into a medically-induced coma. Marco Antonio Raupp died of acute respiratory failure resulting from a brain tumor in São José dos Campos on 24 July 2021 at the age of 83. == References == |
Wikipedia:Marco Avellaneda (mathematician)#0 | Marco Avellaneda (Ph.D.) (February 16, 1955 - June 11, 2022) was an Argentine-American mathematician and financial consultant. He was the director of the Division of Financial Mathematics at the Courant Institute at New York University. == Early life == Avellaneda was born on February 16, 1955, in Miramar, Argentina. His great-grandfather Nicolas Avellaneda was Argentina’s youngest President and was credited with having brought on a period of peace and significant economic output and exports at the end of the 19th century. He spent his formative years living in Rio de Janeiro, Buenos Aires and Paris. Avellaneda attended the University of Buenos Aires from 1977 to 1981. He moved to the United States in 1981, to pursue a doctorate in mathematics at the University of Minnesota–Twin Cities where he graduated with a PhD in 1985. He was married to Cassandra Richmond, a psychotherapist, and lived in New York City. == Academic career == He began his academic career at New York University's Courant Institute as an Instructor in 1985 and has been a member of the faculty since then. He was appointed Director of the Division of Financial Mathematics in 1998. His research interests include applied mathematics and physics, mathematical finance, econometrics of financial markets, derivative securities, portfolio theory and risk-management. He was a visiting member of the Institute for Advanced Study in 1997, the Applied Mathematics Laboratory at Ecole Polytechnique in Paris, the University of Nice’s Institut Jean Dieudonne, the University of Minnesota’s Institute for Mathematics and its Applications, and the University of Coimbra’s International Center for Mathematics. He served in the American Mathematical Society’s Committee for Science Policy from 2000 to 2003. He was best known for the Uncertain Volatility Model for option pricing and his contributions to the formulation of quantitative trading strategies, such as statistical arbitrage, correlation trading, and automated market-making. He taught courses at NYU in Risk and Portfolio Management and Derivative Securities. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. == Entrepreneurial and business activities == Avellaneda was an expert in quantitative finance and has consulted extensively on the subject. His first assignment, in 1996, was with the foreign-exchange derivatives desk at Banque Indousuez in New York. He became Vice-President of the Fixed-Income research and Derivative Products Group at Morgan Stanley in 1996, where he worked for one year before returning to NYU. He was consultant for the fixed-income research team at Banque Paribas in 1999. He headed the options research team at Gargoyle Strategic Investments from 2000 to 2004. Avellaneda consulted with the Royal Bank of Canada, focusing on structured credit derivatives, in 2001-2002. In 2003, he founded the risk management advisory firm Finance Concepts with fellow mathematician Rama Cont and Nicole El Karoui. In 2004, he started Capital Fund Management’s Nimbus Fund, dedicated to the systematic trading of listed equity derivatives. Avellaneda's research interests centered on applications of mathematics and statistics to financial markets, mostly in the areas of trading and risk-management. In 2010, he was recognized as Quant of the Year by Risk magazine, for his paper on pricing options on hard-to-borrow securities co-authored with Michael Lipkin. == Main scientific publications == Avellaneda, Marco; Laurence, Peter (1999). Quantitative Modeling of Derivative Securities: from Theory To Practice. Chapman and Hall. ISBN 9781584880318. Avellaneda, Marco; Levy, Arnon; Paras, Antonio (1995). "Pricing and hedging derivative securities in markets with uncertain volatilities". Applied Mathematical Finance. 2: 73-88. doi:10.1080/13504869500000005. Avellaneda, Marco; Paras, Antonio (1996). "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model". Applied Mathematical Finance. 3: 21-52. doi:10.1080/13504869600000002. Avellaneda, Marco; Stoikov, Sasha (2008). "High-frequency trading in a limit order book". Quantitative Finance. 8: 217-224. doi:10.1080/13504869600000002. Avellaneda, Marco; Lee, Jeong-Hyun (2010). "Statistical Arbitrage in the US Equities Market". Quantitative Finance. 3: 21-52. doi:10.1080/14697680903124632. Avellaneda, Marco; Lipkin, Michael D. (2003). "A Market-Induced Mechanism for Stock Pinning". Quantitative Finance. 3: 417–425. doi:10.1088/1469-7688/3/6/301. == References == |
Wikipedia:Marco Claudio Campi#0 | Marco Claudio Campi is a mathematician with an engineering background and an interest in the philosophy of science, who specializes in data science and inductive methods. He holds a permanent appointment with the University of Brescia, Italy, while also collaborating with various research institutions, universities and NASA. Since 2012, he has been a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and since 2020 a Fellow of the International Federation of Automatic Control. == Academic research == Campi is a co-creator of the scenario approach, which provides solid mathematical foundation to observation-driven decision-making based on consistent rules. His early contributions in this area demonstrated that, within a convex optimization framework, bounds to the probability of invalidating a decision can be directly determined form the dimensionality of the optimization domain. Subsequent advancements extended this result to schemes permitting the exclusion of certain observations to enhance decision-related costs. More recent work has revealed a deep-seated connection between the concept of complexity of a decision (precisely defined in his papers) and its reliability. The scenario approach has found practical applications across various domains, including control theory, portfolio optimization and statistical classification. Campi is also the inventor of the Virtual reference Feedback Tuning (VRFT), an approach to design controllers using batches of data collected from a plant. == Inductive reasoning == Campi’s conceptualization of inductive reasoning adopts a minimalist stance, comprising solely two components: experience and judgements. Experience drives the evolution of judgements in a continuous flow, where observed facts are used to update opinions and opinions are employed to anticipate facts that have yet to happen. Judgements encapsulate an individual’s knowledge, while also playing an essential role in those deliberations that are intended to guide decisions. Judgements are not certain and Campi’s deeply mathematized approach to the study of induction makes prominent use of probability as a tool to quantify one’s degree of belief in judgements. While he does not exclude that alternative interpretations of probability can be useful in other contexts, he contends that, within his theoretical framework, the only possible interpretation is subjective probability. As a result, assuming independent and identically distributed (i.i.d.) or, more generally, exchangeable observations in no way posits a state of nature, it merely presents a modelling assumption regarding how an individual expects the flow of observations to unfold. This conceptualization overcomes Hume’s critique on the impossibility of demonstrating that reality satisfies a “uniformity principle”. By the only use of deductive logic, Campi develops a complexity-based framework that justifies the use of observations in constructing models and principles. In his approach, complexity assumes the role of a measurable quantity from which the probability of falsification of an inductive conclusion can be accurately estimated. These findings hold in an i.i.d. framework without requiring any a priori assumption on the probabilistic distribution of the observations (agnosic setup) and delve deeply into exploring the mechanisms through which knowledge can be generated in light of observations. As a corollary, Campi asserts that adapting theories to observations is scientifically valid provided that this adaptation is guided by an impartial judge - the complexity. This stands in stark contrast with Popper’s perspective that denounces the practice of adjusting theories to observations. While Campi’s results rigorously justify the use of inductive procedures, he also emphasizes a fundamental distinction between the reliability of a procedure and the reliability of the outcome of a procedure in response to a given set of observations (conditional evaluations). He contends that making rigorous statements about the latter is impossible without using additional a priori information. This is what he terms the “unassailable relativism” of conditional beliefs. == Awards and honors == Institute of Electrical and Electronics Engineers Fellow, 2012, for contributions to stochastic and randomized methods in systems and control International Federation of Automatic Control Fellow, 2020, for contributions to data-driven methods in systems and control George S. Axelby Award, 2008. == References == == External links == Interview with Marco C. Campi [16] Introduction to the Scenario Approach - four talks by M.C. Campi: talk 1/4 [17]; talk 2/4 [18]; talk 3/4 [19]; talk 4/4 [20] Monograph Inductive Learning under Consistency [21] |
Wikipedia:Marcos Dajczer#0 | Marcos Dajczer (born 19 November 1948, in Buenos Aires) is an Argentine-born Brazilian mathematician whose research concerns geometry and topology. Dajczer obtained his Ph.D. from the Instituto Nacional de Matemática Pura e Aplicada in 1980 under the supervision of Manfredo do Carmo. In 2006, he received Brazil's National Order of Scientific Merit honour for his work in mathematics. He was a Guggenheim Fellow in 1985. Do Carmo–Dajczer theorem is named after his teacher and him. == Selected publications == do Carmo, M.; Dajczer, M. (1983) . "Rotation hypersurfaces in spaces of constant curvature", Transactions of the American Mathematical Society, Volume 277, Number 2, pp. 685–709. do Carmo, M.; Dajczer, M. (1982) . "Helicoidal surfaces with constant mean curvature", Tohoku Mathematical Journal Second Series, Volume 34, Number 3, pp. 425–435. Submanifolds and Isometric Immersions (1990, Mathematics Lecture Series) ISBN 9780914098225 == References == == External links == "IMPA: International Symposium on Differential Geometry "In honor of Marcos Dajczer on his 60th birthday"". |
Wikipedia:Marek Fila#0 | Marek Fila (29 August 1959 – 20 April 2023) was a Slovak mathematician. His main research focus was diffusion equations and partial differential equations. He was among the most productive scientists in Slovakia. Fila was born in Bratislava to an artistic family. His father was the painter Rudolf Fila and his mother Dorota Filová was a well-known renovator of medieval art. Fila studied Mathematics at the Comenius University, graduating in 1989. His doctoral advisor was Pavol Brunovský. Following his graduation, he remained at the university and became a full professor in 2008. In the 1990s, he was a visiting researcher at the Iowa State University and later a recurrent visitor at the University of Tokyo. He founded the Department of Applied Mathematics and Statistics at the Faculty of Mathematics and Physics of the Comenius University and led it for 11 years. Fila had two children; son Lukáš Fila, who is a journalist and musician, and daughter Natália, who is an architect. Fila's death was announced by his department on the faculty website on 23 April 2023. == References == |
Wikipedia:Margaret Brown (mathematics educator)#0 | Margaret Louise Brown is a British mathematics educator known for her research on numeracy and the learning stages of mathematics. She is an emeritus professor of mathematics education at King's College London, the former head of the School of Education at King's College London, the former president of the British Educational Research Association, , the former director of Graded Assessment in Mathematics (GAIM), the former chair of the trustees of the School Mathematics Project, and the former president of the Mathematical Association. == Education and career == Brown was a secondary school teacher of mathematics in the 1960s before becoming a lecturer at Chelsea College, now part of King's College London. After the 1985 merge of Chelsea and King's College London, she headed the School of Education from 1992 to 1996. She was president of the Mathematical Association in 1990, and president of the British Educational Research Association for 1997–1998. == Recognition == Brown won the 2013 Kavli Medal "for her significant impact on mathematics education within the UK". She was made an Officer of the Order of the British Empire in the 2015 New Year Honours. == References == == External links == Margaret Brown publications indexed by Google Scholar |
Wikipedia:Margaret Buchanan Cole#0 | Margaret Buchanan Cole (August 18, 1885 – September 10, 1959) was an American mathematician and was one of the few women to achieve a PhD in mathematics before World War II. She retired from West Virginia University as a professor emeritus in 1955. == Life and work == Margaret Buchanan was the second of three children born in Clinton, Pennsylvania, to Sarah Wiley and Aaron Moore Buchanan, a minister. In 1886, the family moved from Pennsylvania to Morgantown, West Virginia. From 1898 to 1902 Margaret Buchanan attended the preparatory school of West Virginia University (WVU) and then enrolled as one of the few women attending the university as a student in 1902. She was a member of many clubs and a founder of the Beta Upsilon chapter of the sorority Kappa Kappa Gamma. In 1906, she graduated with her bachelor's degree from WVU in 1906 and started teaching math at Marshall College in Huntington, West Virginia. She returned to WVU in 1907 as a graduate student and taught math there 1909–1912. She enrolled at Bryn Mawr College as a graduate student in 1918 and was awarded a President M. Carey Thomas European fellowship in 1918–1919 but she postponed that award for a year until she could combine it with another fellowship she received from the Association of Collegiate Alumnae European fellowship in 1920–1921. The awards allowed her to attend the Sorbonne in Paris where she studied under Édouard Goursat, Henri Lebesgue, and Émile Picard in mathematics and under Marie Curie and Gabriel Lippmann in physics. In June 1922 at Bryn Mawr, she completed work on her PhD in math with a minor in physics under the direction of Anna J. Pell Wheeler. Her dissertation was titled, Systems of Two Linear Integral Equations with Two Parameters and Symmetrizable Kernels. PhD in hand, she returned to teach at West Virginia University as assistant professor and was promoted to associate professor in 1925. On February 14, 1929 she resigned her position and married an old acquaintance, Harry Outen Cole, a widowed engineer who played a role in the design of the Panama Canal. In 1938, using her new name Margaret Buchanan Cole, she rejoined the WVU faculty and held several positions: instructor 1938–1941, assistant professor 1941–1952 and associate professor 1952–1955. With her retirement in 1955 at age 69 she was promoted to professor emeritus. Cole was an active alumna of the university and became the first woman president of the WVU alumni association in June 1939 after serving four years on the alumni executive council. Margaret Buchanan Cole died in Morgantown in 1959. == Tribute == The Margaret Buchanan Cole Young Alumni Award honored a WVU alumnus or alumna who graduated within the last 10 years and provided outstanding service for their alma mater. The award noted it was named for the founder of WVU's Kappa Kappa Gamma sorority and the first woman to serve as president of the Alumni Association. It was last awarded in 2015. == References == |
Wikipedia:Margaret Grimshaw#0 | Margaret Eleanor Grimshaw (1905–1990) was a mathematician and academic at the University of Cambridge. == Early life == Margaret Eleanor Grimshaw was born on 17 January 1905 in Elland, Yorkshire. Her parents were school teachers, with her father being headmaster at Southowram School in Halifax in 1918. Grimshaw attended Barnsley High School and Halifax Girls Secondary School. She took her B.A First Class in 1926 from Newnham College, the University of Cambridge. She continued with her research after graduation, residing in the Kennedy Building staff accommodation for much of her life. She had an opportunity to work with a number of Fellows as they moved through Cambridge, including Jean Mitchell, Edith Whetham, Joyce Salt, Dorothy Hill and many others. Grimshaw was Mary Ewart Scholar 1924–1926, Arthur Clough Scholar 1926–1927 and Marion Kennedy Residential Student from 1927 to 1928. She took her M.A. in 1930. == Career == Grimshaw was Assistant Lecturer in Mathematics from 1928 to 1930 and Associates Resident Fellow 1930–1933. She worked as a tutor at University of Göttingen and temporary tutor at Oxford University from 1933 to 1934, before joining the staff of Cambridge as a lecturer. This appointment lasted from 1934 to 1958. She was Director of Studies in Mathematics from 1936 to 1958. Her work was in pure mathematics, in particular analysis. Early papers were on integration theory, Fourier series and transforms. She wrote a textbook with Hans Hamburger in 1951, Linear Transformations in n-Dimensional Vector Space. An Introduction to the Theory of Hilbert Space. She published in mathematics journals. Grimshaw was on the Council of Newnham College from 1936 to 1968. She was Vice Principal from 1953 until 1958, when she became Bursar of Newnham College. At this time she stepped away from teaching duties. Her fulfilled the Bursar role until 1968. She maintained the Newnham Roll or register of the students who had graduated from the College from 1971 to 1980. Grimshaw died in 1990 in Cambridge. == Legacy == Grimshaw bequeathed to Cambridge a large number of school prizes and medals, which she had collected in her lifetime. They are held by the Fitzwilliam Museum in Cambridge. == References == |
Wikipedia:Margaret Hayman#0 | Margaret Hayman (1923 – 26 July 1994, born Margaret Riley Crann) was a British mathematics educator who co-founded the British Mathematical Olympiad, wrote mathematics textbooks, and became president of the Mathematical Association. == Life == Margaret Riley Crann was born on 7 August 1923 in New Earswick in North Yorkshire, where her father Thomas Crann was a research chemist and her mother a teacher; she grew up as a Quaker. After studying at the Mill Mount School in York, she read mathematics and then geography in Newnham College, Cambridge, and earned a master's degree from the University of Cambridge, beginning in 1941 and finishing in 1944. She became a social worker in Birmingham for a year before taking a position as a mathematics teacher at Putney High School, a girls' school in London where she eventually became head of mathematics. In 1947, she married mathematician Walter Hayman. He writes that they met at the Jesus Lane Friends Meeting House in Cambridge, in her third and his first year at Cambridge, and that they fell in love after she hit him with a celery stick for making a pun. Beyond her professional interests, she was also an amateur violinist and activist, joining the Aldermaston Marches for CND, fundraising for various causes and, in her later years, joining the board of North Yorkshire MIND. Margaret and Walter had three daughters: Daphne, Carolyn and Sheila. She retired from Putney High School in 1985, and returned with her husband to Yorkshire. She died on 26 July 1994. == Contributions == In 1966, Hayman and her husband founded the British Mathematical Olympiad. Hayman took an active part in the meetings of proponents of the competition, helped negotiate the role of the British Olympiad in the International Mathematical Olympiad, and fought for funding for the competition and for the good will of the Mathematical Association towards the competition. She taught master classes in mathematics teaching for the Royal Institution, and became the author of mathematical textbooks, including: Multiple Choice Modern Mathematics (Nelson, 1969) Essential Mathematics (Macmillan 1971) She became president of the Mathematical Association for the 1974–1975 term, and a member of the council of the Institute of Mathematics and its Applications. Her philosophy as president of the Mathematical Association involved keeping the mathematics curriculum flexible enough to ensure that all pupils received a mathematical education fitting their individual needs. == References == |
Wikipedia:Margaret Rayner#0 | Margaret Eva Rayner (21 August 1929 – 31 May 2019) was a British mathematician who became vice principal of St Hilda's College, Oxford and president of the Mathematical Association. She was known for her research on isoperimetric inequalities, her work in mathematics education, and her publications on the history of mathematics and of St Hilda's College. == Early life and education == Rayner was born on 21 August 1929 in Tamworth, Staffordshire; her parents were dairy farmers and most of her relatives were also farmers, but an aunt who was a local school headmistress encouraged her in her studies. After study at The King's High School for Girls (graduating as prefect in 1947) she read mathematics at Westfield College with the plan of becoming a mathematics teacher, earned a first, and completed a master's degree there. On the advice of tutor Kathleen Chesney, she applied to be a tutor at St Hilda's College, and was appointed to St Hilda's in 1953, with a joint appointment to St Anne's College, Oxford. In 1960, she completed a doctorate (D.Phil.) at Oxford; her dissertation was Some problems in unsteady heat flow. At this time she was named a Fellow of St Hilda's. == Later life and career == In the late 1960s and early 1970s she worked on isoperimetric inequalities with American mathematician Lawrence E. Payne, beginning with a 1965 research visit to the University of Maryland and Cornell University, where Payne worked. Their work resulted in the Payne–Rayner inequality, a type of Reverse Hölder inequality for the eigenvalues of the Laplace operator. In 1980 she was a speaker at the Fourth International Congress on Mathematical Education in Berkeley, California; her talk was entitled Is calculus essential?. Her work in mathematics education also included being chief examiner for the International Baccalaureate, participating in the Secondary Examinations Council and School Examinations and Assessment Council, and working through the Mathematical Association, which she served as president in 1987. She also chaired the board of governors of what is now Oxford Brookes University. She became vice-principal of St Hilda's in 1981, stepping down in 1988. She retired in 1989. After her retirement, her interests shifted to history, and her publications in this period included a chapter on Oxford mathematics in a book on the history of mathematics, and the book Centenary History of St. Hilda's College (1993). She died on 31 May 2019 in Oxford. == Recognition == Rayner was named a Commander of the Order of the British Empire in the 1990 Birthday Honours. == References == |
Wikipedia:Margaret Willerding#0 | Margaret Frances Willerding (1919–2003) was an American mathematician known for her combinatorial enumeration of quadratic forms, for her mathematics textbooks, and for her editorship of the problems department of the mathematics journal School Science and Mathematics. == Early life and education == Willerding was born on April 26, 1919, in St. Louis, Missouri. After graduating from high school in 1936, she went to a local school, Harris Teachers College, despite being highly ambitious academically, because it was free; her parents were not especially supportive and could not afford a more expensive school. She majored in education there, with a minor in mathematics, and graduated in 1940. After a year working as a schoolteacher, she went to Saint Louis University for graduate study in mathematics, choosing it as the best of the two universities local enough to allow her to continue living with her parents, and despite her mother's dismissal of her academic ambitions. During this time she continued working as a schoolteacher to support herself, before obtaining a fellowship in the final year of her program, the first woman to do so. She earned a master's degree in 1943 and completed her Ph.D. in 1947. Her dissertation, Determination of All Classes of Positive Quaternary Quadratic Forms Which Represent All (Positive) Integers, was supervised by Arnold Ross,. A short summary of it was later published in the Bulletin of the American Mathematical Society, the main result of which being that "there are exactly 178 classes of universal classic positive quaternary quadratic forms". This was later found to be incorrect. Based on the use of the 15 theorem, Manjul Bhargava determined the correct number to be 204. As noted by John H. Conway, "Willerding’s work had been unusually defective. [...] she missed 36 forms, listed 1 form twice, and listed 9 non-universal forms!" While she was still working on her doctorate, Ross moved to the University of Notre Dame to become department chair, and she commuted there by train to visit him. She became engaged to an older physicist at Notre Dame, Eugene Guth, but did not end up marrying him, and Ross's plans to hire her at Notre Dame also did not work out. == Career and later life == After completing her doctorate, Willerding became a mathematics instructor at Washington University in St. Louis, beginning in 1947. She returned to Harris Teachers College and began focusing on mathematics education instead of mathematical research. During this time she also became active in the Missouri Section of the Mathematical Association of America. In 1954 she started her work as mathematical problems editor for School Science and Mathematics, a position she held until 1976 despite a colleague undercutting her in the early 1960s by suggesting to the journal's editor-in-chief that she was too old for the position. She moved in 1956 to San Diego State University, and retired as a professor emeritus in 1976. She died on December 29, 2003. == Books == Willerding wrote over 30 mathematical textbooks. They include: The Business of Mathematics (Prindle, Weber & Schmidt, 1977) College Algebra and Trigonometry (with Stephen Hoffman, Wiley, 1971; 2nd ed., 1975) Elementary Mathematics: Its Structure and Concepts (Wiley, 1966) A First Course in College Mathematics: Module 4—The Integers and Their Operations; Equations and Inequalities; Squares, Square Roots, and Similar Triangles (Prindle, Weber & Schmidt, 1975) Mathematics: The Alphabet of Science (with Ruth A. Hayward, 2nd ed., Wiley, 1972) Modern Intermediate Algebra (2nd ed., Wiley, 1975) The Numbers Game (Prindle, Weber & Schmidt, 1977) A Probability Primer (Prindle, Weber & Schmidt, 1968) == References == |
Wikipedia:Margherita Piazzola Beloch#0 | Margherita Beloch Piazzolla (12 July 1879 – 28 September 1976) was an Italian mathematician who worked in algebraic geometry, algebraic topology and photogrammetry. == Biography == Beloch, born in Frascati, was the daughter of the German historian Karl Julius Beloch, who taught ancient history for 50 years at Sapienza University of Rome, and American Bella Bailey (daughter of Gamaliel Bailey) . Beloch studied mathematics at the Sapienza University of Rome and wrote her undergraduate thesis under the supervision of Guido Castelnuovo. She received her degree in 1908 with Laude and dignità di stampa, which means that her work was worthy of publication, and in fact her thesis Sulle trasformazioni birazionali nello spazio (On Birational Transformations in Space) was published in the Annali di Matematica Pura ed Applicata. Castelnuovo was very impressed with her talent and offered her the position of assistant which Beloch took and held until 1919, when she moved to Pavia. In 1920 she moved to Palermo to work under Michele De Franchis, an important figure of the Italian school of algebraic geometry at the time. In 1924, Beloch completed her libera docenza (a degree that at that time had to be obtained before one could become a professor), and three years later she became a full professor at the University of Ferrara, where she taught until her retirement (1955). She died in Rome in 1976. Piazzolla is Beloch's married surname. == Scientific work == Her main scientific interests were in algebraic geometry, algebraic topology and photogrammetry. After her thesis, she worked on the classification of algebraic surfaces by studying the configurations of lines that could lie on surfaces. The next step was to study rational curves lying on surfaces and in this framework Beloch obtained the following important result: "Hyperelliptic surfaces of rank 2 are characterised by having 16 rational curves." Beloch also made contributions to the theory of skew algebraic curves. She continued working on topological properties of algebraic curves either planar or lying on ruled or cubic surfaces for most of her life, writing about a dozen papers on these subjects. Around 1940 Beloch become more and more interested in photogrammetry and the application of mathematics, and in particular algebraic geometry, to it. She is also known for her contribution to the mathematics of paper folding: In particular she seems to have been the first to formalise an origami move which allows, when possible, to construct by paper folding the common tangents to two parabolas. As a consequence she showed how to extract cubic roots by paper folding, something that is impossible to do by ruler and compass. The move she used has been called the Beloch fold. == References == |
Wikipedia:Maria Aparecida Soares Ruas#0 | Maria Aparecida Soares Ruas (born 1948) is a Brazilian mathematician specializing in differential geometry and singularity theory. She is a professor at the University of São Paulo. == Education and career == Ruas was born on 5 January 1948, in Lins, São Paulo. She became interested in mathematics through a junior high school mathematics teacher, Râmisa Jorge, and after entering university study in 1967, earned a licenciate in mathematics in 1970 through what is now the Faculty of Science and Letters of the Araraquara campus of São Paulo State University. She became a teaching assistant at the same campus in 1971, while at the same time studying for a master's degree at the University of São Paulo, working there with Gilberto Francisco Loibel; she completed her degree in 1974, and was promoted to assistant professor. In 1982 she moved to the University of São Paulo as a professor. She defended her doctoral dissertation, Finity Determinacy and Applications at the University of São Paulo in 1983. It was jointly advised by Luiz Antonio Fávaro and Terence Gaffney. She has headed the mathematics department at the University of São Paulo, was a founding member of the Brazilian Mathematical Society, and has organized the biennial Workshop on Real and Complex Singularities in Brazil. She is a coauthor of the book Differential Geometry from a Singularity Theory Viewpoint (World Scientific, 2016, with Shyuichi Izumiya, Maria del Carmen Romero Fuster, and Farid Tari). == Recognition == Ruas is a member of the Brazilian Academy of Sciences, elected in 2008, and in 2009 was named a commander in the National Order of Scientific Merit. == References == |
Wikipedia:Maria Chudnovsky#0 | Maria Chudnovsky (born January 6, 1977) is an Israeli-American mathematician working on graph theory and combinatorial optimization. She is a 2012 MacArthur Fellow. == Education and career == Chudnovsky is a professor in the department of mathematics at Princeton University. She grew up in Russia (attended Saint Petersburg Lyceum 30) and Israel, studying at the Technion, and received her Ph.D. in 2003 from Princeton University under the supervision of Paul Seymour. After postdoctoral research at the Clay Mathematics Institute, she became an assistant professor at Princeton University in 2005, and moved to Columbia University in 2006. By 2014, she was the Liu Family Professor of Industrial Engineering and Operations Research at Columbia. She returned to Princeton as a professor of mathematics in 2015. Chudnovsky is an editor for a number of mathematical journals, including Combinatorica, Journal of Combinatorial Theory Series B, Journal of Graph Theory and Proceedings of the London Mathematical Society. == Research == Chudnovsky's contributions to graph theory include the proof of the strong perfect graph theorem (with Neil Robertson, Paul Seymour, and Robin Thomas) characterizing perfect graphs as being exactly the graphs with no odd induced cycles of length at least 5 or their complements. Other research contributions of Chudnovsky include co-authorship of the first polynomial-time algorithm for recognizing perfect graphs (time bounded by a polynomial of degree 9), a structural characterization of the claw-free graphs, and progress on the Erdős–Hajnal conjecture. == Selected publications == Chudnovsky, Maria; Cornuéjols, Gérard; Liu, Xinming; Seymour, Paul; Vušković, Kristina (2005), "Recognizing Berge graphs", Combinatorica, 25 (2): 143–186, doi:10.1007/s00493-005-0012-8, MR 2127609, S2CID 2229369. Chudnovsky, Maria; Seymour, Paul (2005), "The structure of claw-free graphs", Surveys in Combinatorics 2005, London Mathematical Society Lecture Note Series, vol. 327, Cambridge: Cambridge Univ. Press, pp. 153–171, CiteSeerX 10.1.1.112.4130, doi:10.1017/CBO9780511734885.008, ISBN 9780511734885, MR 2187738. Chudnovsky, Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2006), "The strong perfect graph theorem", Annals of Mathematics, 164 (1): 51–229, arXiv:math/0212070, doi:10.4007/annals.2006.164.51, S2CID 119151552. Chudnovsky, Maria; Sivaraman, Vaidy (2018), "Odd Holes in Bull-Free Graphs", SIAM Journal on Discrete Mathematics, 32 (2): 951–955, arXiv:1704.04262, doi:10.1137/17M1131301, MR 3794342, S2CID 1657094 == Awards and honors == In 2004 Chudnovsky was named one of the "Brilliant 10" by Popular Science magazine. Her work on the strong perfect graph theorem won for her and her co-authors the 2009 Fulkerson Prize. In 2012 she was awarded a "genius award" under the MacArthur Fellows Program. She was elected as a Fellow of the American Mathematical Society in the 2024 class of fellows. == Personal life == In 2011, she married Daniel Panner, a viola player who teaches at Mannes School of Music and Rutgers University. They have a son named Rafael. == References == == External links == Chudnovsky's home page at Princeton University |
Wikipedia:Maria Cibrario#0 | Elisa Maria Eugenia Cibrario Cinquini (6 September 1905 – 16 May 1992) was an Italian mathematician specializing in partial differential equations and known for her research in association with Guido Fubini, Giuseppe Peano, and Francesco Tricomi. == Life == === Early life and education === Maria Cibrario was born in Genoa on 6 September 1905. She was educated at the Liceo classico Pietro Verri in Lodi, Lombardy, and enrolled in 1923 in a program in physical sciences and mathematics at the University of Turin, where she became a student of Guido Fubini, and graduated in 1927. She became an assistant to Giuseppe Peano, and Peano assisted her in earning a habilitation as a secondary-school teacher in 1927. Peano died in 1932, and in the same year she obtained a free lecturership and began working with Francesco Tricomi. === Later life and academic career === In 1938, she married mathematician Silvio Cinquini; they had three children. Soon after marrying, they both took faculty positions at the University of Pavia. In 1947 she won the competition for the chair in mathematical analysis at the University of Cagliari, from which she moved to the University of Modena and then, in 1950, returned to Pavia as a full professor. She retired as professor emerita in 1980. She died on 16 May 1992, in Pavia. == Research == Cibrario's 1927 thesis concerned Laplace transforms and their application to parabolic partial differential equations. From then until the early 1940s, one of her main areas of study concerned partial differential equations of mixed elliptic–hyperbolic type, finding earlier work of Tricomi in this area to be incomplete and publishing a complete classification of these equations and of the solution methods suitable for each type of equation within this classification. This work later had great applicability to the aerodynamics of transonic aircraft, and the Cibrario–Cinquini equation is named for her work from this time. Her later work concerned non-linear differential equations, systems of hyperbolic equations, and the theory of curves and generalized functions. It included the solution of old problems of Édouard Goursat on non-linear hyperbolic equations and of Augustin-Louis Cauchy on systems of first-order equations. == Recognition == In 1929, Cibrario won the Corrado Segre prize for her early research, and in 1933, Cibrario won a prize for junior researchers from the Accademia dei Lincei. She joined the Istituto Lombardo Accademia di Scienze e Lettere in 1951 and became a full member in 1967. In 1968, she became a member of the Academy of Sciences of Turin. After her retirement, in 1981, she was elected as a corresponding member of the Accademia dei Lincei. == References == == Further reading == Mustaţă, P. (1963), "On a theorem of Cinquini-Cibrario", Comunicările Academiei Republicii Populare Romîne, 13: 343–348, MR 0179448 "Maria Cinquini Cibrario", Atti della Accademia delle Scienze di Torino, 127 (5–6): 285–298, 1993, MR 1281872 Cazzani Nieri, M. G. (1994), "Cibrario, Maria, Cinquini – obituary", Bollettino UMI, 7 (8–A): 295–307 Magenes, Enrico (1995), "Maria Cibrario Cinquini", Atti della Accademia Nazionale dei Lincei, 5: 35–47, MR 1384124 == External links == Riddle, Larry (25 February 2016), "Maria Cinquini-Cibrario", Biographies of Women Mathematicians, Agnes Scott College "Maria Cibrario Cinquini", MATEpristem (in Italian), Bocconi University, retrieved 2021-11-21 |
Wikipedia:Maria Colombo (mathematician)#0 | Maria Colombo (born 25 May 1989) is an Italian mathematician specializing in mathematical analysis. She is a professor at the EPFL (École Polytechnique Fédérale de Lausanne) in Switzerland, where she holds the chair for mathematical analysis, calculus of variations and partial differential equations. == Education and career == Colombo was born in Luino, near the Swiss border of Italy. She competed for Italy in the 2005, 2006, and 2007 International Mathematical Olympiads, earning bronze, gold, and silver medals respectively. She earned bachelor's and master's degrees in mathematics at the University of Pisa in 2010 and 2011, and completed a Ph.D. in 2015 at the Scuola Normale Superiore di Pisa, under the joint supervision of Luigi Ambrosio and Alessio Figalli. Her dissertation, Flows of non-smooth vector fields and degenerate elliptic equations: With applications to the Vlasov-Poisson and semigeostrophic systems, was published as a book in 2017 by Edizioni della Normale. After postdoctoral research with Camillo De Lellis at the University of Zurich, she joined the EPFL as an assistant professor in 2018, and was promoted to full professor in 2021. == Recognition == The Accademia dei Lincei gave Colombo their Gioacchino Iapichino Prize for 2016. She was the 2017 winner of the Carlo Miranda Prize of the National Society of Sciences, Letters and Arts of Naples, and the 2019 winner of the Bartolozzi Prize of the Italian Mathematical Union. She is the 2022 winner of the biennial Peter Lax Award, to be given at the International Conference on Hyperbolic Problems, and the 2023 winner of the Collatz Prize of the International Council for Industrial and Applied Mathematics, "for her fundamental contributions to regularity theory and the analysis of singularities in elliptic partial differential equations, geometric variational problems, transport equations, and incompressible fluid dynamics". In 2024, she was awarded the EMS Prize for breakthrough results in fluid dynamics, optimal transport and kinetic theory, and for her impact on analysis more broadly. That same year, she was awarded the Stampacchia Medal. == Personal life == Colombo is married to Simone, an engineer, with whom she has four children. == References == == External links == Home page Website of the Chair of Mathematical Analysis, Calculus of Variations and PDEs Maria Colombo publications indexed by Google Scholar |
Wikipedia:Maria Deijfen#0 | Maria Deijfen (born 1975) is a Swedish mathematician known for her research on random graphs and stochastic processes on graphs, including the Reed–Frost model of epidemics. She is a professor of mathematics at Stockholm University. == Education and career == Deijfen was educated at Stockholm University, earning a licenciate in 2001, a doctorate in 2004, and a habilitation in 2008. Her doctoral dissertation, Stochastic Models for Spatial Growth and Competition, was supervised by Olle Häggström. After completing her doctorate, she became a postdoctoral researcher at the Mittag-Leffler Institute, Vrije Universiteit Amsterdam, Chalmers University, and Delft University of Technology before returning to Stockholm as a junior faculty member in 2006. She was promoted to full professor in mathematical statistics in 2015. == Recognition == Deijfen was one of the 2018 recipients of the Paul R. Halmos – Lester R. Ford Award of the Mathematical Association of America for her paper with Alexander E. Holroyd and James B. Martin, "Friendly Frogs, Stable Marriage, and the Magic of Invariance", using combinatorial game theory to analyze the stable marriage problem. == References == == External links == Home page |
Wikipedia:Maria E. Schonbek#0 | Maria Elena Schonbek is an Argentine-American mathematician at the University of California, Santa Cruz. Her research concerns fluid dynamics and associated partial differential equations such as the Navier–Stokes equations. == Education and career == Schonbek received a bachelor's degree from the University of Buenos Aires. She completed her Ph.D. at the University of Michigan in 1976. Her dissertation, Boundary Value Problems for the Fitzhugh–Nagumo Equations, was supervised by Jeffrey Rauch. Schonbek joined the University of California, Santa Cruz faculty in 1986. Formerly a professor of mathematics there, she has retired to become a professor emeritus. At Santa Cruz, Schonbek advocated replacing the campus's system of narrative evaluations of student performance in each course with the more standard system of letter grades used at most other US universities. == Recognition == In 2012, Schonbek became a member of the inaugural class of fellows of the American Mathematical Society. == References == |
Wikipedia:Maria Emelianenko#0 | Maria Emelianenko is a Russian-American applied mathematician and materials scientist known for her work in numerical algorithms, scientific computing, grain growth, and centroidal Voronoi tessellations. She is a professor of mathematical sciences at George Mason University. == Education and career == Emelianenko earned a bachelor's degree in computer science and mathematics in 1999 and a master's degree in 2001 from Moscow State University, both summa cum laude. Her master's thesis, Numerical approach to solving Andronov–Hopf and Bogdanov–Takkens systems of differential equations, was supervised by Alexander Bratus. She then came to Pennsylvania State University for additional graduate study. She earned a second master's degree in 2002 with the thesis Analysis of Constrained Multidimensional Birth-Death Processes supervised by Natarajan Gautam. Gautam moved to Texas A&M University in 2005, and Emelianenko completed her Ph.D. the same year under the supervision of Qiang Du, with the dissertation Multilevel and Adaptive Methods for Some Nonlinear Optimization Problems. After postdoctoral research at the Carnegie Mellon University Center for Nonlinear Analysis, Emelianenko joined the George Mason University mathematics faculty in 2007. She was promoted to full professor in 2017. At George Mason, she is also affiliated faculty with the Computational Materials Science Center, and directs the Math PhD Industrial Immersion Program. == Activism == Emelianenko has acted as an activist for women in mathematics, writing of differential treatment of female faculty members in mathematics departments and of prejudice against talented women deriving from a misguided belief that their success was due to tokenism. She has been an organizer of many workshops and symposia, including several aimed at women in mathematics. == References == == External links == Home page Maria Emelianenko publications indexed by Google Scholar Maria Emelianenko personal website |
Wikipedia:Maria Eulália Vares#0 | Maria Eulália Vares is a Brazilian mathematical statistician and probability theorist who is known for her expertise in stochastic processes and large deviations theory. She is a professor of statistics in the Institute of Mathematics of the Federal University of Rio de Janeiro, from 2006 to 2009 was the editor-in-chief of the journal Stochastic Processes and their Applications, publisher by Elsevier for the Bernoulli Society for Mathematical Statistics and Probability, and from 2015 to 2017 was the editor-in-chief of the Annals of Probability, published by the Institute of Mathematical Statistics. Vares graduated in 1975 from the Federal University of Rio Grande do Sul with a bachelor's degree in mathematics. After earning a master's degree in statistics in 1977 from the Instituto Nacional de Matemática Pura e Aplicada, she went to the University of California, Berkeley for doctoral study in statistics. She completed her Ph.D. in 1980; her dissertation, supervised by P. Warwick Millar, was On Two Parameter Lévy Processes. With Enzo Olivieri, Vares is the author of the book Large Deviations and Metastability (Encyclopedia of Mathematics and its Applications 100, Cambridge University Press, 2005). She is a Fellow of the Institute of Mathematical Statistics, and an elected member of the International Statistical Institute. == References == == External links == Home page |
Wikipedia:Maria Gordina#0 | Maria (Masha) Gordina is a Russian-American mathematician. She is a professor of mathematics at the University of Connecticut. Her research is at the interface between stochastic analysis, differential geometry, and functional analysis, including the study of heat kernels on infinite-dimensional groups. Gordina is the daughter of mathematician Mikhail (Misha) Gordin. == Education and career == Gordina earned a diploma in 1990 from Leningrad State University, and became an assistant professor at the Leningrad Electrotechnical Institute. She completed her doctorate in 1998 from Cornell University; her dissertation, Holomorphic functions and the heat kernel measure on an infinite dimensional complex orthogonal group, was supervised by Leonard Gross. Gordina held a post-doctoral appointment at McMaster University. She was awarded a National Science Foundation postdoctoral fellowship in 2000, and conducted research at the University of California, San Diego. In 2003 Gordina joined the University of Connecticut faculty. Gordina serves on the editorial boards of Forum Mathematicum, the Electronic Journal of Probability, and Electronic Communications in Probability. == Honors == Gordina was awarded a Humboldt Research fellowship in 2005 (with renewals), and the Ruth I. Michler Memorial Prize of the Association for Women in Mathematics in 2009. She was named a Simons Fellow (2016) in Mathematics and Physical Sciences. She was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to stochastic and geometric analysis, infinite-dimensional analysis, and ergodicity of hypoelliptic diffusions". == Selected publications == Baudoin, Fabrice; Feng, Qi; Gordina, Maria Integration by parts and quasi-invariance for the horizontal Wiener measure on foliated compact manifolds. J. Funct. Anal. 277 (2019), no. 5, 1362–1422. Banerjee, Sayan; Gordina, Maria; Mariano, Phanuel Coupling in the Heisenberg group and its applications to gradient estimates. Ann. Probab. 46 (2018), no. 6, 3275–3312. Eldredge, Nathaniel; Gordina, Maria; Saloff-Coste, Laurent Left-invariant geometries on SU(2) are uniformly doubling. Geom. Funct. Anal. 28 (2018), no. 5, 1321–1367. Baudoin, Fabrice; Gordina, Maria; Melcher, Tai Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups. Trans. Amer. Math. Soc. 365 (2013), no. 8, 4313–4350. Driver, Bruce K.; Gordina, Maria Heat kernel analysis on infinite-dimensional Heisenberg groups. J. Funct. Anal. 255 (2008), no. 9, 2395–2461. Cardetti, Fabiana; Gordina, Maria A note on local controllability on Lie groups. Systems Control Lett. 57 (2008), no. 12, 978–979. Gordina, Maria Heat kernel analysis and Cameron-Martin subgroup for infinite dimensional groups. J. Funct. Anal. 171 (2000), no. 1, 192–232. == References == |
Wikipedia:Maria Gramegna#0 | Maria Paola Gramegna (1887–1915) was an Italian mathematician and a student of Giuseppe Peano. Her work with Peano on systems of linear differential equations has been cited as an important early milestone in the history of functional analysis and its transition from working with concrete matrices to more abstract basis-independent formulations of linear algebra. After becoming a schoolteacher, she died in the 1915 Avezzano earthquake. == Early life and education == Gramegna was born on 11 May 1887 in Tortona, the youngest of five children of a pasta factory owner. After studying mathematics in high school in Voghera with Giuseppe Vitali, she was admitted to the University of Turin in 1906, where she became a student of Peano. She completed her mathematics degree in 1910, with the thesis Serie di equazioni differenziali lineari ed equazioni integro-differenziali [Series of linear differential equations and integro-differential equations], supervised by Peano. Peano also presented this work to the Academy of Sciences of Turin. == Later life == Immediately after finishing her mathematics degree, she also earned a diploma from the mathematics section of the university's school of education, with a second thesis, Area della zona sferica e della sfera [Area of the spherical zone and of the sphere]. With this credential, she became a high school teacher in Avezzano. She began there in 1910 as a substitute mathematics teacher at the normal school, won a competition for a permanent position as extraordinary mathematics teacher in 1912, and directed the associated boarding school for 1912–1913. During this period she also published on the history of mathematics. She was killed by the 1915 Avezzano earthquake, on 13 January 1915. == Recognition == Minor planet 37840 Gramegna, discovered in 1998 by the San Vittore Observatory, was named in honor of Gramegna. == References == |
Wikipedia:Maria Hoffmann-Ostenhof#0 | Maria Hoffmann-Ostenhof (née Bauer, born 1947) is an Austrian mathematician known for her work on the behavior of the Schrödinger equation, and particularly on its asymptotic analysis, nodal lines, and behavior near its singularities. Hoffmann-Ostenhof was born on 12 January 1947 in Vienna. She studied mathematics at the University of Vienna, with a year visiting the University of Zurich, and completed her Ph.D. in 1973 at the University of Vienna. Her dissertation, Über Kongruenzverbände universaler Algebren und binärer Systeme [On congruence relations of universal algebras and binary systems] was supervised by Wilfried Nöbauer. During her studies she married another mathematician, Thomas Hoffmann-Ostenhof. After two years at the Max Planck Institute for Coal Research, she returned to the University of Vienna, where she was employed in various part-time positions. In 1991, she earned a habilitation in mathematics, the first woman at the university to do so; her habilitation thesis was Nullstellen und asymptotisches Verhalten von L2-Lösungen von Schrödingergleichungen [Zeros and asymptotic behavior of L2-solutions of the Schrödinger equation]. She became an associate position at the University of Vienna in 1992, and was given the title of University Professor in 2008. She retired in 2010. == References == == External links == Home page |
Wikipedia:Maria Korovina#0 | Maria Korovina (Russian: Мари́я Ви́кторовна Коро́вина; born 1962) is a Russian mathematician, Professor, Dr. Sc., a professor at the Faculty of Computer Science at the Moscow State University. She defended the thesis «Elliptic problems in spaces with asymptotics and their applications to the construction of self-adjoint extensions of the Laplace operator» for the degree of Doctor of Physical and Mathematical Sciences (1992). The author of the monograph «The theory of functional spaces and differential equations» (2007) and more than 70 scientific articles. == References == == Bibliography == Evgeny Grigoriev (2010). Faculty of Computational Mathematics and Cybernetics: History and Modernity: A Biographical Directory (1 500 экз ed.). Moscow: Publishing house of Moscow University. pp. 166–167. ISBN 978-5-211-05838-5. == External links == Scientific works of Maria Korovina Scientific works of Maria Korovina(in English) |
Wikipedia:Maria Laura Moura Mouzinho Leite Lopes#0 | Maria Laura Moura Mouzinho Leite Lopes or Maria Laura Mouzinho Leite Lopes or Maria Laura Lopes (Timbaúba, October 18, 1917 – Rio de Janeiro, June 20, 2013) was a Brazilian mathematician, the first Brazilian woman PhD in mathematics, specializing in Mathematics education. A renowned mathematician, she fought the dictatorship and articulated the creation of research institutions. She was part of the group that articulated the foundation of the Brazilian Center for Research in Physics (CBPF), an institute she created together with José Leite Lopes and César Lattes in 1949. In addition, she participated in articulations to found other important institutions, such as the National Council for Scientific and Technological Development (CNPq), the National Institute for Pure and Applied Mathematics (IMPA) and the Brazilian Society for Mathematics Education (SBEM). == Personal life == Maria Laura was born in the Zona da Mata of Pernambuco state, on January 18, 1917. Daughter of Laura Moura Mouzinho and Oscar Mouzinho, a self-taught merchant. Her parents encouraged their children's education, and Maria Laura began her school life at the João Barbalho School Group in Recife, graduating in 1931. == Career == In 1932, she entered the Escola Normal de Pernambuco, studying until 1934, where she was a student of teacher Luiz de Barros Freire (1986–1963). According to Maria Laura, he was responsible for her vocation in mathematics. In 1935, the family moved to Rio de Janeiro, where she enrolled in the La-Fayette Institute. In 1939 she entered the Mathematics course at the University of the Federal District (Universidade do Distrito Federal - UDF), but had only 15 days of classes, because the university was extinguished by the Federal Decree No. 1.063/39. Professors and students were transferred to the Mathematics course of the newly created National Faculty of Philosophy (Faculdade Nacional de Filosofia – FNFi). Maria Laura received her bachelor's degree in mathematics in 1941. In 1942 she received her licentiate degree, and in 1949 she obtained her PhD in mathematics, being the first woman to obtain this title in Brazil. Before obtaining her doctorate, she was already an assistant professor in the Mathematics Department of the FNFi, participating in the creation of the CBPF, together with César Lattes (1924–2005) and José Leite Lopes (1918–2006), in 1949. In the same year, she taught Geometry in the Engineering course of the newly created Aeronautics Institute of Technology (Instituto Tecnológico da Aeronáutica – ITA) and worked, in the United States, at the Department of Mathematics of the University of Chicago. In 1952, she founded the IMPA, together with professor Cândido Lima da Silva Dias (1913–1998). In March of the same year, she was graduated in the Brazilian Academy of Sciences (Academia Brasileira de Ciências – ABC). She married in 1956 to the renowned physicist and professor José Leite Lopes. In 1961 she was appointed professor of the Technical Professional Education of the State of Guanabara and in 1967, she assumed the head of the Mathematics Department of the FNFi, until it became the Institute of Mathematics of the UFRJ. == Exile == In 1969, by Institutional Act Number Five (AI-5), she and her husband were exiled and banned from Brazil. The couple left for France, where Maria Laura began her research in Mathematics Education at the Institute for Research in Mathematics Education (Institute de Recherche en Enseignement de Mathematiques). She returned to Brazil only in 1974, already with international experience, and was invited to be the Mathematics coordinator at the Eliezer Eistenbarg Brazilian Jewish School. In 1976, she took part in the foundation of the Group for Teaching and Research in Mathematics Education (Grupo de Ensino e Pesquisa em Educação Matemática – GEPEM), which was chaired by Maria Laura during the first eight years. She coordinated the first research in Mathematics Education in Brazil, the "Teacher-Student Binomial Project in the Initiation to Mathematics Education – an experimental research" (Projeto Binômio Professor-Aluno na Iniciação à Educação Matemática – uma pesquisa experimental). == Return to Brazil == After the Amnesty Law in 1979, still under military rule, Maria Laura resumed her professorship at the Mathematics Institute at UFRJ. In 1981 she and a group of teachers developed the research project "Evaluation of students at the end of the 4th grade in public schools" (Avaliação dos alunos no final da 4ª série primária das escolas públicas) in the city of Rio de Janeiro, and in 1982 she joined the Ministry of Education's "Program for Integration of the University with Primary Education" (Programa de Integração da Universidade com o Ensino do 1º Grau). She did several research projects for the federal and state governments on Mathematics education in the country, trying to identify the deficiencies in schools and in teacher training. In 1980, the first lato sensu post-graduate course in Mathematics Education in Brazil was created, followed by master's and doctorate levels. In 1988, she founded the Brazilian Mathematics Education Society (Sociedade Brasileira de Educação Matemática – SBEM), along with other professors and researchers in the field. == Retirement and death == On July 1, 1996, after 65 years of teaching and research career, she received the title of professor emeritus from the Federal University of Rio de Janeiro (UFRJ). Her work is now a reference worldwide, with several articles and books published. Member of the ABC, Maria Laura died on June 20, 2013. == See also == Brazilian Center for Research in Physics (CBPF) National Council for Scientific and Technological Development (CNPq) Instituto Nacional de Matemática Pura e Aplicada (IMPA) List of women in mathematics Association for Women in Mathematics Timeline of women in mathematics worldwide Women in science == References == |
Wikipedia:Maria Longobardi (mathematician)#0 | Maria Longobardi is an Italian mathematician. After early work in functional analysis, her research has focused on mathematical statistics, information theory, entropy, and extropy. Longobardi earned a laurea (the Italian equivalent of a master's degree) from the University of Naples Federico II. She became a research fellow at the Istituto Nazionale di Alta Matematica Francesco Severi, and then for the National Research Council (Italy), before becoming an assistant at the University of Naples from 2000 to 2019. During this time, in 2002, she completed her Ph.D., with the dissertation Su alcuni risultati in teoria dell'affidabilità basati sulla funzione d'azzardo inversa [Some results on reliability theory based on reversed hazard rate function] supervised by Antonio Di Crescenzo. She has been an associate professor at the University of Naples Federico II since 2019. == References == == External links == Maria Longobardi publications indexed by Google Scholar |
Wikipedia:Maria Pastori#0 | Maria Pastori (10 March 1895 - 17 April 1975) was an Italian mathematician and teacher. She was a Professor of Rational Mechanics at the University of Milan, and worked on differential calculus and the application of mathematics to electromagnets. == Life == Pastori was born in Milan on 10 March 1895, to a family of eight children. The family was of limited means and could not afford education for the children beyond what was provided by the public school system. Pastori excelled in mathematics, which was encouraged by one of her teachers, who aided her in getting a scholarship to Maria Agnesi School, a magisterial school (similar to a teacher's college). After completing her studies at the magisterial school, Pastori then went on to teach elementary school near Milan. While teaching, Pastori studied further with her sister Giuseppina (who became a physician and biologist). At the age of twenty Pastori sat for the state exams, and earned a baccalaureate with highest honors. She earned a scholarship to the University of Pisa where she earned a doctorate, studying under geometer Luigi Bianchi. She earned laureate status on her dissertation. She supported herself during her studies by tutoring. After earning her doctorate Pastori became an assistant professor at the University of Milan, working her way up to professor, and eventually becoming the chair of the rational mechanics department. Most of Pastori's research and publications were focused on extending differential calculus as developed by Gregorio Ricci-Curbastro, as well of the application of mathematics to electromagnets. She was made extraordinary professor in 1965, and in 1971 professor emerita. She died on 17 April 1975 in Milan. == References == |
Wikipedia:Maria Rita D'Orsogna#0 | Maria Rita Rosaria D'Orsogna (born 1972) is an Italian and American applied mathematician and environmental activist. She is a professor of mathematics at California State University, Northridge, where her research interests include swarm behaviour, quantitative methods in criminology, and racial disparities in drug overdoses. She is also known for a successful campaign to prevent offshore drilling for oil near Abruzzo, Italy. == Early life == D'Orsogna was born in The Bronx, New York, in 1972, to parents from Italy; they returned to Italy when she was a child, and she grew up in Abruzzo. == Academics == D'Orsogna earned a laurea in physics from the University of Padua in 1996, focusing on statistical mechanics and mentored by Attilio L. Stella. After a master's degree from the University of Maryland, College Park in 1998, supervised by Theodore L. (Ted) Einstein, she completed a Ph.D. at the University of California, Los Angeles (UCLA) in 2003. Her dissertation, Charge transfer in DNA: the role of thermal fluctuations and of symmetry, was jointly chaired by Joseph Rudnick and Robijn Bruinsma. She became a postdoctoral researcher in chemical engineering at the California Institute of Technology from 2003 to 2004, and then in the mathematics department at UCLA from 2004 to 2007. She took her present position as a professor in the mathematics department at California State University, Northridge (CSUN) in 2007. At CSUN, she also became affiliated with the Institute for Sustainability in 2008. She added an adjunct professorship in computational medicine at UCLA in 2012. At UCLA, she was associate director of the Institute for Pure and Applied Mathematics from 2018 to 2021. == Activism == After D'Orsogna learned in 2007 of a plan by Eni to begin offshore drilling in the Miglianico Oil and Gas Field near Ortona in Abruzzo, her mother's hometown, she began organizing against oil exploration in the area. In 2008 the nearby Ombrina Mare oil field was proposed for development; by 2010, her campaign had succeeded in blocking both plans and in leading to a new Italian law against drilling within five miles of the Italian coast and its marine parks. After continued pressure from her campaign, the drilling limits were expanded to 12 miles in 2016, but in 2022 this led to a large preliminary judgement for the corporate inheritor of the drilling project, Rockhopper Exploration, who argued that the new limits on drilling caused unfair reductions on their potential future profits. For her efforts, she was named ambassador from Abruzzo to the world in 2014, and has been called the "Italian Erin Brockovich". Closer to her home, she has also opposed development in Santa Monica, California. == References == == External links == Home page Maria Rita D'Orsogna publications indexed by Google Scholar |
Wikipedia:Maria Serna#0 | Maria José Serna Iglesias (born 1959) is a Spanish computer scientist and mathematician whose research includes work on parallel approximation, on algorithms for cutwidth and linear layout of graphs, on algorithmic game theory, and on adversarial queueing networks. == Education == Serna earned two licenciates (undergraduate degrees), one in mathematics from the University of Barcelona in 1981 and a second in computer science from the Polytechnic University of Catalonia in 1985. After visiting the University of Patras in Greece to work with Paul Spirakis, with the support of the Spanish Ministry of Education, she completed in Ph.D. in 1990 through the Polytechnic University of Catalonia. Her dissertation, The Parallel Approximability of P-complete Problems, combined the ideas of parallel algorithms and approximation algorithms, and was jointly supervised by Spirakis and Joaquim Gabarró. While in Patras, she continued to hold an associate professor position at the Polytechnic University of Catalonia, in the department of applied mathematics. On her return fram Patras, she was promoted to full professor in 1991, moved to the computer science department in 1992, and has been a university professor since 2006. == Books == Serna is the coauthor of the book Paradigms for Fast Parallel Approximability (with Josep Díaz, Paul Spirakis, and Jacobo Torán, Cambridge University Press, 1997), and of several Spanish and Catalan-language textbooks. == Recognition == In 2021, a special issue of the journal Computer Science Review was published as a festschrift in honor of Serna's 60th birthday. == References == == External links == Home page Maria Serna publications indexed by Google Scholar |
Wikipedia:Maria Silvia Lucido#0 | Maria Silvia Lucido (22 April 1963 – 4 March 2008) was an Italian mathematician specializing in group theory, and a researcher in mathematics at the University of Udine. == Life, education and career == Lucido was originally from Vicenza, where she was born on 22 April 1963. After working for a bank and a travel agency, she entered mathematical study at the University of Padua in 1986, graduating in 1991. Already as an undergraduate she began research into the theory of finite groups, and wrote an undergraduate thesis on the subject under the supervision of Franco Napolitani. She completed a Ph.D. at Padua in 1996 with the dissertation Il Prime Graph dei gruppi finiti [the prime graphs of finite groups], supervised by Napolitani and co-advised by Carlo Casolo. After postdoctoral research at the University of Padua and as a Fulbright scholar at Michigan State University, she obtained a permanent position as a researcher at the University of Udine in 1999. She was killed in an automobile accident on March 4, 2008, survived by her husband and two sons. == Research == Lucido was particularly known for her research on prime graphs of finite groups. These are undirected graphs that have a vertex for each prime factor of the order of a group, and that have an edge p q {\displaystyle pq} whenever the given group has an element of order p q {\displaystyle pq} . Her work in this area included Proving that the connected components of these graphs have diameter at most five, and at most three for solvable groups. Proving that, when the prime graph is a tree, it has at most eight vertices, and at most four for solvable groups. Characterizing the finite simple groups for which all components of the prime graphs are cliques. Lucido founded a series of annual summer schools on the theory of finite groups, held in Venice and sponsored by the University of Udine, beginning in 2004. After her death, the three subsequent offerings of the summer schools in 2010, 2011, and 2013 were dedicated in her honor. == References == |
Wikipedia:Marian P. Roque#0 | Marian P. Roque is a Filipina mathematician. She was the president of the Mathematical Society of the Philippines, a professor in the Institute of Mathematics of the University of the Philippines Diliman, and former Director of the Institute of Mathematics. Her mathematical specialty is the theory of partial differential equations. Roque's interest in a career in Mathematics began in her grade school participation in the first National Quiz Bee. She continued her studies in mathematics at the University of the Philippines Diliman, where she earned her bachelor's (1986), master's (1989), and doctoral degrees (1996). Through the Sandwich Scholarship Program, she did her research work for her dissertation at the University of Essen, where she studied under Bernd Schultze. While studying in Germany, she faced discrimination due to her gender and nationality. She then completed a postdoctoral fellowship at Waseda University. With Doina Cioranescu and Patrizia Donato, she is the author of An Introduction to Second Order Partial Differential Equations: Classical and Variational Solutions (World Scientific, 2018). == Awards == 2012: Gawad Tsanselor para sa Natatanging Guro 2014-2016: UP Scientist 2016: National Research Council of the Philippines Outstanding Achievement Award. == References == |
Wikipedia:Mariangiola Dezani-Ciancaglini#0 | Mariangiola Dezani-Ciancaglini (born 22 December 1946) is an Italian logician and theoretical computer scientist whose research topics include type theory and intersection type disciplines, lambda calculus, and programming language semantics. She is a professor emerita at the University of Turin. == Education and career == She was born on 22 December 1946 in Turin. After earning a master's degree in physics at the University of Turin in 1970, and working as a researcher in Turin as a CNR fellow, she became an assistant professor of computer science at University of Turin in 1972, and full professor in 1981. While continuing as a professor, she earned a Ph.D. from the Catholic University of Nijmegen in the Netherlands in 1996. Her dissertation, Logical Semantics for Concurrent Lambda-Calculus, was jointly promoted by Henk Barendregt and Corrado Böhm. She served as dean of computer science at the University of Turin from 2005 to 2008, and retired to become a professor emerita in 2018. == Recognition == She was elected to the Academia Europaea in 1993. In 2015 she was named a Fellow of the European Association for Theoretical Computer Science "for distinguished and seminal achievements in formal methods and foundations of programming languages, introducing or developing new type systems for the lambda-calculus as well as for the pi-calculus and related calculi". == References == == External links == Home page Mariangiola Dezani-Ciancaglini publications indexed by Google Scholar |
Wikipedia:Marianna Csörnyei#0 | Marianna Csörnyei (born October 8, 1975 in Budapest) is a Hungarian mathematician who works as a professor at the University of Chicago. She does research in real analysis, geometric measure theory, and geometric nonlinear functional analysis. She proved the equivalence of the zero measure notions of infinite dimensional Banach spaces. == Education and career == Csörnyei received her doctorate from Eötvös Loránd University in 1999, supervised by György Petruska. She was a professor at the Mathematics Department of University College London between 1999 and 2011, and spent the 2009–2010 academic year at Yale University as visiting professor. Currently, she is at the University of Chicago. She is contributing editor of the mathematical journal Real Analysis Exchange. == Awards and honors == Csörnyei won a 2002 Whitehead Prize from the London Mathematical Society and a Royal Society Wolfson Research Merit Award that same year. She was also awarded the Philip Leverhulme Prize for Mathematics and Statistics in 2008 for her work in geometric measure theory. She won a gold medal in the International Mathematics Olympiad. She was an invited sectional speaker at the International Congress of Mathematicians in 2010. Csörnyei was selected to deliver the AWM-AMS Noether Lecture at the 2022 Joint Mathematics Meetings in Seattle, Washington. The title of her talk is The Kakeya needle problem for rectifiable sets. She is included in a deck of playing cards featuring notable women mathematicians published by the Association of Women in Mathematics. == External links == Csörnyei's faculty page at the University of Chicago == References == |
Wikipedia:Marianne Korten#0 | Marianne Kathe Korten is an Argentine-German mathematician who works in the United States as a professor of mathematics at Kansas State University. Her research expertise concerns partial differential equations and particularly free boundary problems. == Education and career == Korten is a dual citizen of Argentina and Germany. After a licenciatura at the University of Buenos Aires in Argentina, Korten completed her Ph.D. there in 1993. Her doctoral dissertation, Soluciones generalizadas, localmente integrables, de la ecuación u t = Δ ( u − 1 ) + {\displaystyle u_{t}=\Delta (u-1)_{+}} , was supervised by Julio E. Bouillet. She continued at the University of Buenos Aires as a teaching and research associate until 1998. After visiting Johns Hopkins University in the US, Marie and Louis Pasteur University in France, and the University of Louisville in the US, she became an assistant professor of mathematics at Kansas State University in 2000. At that time, and for several years following, she was the only female faculty member in the department. She was promoted to associate professor in 2006, and to full professor in 2009. At Kansas State University, Korten has organized an annual research conference, the Prairie Analysis Seminar, since 2003. She has directed the SuMAR Math Research Experience for Undergraduates since 2010 and the Center for the Integration of Undergraduate, Graduate, and Postdoctoral Research since 2013. == Recognition == Kansas State University gave Korten their K-State Women of Distinction Award in 2013, and the Commerce Bank and W.T. Kemper Foundation Presidential Faculty and Staff Award for Distinguished Services to Historically Under-Represented Minority Students in 2022. Korten was named a Fellow of the Association for Women in Mathematics, in the 2025 class of fellows, "for her deep commitment to diversity and access in mathematics, supporting the diverse personal lives of mathematicians as students and faculty, helping us achieve success through AWM forums, online mentoring, regional advocacy, and summer research programs". == References == == External links == Home page Marianne Korten publications indexed by Google Scholar |
Wikipedia:Marie Charpentier#0 | Emmanuelle Marie Charpentier (French pronunciation: [emanɥɛl maʁi ʃaʁpɑ̃tje]; born 11 December 1968) is a French professor and researcher in microbiology, genetics, and biochemistry. As of 2015, she has been a director at the Max Planck Institute for Infection Biology in Berlin. In 2018, she founded an independent research institute, the Max Planck Unit for the Science of Pathogens. In 2020, Charpentier and American biochemist Jennifer Doudna of the University of California, Berkeley, were awarded the Nobel Prize in Chemistry "for the development of a method for genome editing" (through CRISPR). This was the first science Nobel Prize ever won by two women only. == Early life and education == Charpentier paternal grandfather, surnamed Sinanian, was an Armenian who escaped to France during the Armenian Genocide and met his wife in Marseille. She was born in 1968 in Juvisy-sur-Orge in France and studied biochemistry, microbiology, and genetics at the Pierre and Marie Curie University (which became the Faculty of Science of Sorbonne University) in Paris. She was a graduate student at the Institut Pasteur from 1992 to 1995 and was awarded a research doctorate. Charpentier's PhD work investigated molecular mechanisms involved in antibiotic resistance. == Career and research == Charpentier worked as a university teaching assistant at Pierre and Marie Curie University from 1993 to 1995 and as a postdoctoral fellow at the Institut Pasteur from 1995 to 1996. She moved to the US and worked as a postdoctoral fellow at Rockefeller University in New York from 1996 to 1997. During this time, Charpentier worked in the lab of microbiologist Elaine Tuomanen. Tuomanen's lab investigated how the pathogen Streptococcus pneumoniae utilizes mobile genetic elements to alter its genome. Charpentier also helped to demonstrate how S. pneumoniae develops vancomycin resistance. Charpentier was an assistant research scientist at the New York University Medical Center from 1997 to 1999. She worked in the lab of Pamela Cowin, a skin-cell biologist interested in mammalian gene manipulation. Charpentier published a paper exploring the regulation of hair growth in mice. She held the position of Research Associate at the St. Jude Children's Research Hospital and at the Skirball Institute of Biomolecular Medicine in New York from 1999 to 2002. After five years in the United States, Charpentier returned to Europe and became the lab head and a guest professor at the Institute of Microbiology and Genetics, University of Vienna, from 2002 to 2004. In 2004, Charpentier published her discovery of an RNA molecule involved in the regulation of virulence-factor synthesis in Streptococcus pyogenes. From 2004 to 2006 she was lab head and an assistant professor at the Department of Microbiology and Immunobiology. In 2006 she became a privatdozentin (Microbiology) and received her habilitation at the Centre of Molecular Biology. From 2006 to 2009 she worked as lab head and associate professor at the Max F. Perutz Laboratories. Charpentier moved to Sweden and became lab head and associate professor at the Laboratory for Molecular Infection Medicine Sweden (MIMS), at Umeå University. She held the position of group leader from 2008 to 2013 and was visiting professor from 2014 to 2017. She moved to Germany to act as department head and W3 Professor at the Helmholtz Centre for Infection Research in Braunschweig and the Hannover Medical School from 2013 until 2015. In 2014 she became an Alexander von Humboldt Professor. In 2015 Charpentier accepted an offer from the German Max Planck Society to become a scientific member of the society and a director at the Max Planck Institute for Infection Biology in Berlin. Since 2016, she has been an Honorary Professor at Humboldt University in Berlin; since 2018, she is the Founding and acting director of the Max Planck Unit for the Science of Pathogens. Charpentier retained her position as visiting professor at Umeå University until the end of 2017 when a new donation from the Kempe Foundations and the Knut and Alice Wallenberg Foundation allowed her to offer more young researchers positions within research groups of the MIMS Laboratory. == CRISPR/Cas9 == Charpentier is best known for her Nobel-winning work of deciphering the molecular mechanisms of a bacterial immune system, called CRISPR/Cas9, and repurposing it into a tool for genome editing. In particular, she uncovered a novel mechanism for the maturation of a non-coding RNA which is pivotal in the function of CRISPR/Cas9. Specifically, Charpentier demonstrated that a small RNA called tracrRNA is essential for the maturation of crRNA. In 2011, Charpentier met Jennifer Doudna at a research conference in San Juan, Puerto Rico, and they began a collaboration. Working with Doudna's laboratory, Charpentier's laboratory showed that Cas9 could be used to make cuts in any DNA sequence desired. The method they developed involved the combination of Cas9 with easily created synthetic "guide RNA" molecules. Synthetic guide RNA is a chimera of crRNA and tracrRNA; therefore, this discovery demonstrated that the CRISPR-Cas9 technology could be used to edit the genome with relative ease. Researchers worldwide have employed this method successfully to edit the DNA sequences of plants, animals, and laboratory cell lines. Since its discovery, CRISPR has revolutionized genetics by allowing scientists to edit genes to probe their role in health and disease and to develop genetic therapies with the hope that it will prove safer and more effective than the first generation of gene therapies. In 2013, Charpentier co-founded CRISPR Therapeutics and ERS Genomics along with Shaun Foy and Rodger Novak. == Awards == In 2015, Time magazine designated Charpentier one of the Time 100 most influential people in the world (together with Jennifer Doudna). Charpentier's awards are: Nobel Prize in Chemistry, the Breakthrough Prize in Life Sciences, the Louis-Jeantet Prize for Medicine, the Gruber Foundation International Prize in Genetics, the Leibniz Prize, the Tang Prize, the Japan Prize, and the Kavli Prize in Nanoscience. She has won the BBVA Foundation Frontiers of Knowledge Award jointly with Jennifer Doudna and Francisco Mojica. === Honorary doctorate degrees === 2016 – École Polytechnique Fédérale de Lausanne 2016 – KU, (Catholic University) Leuven, Belgium 2016 – New York University (NYU) 2017 – Faculty of Medicine, Umeå University, Sweden 2017 – University of Western Ontario, London, Canada 2017 – Hong Kong University of Science and Technology 2018 – Université catholique de Louvain, Belgium 2018 – University of Cambridge 2018 – University of Manchester 2019 – McGill University, Canada 2024 – University of Saskatchewan, Canada 2024 – University of Perugia, Perugia, Italy === Memberships === 2014 – European Molecular Biology Organisation 2015 – National Academy of Sciences Leopoldina 2016 – Berlin-Brandenburg Academy of Sciences 2016 – Austrian Academy of Sciences 2016 – Royal Swedish Academy of Sciences 2017 – U.S. National Academy of Sciences, Foreign Associate 2017 – National Academy of Technologies of France 2017 – French Académie des sciences 2018 – European Academy of Sciences and Arts 2021 – Pontifical Academy of Sciences 2024 – Foreign Member of the Royal Society == In popular culture == In 2019, Charpentier was a featured character in the play STEM FEMMES by Philadelphia theater company Applied Mechanics. In 2021, Walter Isaacson detailed the story of Jennifer Doudna and her collaboration with Charpentier leading to the discovery of CRISPR/CAS-9, in the biography The Code Breaker: Jennifer Doudna, Gene Editing, and the Future of the Human Race. == References == == External links == Official website Extensive biography of Emmanuelle Charpentier Archived 12 February 2021 at the Wayback Machine at the Max Planck Unit for the Science of Pathogens Umeå University Staff Directory: Emmanuelle Charpentier Molecular Infection Medicine Sweden – Short Curriculum Vitae of Emmanuelle Charpentier Crispr Therapeutics: Scientific Founders Emmanuelle Charpentier to become a Director at the Max Planck Institute for Infection Biology in Berlin Emmanuelle Charpentier on Nobelprize.org |
Wikipedia:Marie Duflo#0 | Marie Duflo (19 August 1940 – 15 September 2019) was a French probability theorist, and left-wing internationalist activist, known for her books on probability theory and random processes and on Nicaraguan politics. == Education and career == Duflo was an alumna of the École normale supérieure de jeunes filles, promoted in 1959, and completed a doctorate (Doctorat d'État) at the University of Paris in 1969, with the dissertation Opérateurs potentiels des chaînes et des processus de Markov irréductibles supervised by Jacques Neveu. She became a professor at Université Paris-Nord and the University of Marne-la-Vallée. == Activism == Duflo was active in French left-wing circles concerning Latin America. In 1968, she attended a Cultural Congress in Havana with several other French mathematicians. In the 1980s, she took over the responsibility for Central American affairs in the French Socialist Party when Nicole Bourdillat stepped up to head Latin American affairs more generally for the party, and later under Louis Le Pensec she became the head of Latin American affairs for the party herself. By 2006, when she signed an open letter in support of undocumented students in France, she had retired from Marne-la-Vallée as a professor emerita. She spent her retirement as an activist for the rights of foreigners in France, and a 2020 paper on the legal treatment of noncitizens in overseas France was dedicated in her memory. == Books == Her books include: Décisions statistiques pas à pas [Statistical decisions step by step] (with Danielle Florens-Zmirou, CIMPA, 1981) Probabilités et statistiques (two volumes, with Didier Dacunha-Castelle, Masson, 1982; also published with two separate volumes of exercises; translated into English by David McHale as Probability and statistics, Springer, 1986) Le volcan nicaraguayen [The Nicaraguan Volcano] (edited with Françoise Ruellan, La découverte, 1985) Méthodes récursives aléatoires (Masson, 1990, revised and translated into English by Stephen S. Wilson as Random iterative models, Springer, 1997) Algorithmes stochastiques [Stochastic algorithms] (Springer, 1996) == References == |
Wikipedia:Marie Fabianová#0 | Marie Fabianová (also written as Marie Fabiánová; 11 February 1872 – 7 April 1943) was a Czech mathematician, teacher and school principal, suffragette and feminist. She was one of the first Czech women to obtain a university education, the second female graduate of Charles-Ferdinand University, and the first female to graduate with a PhD in math from the University. == Biography == Fabianová was born 11 February 1872 in Železný Brod into the family of Václav Fabián, the chief engineer of the Austrian Northwestern Railway, and his wife Juliana, née Haklová. She had two siblings, Juliana and Václav. After graduating from a local school, she began studying in Prague at the first, newly opened (1890), private girls' grammar school in Central Europe, called Minerva. After graduating from grammar school in 1895, she began to study mathematics at the Faculty of Philosophy of Charles-Ferdinand University in Prague under Professor František Josef Studnička. Until 1900, girls attended lectures for residential studies (without the status of regular students); in 1900, a new law enabled girls to take exams for the entire period of their studies. Fabianová graduated in November 1901 with a thesis in analytical mathematics becoming the first woman to earn a PhD in mathematics in the country. (In 1902, Anna Honzáková, a classmate of Fabianová's from Minerva, was the very first female with a doctoral degree to graduate from the Faculty of Medicine of Charles-Ferdinand University.) After graduation, Fabianová started teaching mathematics, physics and German at the Minerva gymnasium. At that time, the teaching profession was associated with a promise of celibacy, so Fabianová never married. She lived with her older sister Juliana Fabianová. In 1923, she separated from Minerva to become the director of the Second Czech Girls' Real Municipal Gymnasium. She held that position until she retired in 1929. In retirement, she participated in Czech social activities. She was a member of the Union of Czechoslovak Mathematicians and Physicists, the Association of Academically Educated Women and the Minerva Association. Marie Fabianová died on 7 April 1943 after a long illness in the General Faculty Hospital in Prague at the age of 70. == Selected publications == === Scientific works === On the discovery of Zeeman. Journal for the cultivation of mathematics and physics. 1893. On the development of diperiodic functions in infinite sums and products, in series and products. Dissertation. FK Studnička. 1900. === Literary works === She allegedly used the pseudonym Dr. Abby Faimon. FAIMONOVA Abby History of Austrian education. Part 1-2 of the Šolc handbook for teachers of public and municipal schools. == References == |
Wikipedia:Marie Françoise Ouedraogo#0 | Marie Françoise Ouedraogo (born 3 December 1967) is a Burkinabé mathematician. She has previously served in government as permanent secretary of the national policy of good governance. == Biography == Born in December 1967, Ouedraogo was raised in Ouagadougou. She was drawn to the study of mathematics at a young age as she received good grades without putting forth much effort. She was educated at the University of Ouagadougou, where she wrote her first thesis (Doctorat de 3ème cycle) on Lie superalgebras in 1999. Akry Koulibaly served as her doctoral adviser. From 2005 to 2008 Ouedraogo served as the permanent secretary of the national policy of good governance. She was committed to ending forms of corruption, especially in the realm of public transport. According to her, good governance is a state of mind. She then prepared a Ph.D. thesis at Blaise Pascal University of Clermont-Ferrand in France under the co-direction of Sylvie Paycha and Akry Koulibaly. Her Ph.D. thesis was about pseudodifferential operators and was accepted in 2009. Ouedraogo is the first Burkinabé woman who defended a thesis in mathematics. Ouedraogo teaches in the Mathematics Department of the University of Ouagadougou. Her research interests are pseudodifferential operators and superalgebras. == Service == In 2009, she became president of the African Mathematical Union Commission on Women in Mathematics in Africa. The AMUCWMA seeks to get girls in Africa more interested in mathematics and potentially choose it as a career. In October 2012, she co-hosted a workshop with the International Center of Pure and Applied Mathematics (ICPAM) to generate interest in mathematics among African women. On 11 July 2013, Ouedraogo was elected president of the newly formed African Women in Mathematics Association. She gave a talk entitled "Mathematics and Women: Different Regions, Similar Struggles" at the ICWM forum in August 2014. == Publications == Extension of the canonical trace and associated determinants, thèse de l'université Blaise Pascal (Clermont-Ferrand II), under the direction of Akry Koulibaly, Sylvie Paycha, 2009. On the existence of ad-nilpotent elements, Afrika Matematika (2014), DOI 10.1007/s13370-014-0246-y (with Come Jean Antoine Bere and Nakelgbamba Boukary Pilabre). A symmetrized canonical determinant on odd-class pseudodifferential operators, Geometric and topological methods for quantum field theory, 381–393, Cambridge Univ. Press, Cambridge, 2010. Uniqueness of traces on log-polyhomogeneous pseudodifferential operators, J. Aust. Math. Soc. 90, No. 2, 171–181 (2011) (with Catherine Ducourtioux). The multiplicative anomaly for determinants revisited; locality, Commun. Math. Anal. 12, no 1, 28–63 (2012) (with Sylvie Paycha). Classification of traces and associated determinants on odd-class operators in odd dimensions, SIGMA Symmetry Integrability Geom. Methods Appl. 8 Paper 023, 25pp (2012) (with Carolina Neira). A symmetrized canonical determinant on Odd-Class pseudodifferential operators Supersystèmes triples de Lie associés aux superalgèbres de Malcev, Afrika Matematica (3) 14 (2002), 19–30 (with Akry Koulibaly). Super-représentations faibles de superalgèbres de Malcev, Afrika Matematica (3) 14 (2002), 5–17 == References == == External links == O'Connor, John J.; Robertson, Edmund F., "Marie Françoise Ouedraogo", MacTutor History of Mathematics Archive, University of St Andrews |
Wikipedia:Marie Rognes#0 | Marie Elisabeth Rognes (born 7 October 1982) is a Norwegian applied mathematician specializing in scientific computing and numerical methods for partial differential equations. She works at the Simula Research Laboratory, as one of their chief research scientists. == Education and career == Rognes was a student in applied mathematics at the University of Oslo, earning a master's degree in 2005 and completing a Ph.D. in 2009. Her dissertation, Mixed finite element methods with applications to viscoelasticity and gels, was jointly supervised by Ragnar Winther and Hans Petter Langtangen. After postdoctoral research at the University of Minnesota and the Simula Research Laboratory, she joined the University of Oslo as a lecturer in 2012, and in the same year became a senior researcher for Simula Research. She remained affiliated on a part-time basis with the University of Oslo until 2016, when she became a chief research scientist for Simula Research. == Recognition == Rognes became one of 20 founding members of the Young Academy of Norway in 2015. In the same year she was part of a team that won the J. H. Wilkinson Prize for Numerical Software, given every four years at the International Congress on Industrial and Applied Mathematics. The award cited their work on dolfin-adjoint, a software package for adjoint and tangent linear equations. In 2018 she was the winner of the Royal Norwegian Society of Sciences and Letters Prize for Young Researchers in the Natural Sciences. == References == == External links == Home page Marie Rognes publications indexed by Google Scholar |
Wikipedia:Marie Torhorst#0 | Marie Torhorst (28 December 1888 – 7 May 1989) was a German school teacher and political activist who became an East German politician. She served as Minister for People's Education in the state of Thuringia between 1947 and 1950. Some sources identify her as "the first-ever female minister (on state or national level) in the history of Germany". Others are content to record that, within Germany, she was the first-ever female minister in the state of Thuringia. Marie Torhorst stated and proved what is today known as the Carathéodory-Torhorst theorem in her 1918 doctoral dissertation. The dissertation was subsequently lost and Torhorst's contribution was for many decades overlooked; but in the twenty-first century mathematics scholars are happy to acknowledge and celebrate her work. == Life == === Provenance === Marie Torhorst was born at the end of the so-called "Year of the Three Emperors" in Ledde, then as now a sleepy village in the flat countryside west of Osnabrück. She was the seventh and youngest child of Arnold Torhorst (1841–1909), the local parson and his wife, born Luise Smend (1847–1923). The family seems to have been intellectually gifted. Marie's elder sister, Adelheid, would also achieve a measure of eminence in teaching and, after 1945, in politics. The sisters would later, jointly, have a secondary school named after them. Luise Torhorst had inherited a useful sum of money as a result of which she was able to see to it that not just her four sons, but also her three daughters, received a full education. Marie completed her own schooling at an "Oberlyzeum" (single-sex girls' secondary school). === Student === Sources are not completely consistent as to when she embarked on her university education, much of which coincided with the First World War. She attended the University of Bonn, studying Geography, Mathematics and Physics. There are at least two reference to her having also studied at the University of Göttingen.It was from Bonn that in 1918 she received her doctorate: the work was supervised by Hans Hahn. Her dissertation was entitled "Über die Randmenge einfach-zusammenhängender ebener Gebiete": a core conclusion has become known among her scholarly admirers as the Carathéodory-Torhorst theorem or, more simply, as the Torhorst theorem. It might have been thought that her doctorate should have provided a launch pad for a life-long career in the universities sector. There were still vanishingly few women working in high-level academic research at this time, however, and at least one commentator has identified "a lack of confidence in her own mathematical ability" in her autobiography. Also, with Germany economically, militarily and politically broken and on the brink of a year of revolutions in the ports and industrial centres, there was widespread nervousness that Lenin's so-called October Revolution might yet spread uncontrollably through the European continent. Marie Torhorst's own student record of left-wing political activism was no secret. She joined the socialist "Studenten-Arbeitsgemeinschaft" (apparently an umbrella group of socialist student associations) in 1917. According to one source she passed the exams necessary to qualify her for teaching in state schools in 1919 and 1920. Elsewhere it is indicated that she had already attended the "Stift Keppel" in Allenbach, where she successfully completed a two years teacher-training course in her early 20s, between 1903 and 1905. During the early twentieth century her political record made it hard for her to find a permanent teaching post. She was able to find a part-time teaching position at a Catholic girls' school in Bonn, however, and also found work with the university as a university librarian. It was probably in 1922/23 that she completed several terms of study at the "Handelshochschule" (loosely, "business college", at the time being subsumed into the university) in Cologne, studying business administration and economics, following which she received a qualification in teaching business studies. === Teacher === In 1923 Torhorst took on the headship of a private business school for the "Frauenerwerbs- und Ausbildungsverein" (loosely, "Women's employment and training association") in Bremen. She continued to lead the business school till 1929. She also teamed up with politically like-minded teacher colleagues, during this period, to organise evening courses for young people who had been excluded from state schools in the area. Her political and feminist beliefs had been deeply rooted in Torhorst's personal values and life choices since at least as far back as the First World War, but it was only in 1928 that she became a member of the Social Democratic Party (SPD). It was in the same year that she joined the "Freie Lehrergewerkschaft Deutschlands" / FLGD, a teachers' trades union committed to socialist principals. There are indications that within the SPD, as a left-wing member of the party, she often found herself out of sympathy with the party leadership. Between 1929 and 1933, Marie Torhorst taught and worked as a "Studienrätin" (loosely, "student counsellor") at the Karl Marx School which had been set up in 1921 in Berlin-Neukölln by the education pioneer Fritz Karsen, and then progressively expanded under Karsen's direction during the years that followed. There was much about the school which was considered innovative at the time. In 1929 Karsen took the bold step of turning it into a "Gesamtschule" (loosely, "comprehensive school"), intended to educate children displaying the widest possible range of abilities. Another appealing feature for Torhorst was an underpinning philosophy which insisted that academically talented working class children should have the same opportunities as the children of more prosperous and/or well educated parents to pass the "Abitur" (secondary school final exam). The significance of the "Abitur" in Germany was (and is) that passing it opens the way to university-level education. Torhorst's four years at the school included, in 1932, a six month study trip to the Soviet Union. Her half year in the Soviet Union left a lasting impression. The early 1930s were marked by an intensification of Germany's political polarisation. In the Reichstag (parliament) this was reflected in political deadlock. In January 1933 the Hitler government took power and rapidly transformed Germany into a one-party dictatorship. A progressive school in a traditionally left-wing district of Berlin named in honour of Karl Marx was, unsurprisingly, high on the National Socialist hate list. Bernhard Rust was installed as acting Prussian Minister for the Arts and Education on 4 February 1933 (following the dismissal of his predecessor in the office), and on 21 February 1933 Rust dismissed Karsen from the headship of his own school. The teaching staff were dismissed, and when the school reopened later that year it was with a new name, a new set of teachers, and a large swastika flag hanging in the main hall. Karsen emigrated. Marie Torhorst's teaching career was evidently over. === Twelve years of Hitler === As soon as Hitler took power Marie's older sister, Adelheid, emigrated to the Netherlands and stayed there for the next twelve years. In 1934 she embarked on a six month marriage of convenience with a man called Jacob Jacobs. Her own resulting change of name, from Adelheid Torhorst to Adelheid Jacobs, turned out to have been prescient. After the German army invaded the Netherlands in 1940, her new name protected her from Nazi persecution. The two sisters had always been close, both politically engaged, both teachers, both unmarried and childless. But Marie Torhorst chose a different course and stayed in Germany. As far as her public self was concerned, hr first job after losing her teaching position was as a catering assistant. She later found a job as an appointments administrator at the Berlin University Hygiene Institute, and another as a typist in the travel office correspondence section of an American Express (AMEXCO) branch. She was, in addition, entitled to receive a pension in respect of the six years during which she had worked as head of a private business school in Bremen between 1923 and 1929, but this pension was payable by the "Reichsversicherungsanstalt", a government agency. It was not paid to her. According to her own understanding set out in a letter to a friend at the time, changes to the law implemented in 1934/35 meant that she was unable to litigate the matter. In addition to her day jobs, Torhorst gave every sign of being part of the new social order emerging in Germany. Between 1935 and 1940 she was a registered member both of the German Labour Front and of the German Red Cross. According to her own detailed, albeit largely uncorroborated, records she was also a member of other organisations that operated, as far as possible, out of the sight of the homeland security. As soon as she lost her teaching job at beginning of 1933 she became an activist member of "Parole", a locally based resistance group in Berlin-Neukölln. In this group, together with former pupils from the progressive school at which she had taught between 1929 and 1933, she produced an underground anti-government newspaper, also called "Parole". There are indications that she was also involved in underground political discussion groups, and in smuggling out information about conditions in Germany to the exiled Communist Party leadership groups that had ended up after 1933 in Paris, Prague and Moscow, using her communications with her sister in the Netherlands as a conduit. The authorities seem to have known (or suspected) that the teachers who had lost their jobs when the Karl Marx School in Neukölln had been taken over would (or might) have kept in touch and formed some sort of a resistance organisation. Marie Torhorst was first called in for questioning by the Gestapo in 1937. She was accused of undertaking political work for the (by now illegal) SPD, but she was able to refute the accusation and was released, presumably "for lack of evidence". War broke out in September 1939. Within Germany, government persecution of political opponents and of Jews intensified progressively till the Shoah reached its brutish nadir in 1942. During this time Marie Torhorst concealed one of her former pupils and his mother, also providing the two of them with food. The young man was in particular danger from the government, since he was both Jewish and a Communist. At some point during 1943 someone informed the authorities of the situation. Sources are silent over what happened to the people she had been hiding, but Marie Torhorst herself was detained and taken to the "Hallendorf labour camp" by Watenstedt, near Braunschweig. Given the personal network that she would have acquired during her teaching career, and given her strong political and social opinions, it is likely that Torhorst will have responded to many opportunities to help victims and potential victims of government persecution between 1933 and 1945, and commentators bemoan the lack of relevant research undertaken on the details of resistance activism in Berlin and other German cities. However, many of the actions involved will have depended on maximum secrecy to have been effective, and it therefore seems likely that most of the details will remain unknown. Before the war ended Torhorst had been released from the labour camp and returned to Berlin. Here she returned to the job in the archives department job with the "Deutsche Gesellschaft für Betriebswirtschaft" (loosely, "German Society for Business Administration") in which she had already been employed between 1939 and her arrest in 1943. During the final months of the war she was also involved in looking after German prisoners of War under the auspices of the "Reichsgruppe Handwerk" (a government backed craftworkers' organisation). === 1945 and new beginnings === The end of the war in May 1945 marked an end to the Hitler nightmare and new beginnings for millions of Germans. There were choices to be made. The western two thirds of Germany had ended up divided into four military occupation zones, administered respectively by the British, the Americans, the French and the Soviets. The region surrounding Berlin, along with the ruins and rubble comprising eastern part of the city itself, were administered as the Soviet occupation zone. Torhorst had spent the Hitler years based in Berlin and she now made her choice: she joined the (no longer outlawed) Communist Party in or before January 1946. She was actively engaged in various education related functions from the middle part of 1945. Between August 1945 and July 1946 she took charge at the department in charge of teacher training for the education department of Greater Berlin. In April 1946 a new political party was created in the Soviet occupation zone by means of a contentious political merger between the Communist Party and the Social Democratic Party. It is probable that the architects of this arrangement intended that it should take effect across all four occupation zones, but as matters turned out the Socialist Unity Party ("Sozialistische Einheitspartei Deutschlands" / SED) never gained traction outside the Soviet zone. Nevertheless, in East Berlin Marie Torhorst was one of hundreds of thousands of Communist Party members who lost no time in signing their party memberships over to what became, over the next few years, the ruling party in a new kind of German one-party dictatorship. The party unification congress of April 1946 also saw a widespread transfer of political powers over various aspects of daily life, including education, to the control of the new Party. Marie Torhorst meanwhile emerged as a true believer in the new order. She saw herself as an intellectual-worker, determined to support the building of a new Germany, truly socialist in spirit and vision. After twelve years of Hitler, actions for the creation of an antifascist future must be genuine, and not just a matter for empty rhetoric. The political beliefs which she had developed and by which she had lived under the German Republic before 1933 provided a sound basis on which, under the Soviet military administration, it would be possible develop and apply her ideas for the education system. It now became apparent just how much she had been impressed by Soviet education during her six month study visit to Moscow in 1932. Towards the end of 1946 she held a meeting with Fritz Karsen, the education pioneer at whose school she had worked as a teacher between 1929 and 1933. He was back in (west) Berlin, now working for the US military administration as an education officer. When he asked Torhorst how it could be possible to work only "under Russian pressure", she replied that she had never felt "so free and happy". Now she found she could "join in with the creation of everything that she had always strived to achieve as a teacher, without having to make any of those fundamental comprises". === Nation building === Between May 1945 and October 1949 the Soviet occupation zone underwent a carefully choreographed nation building programme based on plans many of which had, as it turned out, been devised in some detail in Moscow between 1941 and 1945 by the men who now held the levers of power (subject to Soviet supervision). On 29 May 1947 Torhorst was chosen to serve as "Minister for People's Education" in the state of Thuringia. It was a remarkable development. The recently launched women's weekly magazine "Die Frau von heute" carried her portrait on its front page, accompanied by the headline "Frauen als Minister ..... [habe] Deutschland noch nicht gesehen" (loosely, "Women as ministers .... a new experience for Germany" There was a brief article spelling out that her appointment was justified by "long years of specialist knowledge", but also acknowledging that "as a woman she ... [would be] exposed to exceptional levels of criticism". Nevertheless, "for all the women in the east" the appointment represented a melting away of the former indifference over women being able to determine their own futures. Even though it had in the past been the case that "a few thousand of her gender-comrades, who came from the more favourably positioned classes, found their way into some of the higher professions, such as medicine, academic life or equivalent levels in public service", Torhorst's appointment as a minister showed that "the whole situation for the female gender has changed fundamentally, since their equality of value and equality of entitlement with men" was officially recognised, and thereby their "gender-subservience" had been done away with. Torhorst herself also used the press to share with comrades some of her ambitions for her new role. These included the necessity "to bring an end to the still major differences between urban and rural schooling provision". She also shared her opinion that there was "still much more to be done to lay down a genuinely democratic basis for the development of a highly qualified and progressive German intelligentsia". Indispensable to that ambition was "a substantial increase in the proportion of university students with working class backgrounds". She would therefore make it her top priority to ensure that "the treasures of culture and learning do not simply benefit a small number of comrades at the top of society". An interesting insight into her education philosophy as minister comes from a surviving record of a "conversation" that Torhorst held with an American delegation on 27 June 1947, shortly after her appointment to ministerial office: "The most important work ... would be implementation of the law to democratise German schools". In this connection "Unity schools must be implemented in the Soviet zone". There was a strong, if ill-defined, expectation on both sides of what would become known as the "inner German border" that the four military occupation zones of Germany would at some stage be rehabilitated and unified into a single post-fascist state, but visions of how such a state would be governed differed starkly, especially after 1948. During the twelve month Berlin blockade thoughts of any future German reunification disappeared over the horizon, and in October 1949 the Soviet zone was relaunched as the Soviet sponsored German Democratic Republic (East Germany). It was also during 1949 that Adelheid returned from the Netherlands and moved in with Marie. The two sisters, still unmarried, childless, and still – in their different ways – deeply engaged in the politics of education, made their home together in Weimar, which till 1952 was the seat of the state government for Thuringia. In 1950 Marie Torhorst lost her position as Thuringian Minister for People's Education. Significantly Isolde Oschmann, her successor, appointed only in 1951, was another woman. Isolde Oschmann was a former Kindergarten teacher who turned out to be very much less of a hands-on education minister that Torhorst had been: her footprint on East German history remained slight despite her having held ministerial office for more than a year. It remains unclear why Marie Torhorst was replaced in the role. There is no very obvious indication from her subsequent public career that she was among those who fell out of favour with the party leadership at this time. === Ex-minister === Torhorst then served, briefly during 1951/52, as political secretary with the East Berlin office of the "Internationale Demokratische Frauenföderation" (IDFF / "Women's International Democratic Federation"). She also accepted an invitation from Paul Wandel, East Germany's Minister for Education, to take over the running of the important "Arts Exhibition of the People's Republic of China" which was held in East Berlin during 1950/51. In 1952 she joined the East German Education Ministry as head of the department for cultural relations with foreign countries, a position she retained till 1957. Between 1958 and 1962 she taught at the (East) German National Pedagogical Institute, where in 1962 she also accepted a professorship. Through the 1950s and early 1960s Torhorst held a number of other, mostly short-term and part-time complementary appointments relating to her educational experience and expertise. Beyond the world of education, she also served between 1957 and 1960 as an honorary deputy president of the "Demokratischer Frauenbund Deutschlands" (DFD / "(East) German Democratic Women's League". After 1964, the year of her seventy-sixth birthday, she continued to engage actively in education related projects and discussions, but now on a free-lance basis. Marie Torhorst died in East Berlin on 7 May 1989. Despite her considerable age, she was very far from forgotten at the time of her death. There were obituaries both from the East German ministry of Education and from the Central Committee. She had lived out her final years in a special retirement home set aside for "party veterans". === Stasi links === After reunification it emerged that Marie Torhorst had been a longstanding and active Secret Informant for the Ministry for State security. When the Stasi files were investigated, her earliest surviving report was found to date from 1953. Most Stasi informants produced reports on the daily movements and conversations of their work colleagues and / or family members, but Torhorst had been targeted and recruited after it was noticed, from routine monitoring of her personal letters, that she had excellent contacts with a number of persons of interest on the far side of the "inner German border". No doubt it was considered useful that she was always herself a compulsive writer of long detailed letters to friends and contacts. On account of her links to the East German government she also enjoyed exceptional travel privileges at a time when East Germany was becoming became ever more physically isolated from the west. Those on whom she submitted reports included her cousin, the respected professor of church law Rudolf Smend, the popular historian Wolfgang Leonhardt and the journalist Stephan Grzeskowiak. (Stephan Grzeskowiak was, in addition, one of Torhorst's former pupils from her time as a teacher at the Karl Marx School in Neukölln during the early 1930s and, more recently, had been a party insider with the team surrounding Kurt Schumacher, the recently deceased leader if the SPD in the west. His ongoing links, as a journalist, with SPD politicians in Bonn during the 1950s, 60s and 70s were of particular interest to Torhorst's Stasi handlers.) In 1958 her Stasi handlers marked the seventieth birthday of "GI Sophie" (the codename by which she was identified in the files) with a hamper worth 75 (western) marks, accompanied by a note commending the way in which she had "fulfilled all her assignments in an exemplary manner ... [and showed] a keen of interest in [the Stasi's] work". It does appear that her reports were not just long, but also both detailed and, at times, remarkably "readable" and even "chatty". She was indeed unusual among Stasi informants in her willingness to submit unsolicited advice, for instance concerning books from the west which should probably not be permitted to circulate in East Germany, or ways in which East German radio programmes might more effectively counter the "western propaganda" broadcast by the U.S. backed RIAS (radio station) from West Berlin. After her seventieth birthday a regular "secret collaborative relationship" was deemed no longer appropriate on account of her age, but she continued to receive "official visits" and her advice continued to be solicited, according to the reports of her Stasi handler at the time, Officer Hüther. == Notes == == References == |
Wikipedia:Marie-Hélène Schwartz#0 | Marie-Hélène Schwartz (1913 – 5 January 2013) was a French mathematician, known for her work on characteristic numbers of spaces with singularities. == Education and career == Born Marie-Hélène Lévy, she was the daughter of mathematician Paul Lévy and the great-granddaughter of philologist Henri Weil. After studying at the Lycée Janson-de-Sailly, she began studies at the École Normale Supérieure in 1934 but contracted tuberculosis which forced her to drop out. She married another Jewish mathematician, Laurent Schwartz, in 1938, and both soon went into hiding while the Nazis occupied France. After the war, she taught at the University of Reims Champagne-Ardenne and finished a thesis on generalizations of the Gauss–Bonnet formula in 1953. In 1964, she moved to the University of Lille, from where she retired in 1981. == Recognition == A conference was held in her honour in Lille in 1986, and a day of lectures in Paris honoured her 80th birthday in 1993, during which she presented a two-hour talk herself. She continued publishing mathematical research into her late 80s. == References == |
Wikipedia:Marie-Louise Dubreil-Jacotin#0 | Marie-Louise Dubreil-Jacotin (7 July 1905 – 19 October 1972) was a French mathematician, the second woman to obtain a doctorate in pure mathematics in France, the first woman to become a full professor of mathematics in France, the president of the French Mathematical Society, and an expert on fluid mechanics and abstract algebra. == Early life and education == Marie-Louise Jacotin was the daughter of a lawyer for a French bank, and the grand-daughter (through her mother) of a glassblower from a family of Greek origin. Her mathematics teacher at the lycée was a sister of mathematician Élie Cartan, and after passing the baccalaureate she was allowed (through the intervention of a friend's father, the head of the institution) to continue studying mathematics at the Collège de Chaptal. On her second attempt, she placed second in the entrance examination for the École Normale Supérieure in 1926 (tied with Claude Chevalley), but by a ministerial decree was moved down to 21st position. After the intervention of Fernand Hauser, the editor of the Journal of the ENS, she was admitted to the school. Her teachers there included Henri Lebesgue and Jacques Hadamard, and she finished her studies in 1929. With the encouragement of ENS director Ernest Vessiot she traveled to Oslo to work with Vilhelm Bjerknes, under whose influence she became interested in the mathematics of waves and the work of Tullio Levi-Civita in this subject. She returned to Paris in 1930, married another mathematician, Paul Dubreil, and joined him on another tour of the mathematics centers of Germany and Italy, including a visit with Levi-Civita. The Dubreils returned to France again in 1931. == Career and research == While her husband taught at Lille, Dubreil-Jacotin continued her research, finishing a doctorate in 1934 concerning the existence of infinitely many different waves in ideal liquids, under the supervision of Henri Villat. Before her, the only women to obtain doctorates in mathematics in France were Marie Charpentier in 1931 (also in pure mathematics) and Edmée Chandon in 1930 (in astronomy and geodesy). Following her husband, she moved to Nancy, but was unable to obtain a faculty position there herself because that was viewed as nepotism; instead, she became a research assistant at the University of Rennes. She was promoted to a teaching position in 1938, and became an assistant professor at the University of Lyon in 1939, while also continuing to teach at Rennes. In 1943 she became a full professor at the University of Poitiers, the first woman to become a full professor of mathematics in France, and in 1955 she was given a chair there in differential and integral calculus. In 1956 she moved to the University of Paris and after the university split she held a professorship at Pierre and Marie Curie University. In the 1950s, motivated by the study of averaging operators for turbulence, Dubreil-Jacotin's interests turned towards abstract algebra, and she later performed research in semigroups and graded algebraic structures. She was the author of two textbooks, one on lattice theory and the other on abstract algebra. As well as her technical publications, Jacotin was the author of a work in the history of mathematics, Portraits of women mathematicians. She was president of the French Mathematical Society for 1952. == Legacy == Rue Marie-Louise-Dubreil-Jacotin, a street in the 13th arrondissement of Paris within Paris Diderot University, is named after her, and the University of Poitiers also has a street with the same name. In semigroup theory, the Dubreil-Jacotin semigroups are also named after her, as is the Dubreil-Jacotin–Long equation, "the standard model for internal gravity waves" in fluid mechanics. == References == == External links == O'Connor, John J.; Robertson, Edmund F., "Marie-Louise Dubreil-Jacotin", MacTutor History of Mathematics Archive, University of St Andrews Marie-Louise Dubreil-Jacotin at the Mathematics Genealogy Project Marie-Louise Dubreil-Jacotin, from Annuaire des Anciens Élèves de l'École Normale Supérieure (1974) |
Wikipedia:Marie-Paule Malliavin#0 | Marie-Paule Malliavin, née Brameret, (1935 in Mahdia – 25 September 2019 in Paris) was a French mathematician who specialised in the field of algebra. == Family == She was married to the mathematician Paul Malliavin since 27 April 1965. They had two children (Thérèse and Marie-Joseph). == Career == She published her first mathematical article in 1960 and received her doctorate in 1965. After her doctorate, she first became maître de conférences at the University of Caen. Later she became a professor at the Pierre and Marie Curie University (UPMC, Paris 6) in Paris, where she remained until her retirement. Her mathematical students include Jacques Alev and Youssef El From. She wrote several textbooks; the books on commutative algebra and representation theory of finite groups are frequently cited. At the beginning of her career, she worked on commutative algebra, later on non-commutative algebra. This was at a time when enveloping algebras and then quantum groups were evolving. She collaborated with her husband Paul Malliavin in particular in the study of measures on infinite-dimensional groups. Marie-Paule Malliavin was editor of top-ranked international research journals. She also organised the Algebra Seminar at the Institut Henri Poincaré for several decades, succeeding the deceased Professor Paul Dubreil. == References == == External links == Marie-Paule Malliavin at the Mathematics Genealogy Project |
Wikipedia:Mariel Vázquez#0 | Mariel Vázquez (born 1971 or 1972) is a Mexican mathematical biologist who specializes in the topology of DNA. She is a professor at the University of California, Davis, jointly affiliated with the departments of mathematics and of microbiology and molecular genetics. == Education == Vázquez received her Bachelor of Science in Mathematics from the National Autonomous University of Mexico in 1995. She received her Ph.D. in mathematics from Florida State University in 2000. Her dissertation was entitled Tangle Analysis of Site-specific Recombination: Gin and Xer Systems and her advisor was De Witt Sumners. == Career == Vázquez was a postdoctoral fellow at the University of California, Berkeley from 2000 to 2005, where she researched mathematical and biophysical models of DNA repair in human cells with Rainer Sachs as part of the mathematical radiobiology group. She was a faculty member in the mathematics department at San Francisco State University from 2005 to 2014. In 2014, she joined the faculty at the University of California, Davis as a CAMPOS scholar. == Awards and honors == In 2011, Vázquez received a National Science Foundation CAREER Award to research topological mechanisms of DNA unlinking. In 2012, she was the first San Francisco State University faculty member to receive the Presidential Early Career Award for Scientists and Engineers. She received a grant for computer analysis of DNA unknotting from the National Institutes of Health in 2013. In 2016, she was chosen for the Blackwell-Tapia prize, which is awarded every other year to a mathematician who has made significant research contributions in their field, and who has worked to address the problem of under-representation of minority groups in mathematics. She was selected for the inaugural class of Association for Women in Mathematics fellows in 2017. She was elected a Fellow of the American Mathematical Society in the 2020 class "for contributions in research and outreach at the interface of topology and molecular biology, and for service to the mathematical community in particular to underrepresented groups." In 2023, Vázquez was elected a Fellow of the American Association for the Advancement of Science. == References == == External links == The Shape of DNA - Numberphile How DNA unties its own knots - Numberphile Stern, Gary M. A Scientific Star. The Hispanic Outlook in Higher Education. 18 February 2013. |
Wikipedia:Mariette Yvinec#0 | Mariette Yvinec is a French researcher in computational geometry at the French Institute for Research in Computer Science and Automation (INRIA) in Sophia Antipolis. She is one of the developers of CGAL, a software library of computational geometry algorithms. Yvinec is the co-author of two books in computational geometry: Géometrie Algorithmique (with Jean-Daniel Boissonnat, Edusciences 1995), translated as Algorithmic Geometry (Hervé Brönnimann, trans., Cambridge University Press, 1998) Geometric and Topological Inference (with Jean-Daniel Boissonnat and Frédéric Chazal, Cambridge Texts in Applied Mathematics, 2018) == References == |
Wikipedia:Marilda Sotomayor#0 | Marilda A. Oliveira Sotomayor (born March 13, 1944) is a Brazilian mathematician and economist known for her research on auction theory and stable matchings. She is a member of the Brazilian Academy of Sciences, Brazilian Society of Econometrics, and Brazilian Society of Mathematics. She was elected fellow of the Econometric Society in 2003 and international honorary member of the American Academy of Arts and Sciences in 2020. == Education == Sotomayor grew up in Rio de Janeiro, Brazil. She began her education at Federal University of Rio de Janeiro where she received her degree in Mathematics in 1967. Sotomayor continued her education at Institute of Pure and Applied Mathematics where she received her master's degree in Mathematics in 1972. She received her Ph.D. in Mathematics from Catholic University of Rio de Janeiro in 1981. == Areas of interest == Marilda Sotomayor specializes in game theory, matching markets, and market design. She is the only expert in both game theory and matching markets in Brazil. == Personal == Sotomayor married Jorge Sotomayor and had two children, a son and a daughter. == Selected works == Roth, A.E.; Sotomayor, M.A.O. (1992). Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis. Econometric Society Monographs. Cambridge University Press. ISBN 978-0-521-43788-2. == References == == External links == Marilda Sotomayor publications indexed by Google Scholar |
Wikipedia:Marin Mersenne#0 | Marin Mersenne, OM (also known as Marinus Mersennus or le Père Mersenne; French: [maʁɛ̃ mɛʁsɛn]; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those written in the form Mn = 2n − 1 for some integer n. He also developed Mersenne's laws, which describe the harmonics of a vibrating string (such as may be found on guitars and pianos), and his seminal work on music theory, Harmonie universelle, for which he is referred to as the "father of acoustics". Mersenne, an ordained Catholic priest, had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s" and, because of his ability to make connections between people and ideas, "the post-box of Europe". He was also a member of the ascetical Minim religious order and wrote and lectured on theology and philosophy. == Life == Mersenne was born of Jeanne Moulière, wife of Julien Mersenne, peasants who lived near Oizé, County of Maine (present-day Sarthe, France). He was educated at Le Mans and at the Jesuit College of La Flèche. On 17 July 1611, he joined the Minim Friars and, after studying theology and Hebrew in Paris, was ordained a priest in 1613. Between 1614 and 1618, he taught theology and philosophy at Nevers, but he returned to Paris and settled at the convent of L'Annonciade in 1620. There he studied mathematics and music and met with other kindred spirits such as René Descartes, Étienne Pascal, Pierre Petit, Gilles de Roberval, Thomas Hobbes, and Nicolas-Claude Fabri de Peiresc. He corresponded with Giovanni Doni, Jacques Alexandre Le Tenneur, Constantijn Huygens, Galileo Galilei, and other scholars in Italy, England and the Dutch Republic. He was a staunch defender of Galileo, assisting him in translations of some of his mechanical works. For four years, Mersenne devoted himself entirely to philosophic and theological writing, and published Quaestiones celeberrimae in Genesim (Celebrated Questions on the Book of Genesis) (1623); L'Impieté des déistes (The Impiety of the Deists) (1624); La Vérité des sciences (Truth of the Sciences Against the Sceptics, 1624). It is sometimes incorrectly stated that he was a Jesuit. He was educated by Jesuits, but he never joined the Society of Jesus. He taught theology and philosophy at Nevers and Paris. In 1635 he set up the informal Académie Parisienne (Academia Parisiensis), which had nearly 140 correspondents, including astronomers and philosophers as well as mathematicians, and was the precursor of the Académie des sciences established by Jean-Baptiste Colbert in 1666. He was not afraid to cause disputes among his learned friends in order to compare their views, notable among which were disputes between Descartes, Pierre de Fermat, and Jean de Beaugrand. Peter L. Bernstein, in his book Against the Gods: The Remarkable Story of Risk, wrote, "The Académie des Sciences in Paris and the Royal Society in London, which were founded about twenty years after Mersenne's death, were direct descendants of Mersenne's activities." In 1635 Mersenne met with Tommaso Campanella but concluded that he could "teach nothing in the sciences ... but still he has a good memory and a fertile imagination." Mersenne asked if Descartes wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Italy fifteen times, in 1640, 1641 and 1645. In 1643–1644 Mersenne also corresponded with the German Socinian Marcin Ruar concerning the Copernican ideas of Pierre Gassendi, finding Ruar already a supporter of Gassendi's position. Among his correspondents were Descartes, Galileo, Roberval, Pascal, Beeckman and other scientists. He died on 1 September 1648 of complications arising from a lung abscess. === Work === Quaestiones celeberrimae in Genesim was written as a commentary on the Book of Genesis and comprises uneven sections headed by verses from the first three chapters of that book. At first sight the book appears to be a collection of treatises on various miscellaneous topics. However Robert Lenoble has shown that the principle of unity in the work is a polemic against magical and divinatory arts, cabalism, and animistic and pantheistic philosophies. Mersenne was concerned with the teachings of some Italian naturalists that all things happened naturally and determined astrologically; for example, the nomological determinism of Lucilio Vanini ("God acts on sublunary beings (humans) using the sky as a tool"), and Gerolamo Cardano's idea that martyrs and heretic were compelled to self-harm by the stars; Historian of science William Ashworth explains "Miracles, for example, were endangered by the naturalists, because in a world filled with sympathies and occult forces—with what Lenoble calls a "spontanéité indéfinie"—anything could happen naturally".: 138 Mersenne mentions Martin Del Rio's Investigations into Magic and criticises Marsilio Ficino for claiming power for images and characters. He condemns astral magic and astrology and the anima mundi, a concept popular amongst Renaissance neo-platonists. Whilst allowing for a mystical interpretation of the Cabala, he wholeheartedly condemned its magical application, particularly angelology. He also criticises Pico della Mirandola, Cornelius Agrippa, Francesco Giorgio and Robert Fludd, his main target. Harmonie universelle is perhaps Mersenne's most influential work. It is one of the earliest comprehensive works on music theory, touching on a wide range of musical concepts, and especially the mathematical relationships involved in music. The work contains the earliest formulation of what has become known as Mersenne's laws, which describe the frequency of oscillation of a stretched string. This frequency is: Inversely proportional to the length of the string (this was known to the ancients; it is usually credited to Pythagoras) Proportional to the square root of the stretching force, and Inversely proportional to the square root of the mass per unit length. The formula for the lowest frequency is f = 1 2 L F μ , {\displaystyle f={\frac {1}{2L}}{\sqrt {\frac {F}{\mu }}},} where f is the frequency [Hz], L is the length [m], F is the force [N] and μ is the mass per unit length [kg/m]. In this book, Mersenne also introduced several innovative concepts that can be considered the basis of modern reflecting telescopes: Much earlier than Laurent Cassegrain, he found the fundamental arrangement of the two-mirror telescope combination, a concave primary mirror associated with a convex secondary mirror, and discovered the telephoto effect that is critical in reflecting telescopes, although he was far from having understood all the implications of that discovery. Mersenne invented the afocal telescope and the beam compressor that is useful in many multiple-mirror telescope designs. He recognized also that he could correct the spherical aberration of the telescope by using aspherical mirrors and that in the particular case of the afocal arrangement he could do this correction by using two parabolic mirrors, though a hyperboloid is required. Because of criticism that he encountered, especially from Descartes, Mersenne made no attempt to build a telescope of his own. Mersenne is also remembered today thanks to his association with the Mersenne primes. The Mersenne Twister, named for Mersenne primes, is frequently used in computer engineering and in related fields such as cryptography. However, Mersenne was not primarily a mathematician; he wrote about music theory and other subjects. He edited works of Euclid, Apollonius, Archimedes, and other Greek mathematicians. But perhaps his most important contribution to the advance of learning was his extensive correspondence (in Latin) with mathematicians and other scientists in many countries. At a time when the scientific journal had not yet come into being, Mersenne was the centre of a network for exchange of information. It has been argued that Mersenne used his lack of mathematical specialty, his ties to the print world, his legal acumen, and his friendship with the French mathematician and philosopher René Descartes (1596–1650) to manifest his international network of mathematicians. Mersenne's philosophical works are characterized by wide scholarship and the narrowest theological orthodoxy. His greatest service to philosophy was his enthusiastic defence of Descartes, whose agent he was in Paris and whom he visited in exile in the Netherlands. He submitted to various eminent Parisian thinkers a manuscript copy of the Meditations on First Philosophy, and defended its orthodoxy against numerous clerical critics. In later life, he gave up speculative thought and turned to scientific research, especially in mathematics, physics and astronomy. In this connection, his best known work is Harmonie universelle of 1636, dealing with the theory of music and musical instruments. It is regarded as a source of information on 17th-century music, especially French music and musicians, to rival even the works of Pietro Cerone. One of his many contributions to musical tuning theory was the suggestion of 2 3 − 2 4 {\displaystyle {\sqrt[{4}]{\frac {2}{3-{\sqrt {2}}}}}} as the ratio for an equally-tempered semitone ( 2 12 {\displaystyle {\sqrt[{12}]{2}}} ). It was more accurate (0.44 cents sharp) than Vincenzo Galilei's 18/17 (1.05 cents flat), and could be constructed using straightedge and compass. Mersenne's description in the 1636 Harmonie universelle of the first absolute determination of the frequency of an audible tone (at 84 Hz) implies that he had already demonstrated that the absolute-frequency ratio of two vibrating strings, radiating a musical tone and its octave, is 1 : 2. The perceived harmony (consonance) of two such notes would be explained if the ratio of the air oscillation frequencies is also 1 : 2, which in turn is consistent with the source-air-motion-frequency-equivalence hypothesis. He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums, reported in his Cogitata Physico-Mathematica in 1644. He was the first to measure the length of the seconds pendulum, that is a pendulum whose swing takes one second, and the first to observe that a pendulum's swings are not isochronous as Galileo thought, but that large swings take longer than small swings. === Battles with occult and mystical thinkers === Two German pamphlets that circulated around Europe in 1614–15, Fama fraternitatis and Confessio Fraternitatis, claimed to be manifestos of a highly select, secret society of alchemists and sages called the Brotherhood of Rosicrucians. The books were allegories, but were obviously written by a small group who were reasonably knowledgeable about the sciences of the day, and their main theme was to promote educational reform (they were anti-Aristotelian). These pamphlets also promoted an occult view of science containing elements of Paracelsian philosophy, neo-Platonism, Christian Cabala and Hermeticism. In effect, they sought to establish a new form of scientific religion with some pre-Christian elements. Mersenne led the fight against acceptance of these ideas, particularly those of Rosicrucian promoter Robert Fludd, who had a lifelong battle of words with Johannes Kepler. Fludd responded with Sophia cum moria certamen (1626), wherein he discusses his involvement with the Rosicrucians. The anonymous Summum bonum (1629), another critique of Mersenne, is a Rosicrucian-themed text. The cabalist Jacques Gaffarel joined Fludd's side, while Pierre Gassendi defended Mersenne. The Rosicrucian ideas were defended by many prominent men of learning, and some members of the European scholarly community boosted their own prestige by claiming to be among the selected members of the Brotherhood. However, it is now generally agreed among historians that there is no evidence that an order of Rosicrucians existed at the time, with later Rosicrucian Orders drawing on the name, with no relation to the writers of the Rosicrucian Manifestoes. During the mid-1630s Mersenne gave up the search for physical causes in the Aristotelian sense (rejecting the idea of essences, which were still favoured by the scholastic philosophers) and taught that true physics could be only a descriptive science of motions (Mécanisme), which was the direction set by Galileo Galilei. Mersenne had been a regular correspondent with Galileo and had extended the work on vibrating strings originally developed by his father, Vincenzo Galilei. === Music === An air attributed to Mersenne was used by Ottorino Respighi in his second suite of Ancient Airs and Dances == List of works == Euclidis elementorum libri, etc. (Paris, 1626) Les Mécaniques de Galilée (Paris, 1634) Questions inouies ou récréation des savants (1634) Questions théologiques, physiques, etc. (1634) Harmonie universelle First edition online from Gallica (Paris, 1636). Translation to English by Roger E. Chapman (The Hague, 1957) Nouvelles découvertes de Galilée (1639) Cogitata physico-mathematica (1644) Universae geometriae synopsis (1644) Tractatus mechanicus theoricus et practicus (in Latin). Paris: Antoine Bertier. 1644. == See also == Cassegrain reflector Catalan–Mersenne number/Catalan's Mersenne conjecture Cycloid Equal temperament Euler's factorization method List of Roman Catholic scientist-clerics Renaissance skepticism Seconds pendulum == References == === Explanatory notes === === Citations === === General and cited sources === == Further reading == == External links == IMSLP Traité de l'Harmonie Universelle. The Correspondence of Marin Mersenne in EMLO "Marin Mersenne" entry by Philippe Hamou in the Stanford Encyclopedia of Philosophy, June 13, 2022 O'Connor, John J.; Robertson, Edmund F., "Marin Mersenne", MacTutor History of Mathematics Archive, University of St Andrews Herbermann, Charles, ed. (1913). "Marin Mersenne" . Catholic Encyclopedia. New York: Robert Appleton Company. "Marin Mersenne", Mathematics Genealogy Project. Minimospedia "Marin Mersenne" especially for bibliography Scholars and Literati at the "Mersenne" Academy (1635–1800), in Repertorium Eruditorum Totius Europae/RETE . Documentaries Marin Mersenne—The Birth of Modern Geometry (UK Open University TV documentary made in 1986 and transmitted on BBC2) |
Wikipedia:Marina Iliopoulou#0 | Marina Iliopoulou (Greek: Μαρίνα Ηλιοπούλου) is a Greek mathematician. Her main research focus is harmonic analysis, but she has also published research in discrete geometry including new results on the Erdős–Anning theorem. She is a professor of mathematics at the National and Kapodistrian University of Athens. == Education and career == Iliopoulou did her undergraduate studies in mathematics at the National and Kapodistrian University of Athens, finishing in 2009. She received a Ph.D. in 2013 from the University of Edinburgh in Scotland, with the dissertation Discrete analogues of Kakeya problems supervised by Tony Carbery. After postdoctoral research at the University of Birmingham in England and the Mathematical Sciences Research Institute and University of California, Berkeley in the US, she became an assistant professor at the University of Kent in England in 2019. In 2022 she took an associate professorship at the University of Birmingham, and in 2023 she returned to the University of Athens as a full professor. == Recognition == Iliopoulou is one of three recipients of the 2024 L'Oréal-UNESCO Greek Awards for Women in Science. == References == == External links == Home page Marina Iliopoulou publications indexed by Google Scholar |
Wikipedia:Marino Ghetaldi#0 | Marino Ghetaldi (Latin: Marinus Ghetaldus; Croatian: Marin Getaldić; 2 October 1568 – 11 April 1626) was a Ragusan scientist. A mathematician and physicist who studied in Italy, England and Belgium, his best results are mainly in physics, especially optics, and mathematics. He was one of the few students of François Viète and friend of Giovanni Camillo Glorioso. == Biography == Born into the Ghetaldi noble family, he was one of six children. He was known for the application of algebra in geometry and his research in the field of geometrical optics on which he wrote 7 works including the Promotus Archimedus (1603) and the De resolutione et compositione mathematica (1630). He also produced a leaflet with the solutions of 42 geometrical problems, Variorum problematum colletio, in 1607 and set grounds of algebraization of geometry. His contributions to geometry had been cited by Dutch physicist Christiaan Huygens and Edmond Halley, who calculated the orbit of what is known as Halley's comet, in England. Ghetaldi was the constructor of the parabolic mirror (66 cm in diameter), kept today at the National Maritime Museum in London. He was also a pioneer in making conic lenses. During his sojourn in Padua he met Galileo Galilei, with whom he corresponded regularly. He was a good friend to the French mathematician François Viète. He was offered the post of professor of mathematics at Old University of Leuven in Belgium, at the time one of the most prestigious university centers in Europe. He was also engaged in politics and was the envoy of the Republic of Ragusa in Constantinople in 1606 as well as a member of the Great and Small Council, the political bodies of the Republic. He was married to Marija Sorkočević, who died giving birth to their third daughter; they had three daughters: Anica, Franica, and Marija. == Works == Promotus Archimedis seu De varijs corporum generibus grauitate & magnitudine comparatis (in Latin). Roma: Luigi Zanetti. 1603. Variorum problematum collectio (in Latin). Venezia: Vincenzo Fiorina. 1607. == Legacy == Two notable localities in Dubrovnik are associated with the name of Getaldić: Bete's Cave, named after Marino's nickname, where he conducted experiments with igniting mirrors; and Pozvizd, a key strategic tower in the Ston fortification system which he was commissioned to build by the authorities of the Republic of Dubrovnik in 1604. == See also == House of Getaldić List of notable Ragusans == References == == Sources == Vujić, Marko. "Marin Getaldić - Život i djelo" (PDF). SVEUČILIŠTE JOSIPA JURJA STROSSMAYERA U OSIJEKU ODJEL ZA FIZIKU. {{cite journal}}: Cite journal requires |journal= (help) == Bibliography == A. Favaro, "Marino Ghetaldi," Amici e corrisponsdenti di Galileo, 3 vols. (Firenze, 1983), 2, 911-34. H. Wieleitner, "Marino Ghetaldi und die Anfänge der Koordinatengeometrie," Bibliotheca mathematica, 3rd ser., 13, pp. 242–247. G. Barbieri, "Marino Ghetaldi," in Pietro F. Martecchini, Galleria di Ragusei illustri, (Ragusa, 1840). == External links == O'Connor, John J.; Robertson, Edmund F., "Marino Ghetaldi", MacTutor History of Mathematics Archive, University of St Andrews "Ghetaldi [Ghettaldi], Marino". The Galileo Project. Works by Marino Ghetaldi at Open Library |
Wikipedia:Mario Pulvirenti#0 | Mario Pulvirenti is an Italian mathematician, Professor emeritus of Mathematical Physics at Sapienza University of Rome. == Biography == Mario Pulvirenti received a master's degree in physics from the Sapienza University in 1970, where he is Professor emeritus of Mathematical Physics. He also worked at University of L'Aquila and University of Camerino. He spent research periods at École Normale Supérieure, Institut des Hautes Études Scientifiques and Rutgers University. He is currently member of Istituto Nazionale di Alta Matematica and of Accademia dei Lincei, one of the highest Italian academic institutions. In 2006 has been invited speaker at International Congress of Mathematicians in Madrid. In the same year he won the Tartufari prize form Accademia dei Lincei. He is one of the major experts in mathematical aspects of kinetic theory, and among his research topics are also fluid dynamics and statistical mechanics. In particular, he obtained (together with Reinhard Illner) the only rigorous global derivation in time of the Boltzmann equation from particle dynamics known up to now. He is also interested in clarifying some particular aspects of history of mechanics. == Bibliography == Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum (with R. Illner). Communications in Mathematical Physics, 105(2), 189–203 (1986). Global validity of the Boltzmann equation for two-and three-dimensional rare gas in vacuum: Erratum and improved result (with R. Illner). Communications in Mathematical Physics, 121(1), 143–146 (1989). Kinetic equations and asymptotic theory. Ed. by Benoît Perthame and Laurent Desvillettes. Series in Applied Mathematics (Paris). 4. Paris: Gauthier-Villars/ Elsevier (with F.Bouchut, F.Golse, B.Perthame e L.Desvillettes), (2000). ISBN 2-84299-110-9 The mathematical theory of dilute gases. Applied Mathematical Sciences. 106. New York, NY: Springer-Verlag (with C. Cercignani), (1994). ISBN 0-387-94294-7 Nonequilibrium problems in many-particle systems. Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini, Italy, June 15–27, 1992. Lecture Notes in Mathematics. 1551. Berlin: Springer-Verlag (with C. Cercignani), (1993). ISBN 3-540-56945-6 Vortex methods in two-dimensional fluid dynamics. Lecture Notes in Physics, 203. Berlin etc.: Springer-Verlag (with C. Marchioro), (1984). Propagation of chaos and effective equations in kinetic theory: a brief survey (with S. Simonella), Mathematics and Mechanics of Complex Systems, Vol. 4 (2016), No. 3-4, 255–274. == References == |
Wikipedia:Mariolina Padula#0 | Mariarosaria (Mariolina) Padula (died 29 September 2012) was an Italian mathematical physicist specializing in fluid dynamics, including free boundary problems and compressible flow with viscosity. She was a professor of mathematical physics at the University of Ferrara, and is also known for revitalizing and heading the university's mathematical journal, Annali dell’Università di Ferrara, and forging it into an internationally known journal. == Education and career == Padula studied mathematics at the University of Naples Federico II, and published her first works in mathematical physics in 1973. She was a student of Salvatore Rionero. She continued at the University of Naples as an assistant and associate professor until 1994, when she won a professorship at the University of Basilicata. In 1995, she moved to the department of mathematics and computer science at the University of Ferrara, where she remained for the rest of her career. == Book == Padula was the author of a monograph on her research specialty, Asymptotic stability of steady compressible fluids (Lecture Notes in Mathematics 2024, Springer, 2011). == Recognition == A symposium on mathematical fluid dynamics in Padula's honor was held at the University of Ferrara in 2014. In the same year, a special issue of Annali dell’Università di Ferrara was published in her memory. == Personal life == Padula married another student of Rionero, Giovanni Paolo Galdi; they later separated. She was the mother of Giovanbattista Galdi, a professor of linguistics at Ghent University. == References == |
Wikipedia:Marion Ballantyne White#0 | Marion Ballantyne White (1871–1958) was an American mathematician and university professor. She was one of the few American women to earn her doctorate in mathematics before World War II. == Biography == Marion White was born March 28, 1871, in Peoria, Illinois to two teachers, Jennie E. McLaren and Samuel Holmes White. After her secondary school studies in Peoria, she attended Smith College in 1888 but left after one year to teach at a public school in Peoria. From 1890 to 1893 she studied at the University of Michigan, where she received a Bachelor of Philosophy degree in 1893. She then taught high school in Pueblo, Colorado for two years, before returning to join the faculty at Peoria High School. From 1901 to 1908 she taught at the University of Illinois, and in 1906 she earned her master's degree from the University of Wisconsin. From 1908 to 1910 she earned her doctorate in mathematics at the University of Chicago under the direction of Gilbert Ames Bliss as his third doctoral student. Her dissertation was titled: The Dependence of the Focal Point on Curvature in Space Problems of the Calculus of Variations. She began teaching at the University of Kansas in 1910. In 1914 she relocated to Michigan State Normal College (now Eastern Michigan University) in Ypsilanti, Michigan and assumed the position of associate professor of mathematics and dean of women until 1918 when she went on to teach at Carleton College in Northfield, Minnesota. She was dean of women there from 1922 to 1924 and also served as associate professor until 1937. After her retirement at 66 in 1937, she moved to Pasadena, California, where she spent the last two decades of her life. Marion White died there on January 30, 1958. After she died the Carleton alumni magazine said "she was an especially successful classroom teacher known... for the personal stimulus and encouragement she gave the students." == Selected publications == 1907 The asymptotic lines on the anchor ring. Ann. of Math. 2nd ser., 8:103-117. Published version of MA thesis. Reviews: JFM 38.0662.01 (P. Zuhlke); Rev. semestr. publ. math. 16, pt. 1: 11 (W. A. Wythoff). 1910 The dependence of the focal point on curvature in space problems of the calculus of variations. PhD dissertation, University of Chicago, directed by Gilbert Ames Bliss. Printed version, 1912, New Era Printing Co., Lancaster, PA, reprinted from Trans. Amer. Math. Soc. 13:175-198. 1912 The dependence of focal points upon curvature for problems of the calculus of variations in space. Trans. Amer. Math. Soc. 13:175-198. Published version of PhD dissertation. Reviews: JFM 43.0464.02 (H. Hahn) 43:464-465; Rev. semestr. publ. math. 21, pt. 1: 7-8 (P. Mulder). Presented by J. N. Van der Vries as The dependence of the focal point on curvature in space problems in the calculus of variations to the AMS, St. Louis, MO, 2 Dec 1911; abstract: Bull. Amer. Math. Soc. 18:234 #5. == Memberships == According to Judy Green, Wiggin belonged to several professional societies. American Mathematical Society Mathematical Association of America American Association of University Women Phi Beta Kappa Sigma Xi == References == |
Wikipedia:Marion Scheepers#0 | Marion Scheepers is a South African-born mathematician, lecturer and researcher in the Department of Mathematics of Boise State University in Boise, Idaho since 1988. He is particularly known for his work on selection principles and on infinite topological and set-theoretical games. He introduced themes that are common to many selection principles and is responsible for the Scheepers diagram. == Life == Scheepers was born in December 1957, in Thabazimbi, South Africa. He completed his Ph.D. thesis entitled The Meager-Nowhere Dense Game at the University of Kansas under the supervision of Fred Galvin. His research interests cover set theory and its relatives, game theory, cryptology, elementary number theory and algorithmic phenomena in biology. He was appointed Assistant Professor in the Department of Mathematics at Boise State University (BSU) in 1988 and promoted to Associate Professor in 1993. He has been Professor in the Department of Mathematics at BSU since 1996. In 2016 he was part of a group at BSU that started an interdisciplinary course called Transdisciplinary Research Methods. In 2019 Scheepers was one of the coaches for BSU's elective Vertically Integrated Projects including Portable Secure Devices, a team aiming to develop methods to mitigate cyber-threats against active implantable medical devices. Presently, Scheepers is studying biological encryption mechanisms in certain single-cell organisms in collaboration with researchers from the University of Witten-Herdecke in Germany, and the BSU Department of Biological Sciences. For this study, he has received grant funding from the National Science Foundation. The National Science Foundation has funded his research and curriculum activities on several occasions, including in 2005 for Crypto Systems in Ciliates == Recognition, awards, membership == 2012 Distinguished Professor in Mathematics, Boise State University. 2014 BSU recognised Scheepers' 26 years of academic service. 2017 The conference Frontiers of Selection Principles at Cardinal Stefan Wyszyński University in Warsaw, Poland was dedicated to Scheepers. == Selected publications == "Set theory and its applications : annual Boise Extravaganza in Set Theory". Boise State University Albertsons Library. 14 August 2019. Retrieved 4 September 2019. Babinkostova, L.; Pansera, B.A.; Scheepers, M. (2019). "Selective versions of θ-density". Topology and Its Applications. 258. Elsevier BV: 268–281. doi:10.1016/j.topol.2019.02.061. ISSN 0166-8641. S2CID 126972852. Galvin, Fred; Scheepers, Marion (19 December 2015). "Baire spaces and infinite games". Archive for Mathematical Logic. 55 (1–2). Springer Science and Business Media LLC: 85–104. arXiv:1401.6061. doi:10.1007/s00153-015-0461-8. ISSN 0933-5846. S2CID 206887747. Scheepers, Marion (2011). "Rothberger bounded groups and Ramsey theory". Topology and Its Applications. 158 (13). Elsevier BV: 1575–1583. arXiv:1011.1869. doi:10.1016/j.topol.2011.05.025. ISSN 0166-8641. S2CID 119155731. Samet, Nadav; Scheepers, Marion; Tsaban, Boaz (2009). "Partition relations for Hurewicz-type selection hypotheses". Topology and Its Applications. 156 (3): 616–623. arXiv:0811.1016. doi:10.1016/j.topol.2008.08.013. ISSN 0166-8641. S2CID 16410566. == References == == External links == European Mathematical Information Service Marion Scheepers publications at the American Mathematical Society Publications by Marion Scheepers at ResearchGate |
Wikipedia:Mariusz Lemańczyk#0 | Mariusz Tomasz Lemańczyk (born 3 February 1958) is a Polish mathematician known for his contributions in ergodic theory and dynamical systems. == Life and career == He graduated from the Nicolaus Copernicus University in Toruń in 1981, in mathematics, and completed his PhD in 1985. In 1987, he received the Kazimierz Kuratowski Prize, considered one of the most prestigious awards for young Polish mathematicians. He received his habilitation at the University of Warsaw in 1991, after which he joined the faculty at Nicolaus Copernicus University. In 1997, he received the Stefan Banach Prize from the Polish Mathematical Society. In 2016, he held the Jean-Morlet Chair at the Centre International de Rencontres Mathématiques. On December 3rd 2021 he was selected to join the Polish Academy of Sciences. In July 2022 he gave an invited lecture entitled 'Furstenberg disjointness, Ratner properties and Sarnak’s conjecture' at the International Congress of Mathematicians. == See also == List of Polish mathematicians == References == |
Wikipedia:Mariusz Wodzicki#0 | Mariusz Wodzicki (Polish: [ˈmarjuʂ vɔˈd͡ʑit͡skʲi]; born 1956) is a Polish mathematician and professor of mathematics at the University of California, Berkeley, whose works primarily focus on analysis, algebraic k-theory, noncommutative geometry, and algebraic geometry. == Life and career == Wodzicki was born in Bytom, Poland in 1956. He received a MSc from Moscow State University in 1980, and he completed his doctoral degree in 1984 at the Steklov Institute of Mathematics in Moscow under the advisement of Yuri Manin (Spectral Asymmetry and Zeta-Functions). In 1985–1986 he was a research assistant at the Mathematical Institute, University of Oxford, after which he became an assistant professor at the Mathematical Institute of the Polish Academy of Sciences. He is currently a professor of mathematics at the University of California, Berkeley. In 1992, Wodzicki was an invited speaker of the European Congress of Mathematics in Paris (Algebraic K-theory and functional analysis). In 1994, he was an invited speaker of the International Congress of Mathematicians in Zürich (The algebra of functional analysis). == Selection of writings == Dykema, Ken; Figiel, Tadeusz; Weiss, Gary; Wodzicki, Mariusz (2004). "Commutator structure of operator ideals". Advances in Mathematics. 185 (1): 1–79. doi:10.1016/S0001-8708(03)00141-5. Vestigia investiganda. Moscow Mathematical Journal, vol 2, 2002, pp. 769–798, 806. with Ken Dykema, Gary Weiss: Unitarily invariant trace extensions beyond the trace class. In: Complex analysis and related topics (Cuernavaca, 1996) Oper. Theory Adv. Appl. vol. 114, 2000, pp. 59–65 Algebraic K-theory and functional analysis, ECM Paris 1992, Birkhäuser, Progress in Mathematics, 1994 Suslin, Andrei A.; Wodzicki, Mariusz (1992). "Excision in algebraic K-theory". Annals of Mathematics. 136 (1): 51–122. doi:10.2307/2946546. JSTOR 2946546. MR 1173926. Zbl 0756.18008. Wodzicki, Mariusz (1989). "Excision in cyclic homology and in rational algebraic K-theory". Annals of Mathematics. 129 (3): 591–639. doi:10.2307/1971518. JSTOR 1971518. MR 0997314. Zbl 0689.16013. == See also == List of Polish mathematicians == References == https://math.berkeley.edu/~wodzicki/Lubar.html |
Wikipedia:Marja Holecyová#0 | Marja Holecyová (born Mária Holecyová 28 August 1988) is a Slovak mathematician and fantasy writer. == Education == Holecyová was born in Nitra. She studied Mathematics at the Comenius University. Her PhD thesis Maximum Principle for Infinite Horizon Discrete Time Optimal Control Problems was supervised by professor Pavel Brunovský and defended in 2016. == Writing == Holecyová started writing Harry Potter fan fiction as a 16 years old under the pseudonym Marja Holecyová. Encouraged by the popularity of her writing she send a manuscript of her own fantasy story set in Slovakia and based on local mythology Mariotovi dediči (Heirs of Mariot) to the Slovak branch of Czech fantasy and sci-fi published Fragment at the age of 20. The success of the book resulted in three sequels published over the course of 2010 and 2011. In 2016, she published a historical fantasy novel set in the 16th century Kingdom of Hungary called Korene Hriechu (Roots of sin) == References == |
Wikipedia:Marjan Dema#0 | Marjan Dema (born May 27, 1957, in Klina, FPR Yugoslavia) is a professor of mathematics. He was involved for many years in the Balkan Universities Network and from March 2016 until September 2020 he was Rector of the University of Pristina. == Biography == Marjan Dema earned a master's degree in mathematics with the thesis "Some interpolation features of analytical functions within the Hilbert transform and Doctor of Mathematical Sciences in 1987 with the work Multiple interpolation in HP premises, at the University of Pristina. He has taught as visiting professor at the Faculty of Economics of the University of Tetova (1997-1999) and at the American College "Midwestern Baptist College" in Pontiac, United States (2002-2005). He has scientific connections within the framework of the Balkan Universities Network to the Trakya University in Edirne and especially with Hilmi Ibar. In the years 2009-2012 he was a member of the University Council of the University of Pristina. After his election as Rector of the University of Pristina, he took office in March 2016. In 2019, Rector Dema was the patron of an international seminar hosted by Rotary International with students from Germany, Greece, Turkey and Kosovo on the subject of malaria control. == References == == External links == Webpage of the University Pristina Webpage of Rektor Marjan Dema Marjan Dema on Researchgate Marjan Dema in Berkleycenter Marjan Dema Member of DAAAM Marjan Dema on USAID == Literature == Marjan Dema opening speech in: Manfred G. Raupp und Wolfgang Uebel: The fight against Malaria and other related mosquito-born Diseases, Results and proposed next Steps of the Rotary Seminar at the University Prishtina (Kosovo) 2019: Publisher: madora gmbh Lörrach & Lörrach International e.V. Mai 2019, ISBN 978-3-945046-16-6 |
Wikipedia:Marjorie Batchelor#0 | Marjorie Blake (Marj) Batchelor-Winter is an American mathematician known for her work on coalgebras and supermanifolds. She is an emeritus staff member in the department of pure mathematics and mathematical statistics at the University of Cambridge in England, where she was formerly the graduate education officer and director of the Cambridge Mathematics Placements summer programme. == Education == Batchelor is the daughter of William Henry Batchelor, a medical researcher and administrator at the National Institutes of Health. She graduated from Smith College in 1973, and in 2008 returned to Smith with her husband, Alan Winter, to help revive the tradition of change ringing at Smith. She became a student of Bertram Kostant at the Massachusetts Institute of Technology, completing her Ph.D. there in 1978 with a dissertation on The Structure of Supermanifolds. == Research == In the theory of supermanifolds, Batchelor's theorem states that every supermanifold can be realized as a sheaf of differential forms over the exterior bundle of a vector bundle. Batchelor published its proof in her 1979 paper, "The structure of supermanifolds". == Activism == At Cambridge, Batchelor became known for her efforts to encourage women in mathematics, and to build a more collegial and interactive atmosphere among the students studying for the Mathematical Tripos. == References == == External links == Home page Marj Batchelor, Women in Maths, 18 January 2017 |
Wikipedia:Mark Ainsworth#0 | Mark Ainsworth is a British mathematician. He is the Francis Wayland Professor of Applied Mathematics at Brown University. == Education == Ainsworth studied mathematics at Durham University, where he graduated in 1986 with first-class honours and received the Collingwood Memorial Prize for the strongest performance in final exams. He completed his doctorate in 1989 from the same institution under the supervision of A. W. Craig. == Research and career == Ainsworth held the 1825 Chair at the University of Strathclyde before joining Brown University. He received the Whitehead Prize from the London Mathematical Society in 2004 for his contributions to numerical analysis. == Selected publications == === Books === Ainsworth, Mark; Oden, J. Tinsley (2000). A Posteriori Error Estimation in Finite Element Analysis. Wiley-Interscience. doi:10.1002/9781118032824. ISBN 978-0471294115. === Articles === Ainsworth, Mark; Craig, Alan (1991). "A posteriori error estimators in the finite element method". Numerische Mathematik. 60 (4): 429–464. doi:10.1007/BF01385730. Ainsworth, Mark; Fu, Guosheng (2017). "Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations". arXiv:1706.05778 [math.NA]. Ainsworth, Mark; Vejchodský, Tomáš (2019). "A simple approach to reliable and robust a posteriori error estimation for singularly perturbed problems". Computer Methods in Applied Mechanics and Engineering. 353: 373–390. arXiv:1812.07972. Bibcode:2019CMAME.353..373A. doi:10.1016/j.cma.2019.05.014. == References == == External links == Faculty page at Brown University Google Scholar |
Wikipedia:Mark Braverman (mathematician)#0 | Mark Braverman (Hebrew: מארק ברוורמן; born 1984) is an Israeli mathematician and theoretical computer scientist. He was awarded an EMS Prize in 2016 as well as Presburger Award in the same year. In 2019, he was awarded the Alan T. Waterman Award. In 2022, he won the IMU Abacus Medal. He earned his doctorate from the University of Toronto in 2008, under the supervision of Stephen Cook. After this, he did post-doctoral research at Microsoft Research and then joined the faculty at University of Toronto. In 2011, he joined the Princeton University department of computer science. In 2014, he was an Invited Speaker with talk Interactive information and coding theory at the International Congress of Mathematicians in Seoul. Braverman is the son of mathematician Elena Braverman and, through her, the grandson of his co-author, mathematical statistician Yan Petrovich Lumel'skii. == References == == External links == Mark Braverman's results at International Mathematical Olympiad |
Wikipedia:Mark D. McDonnell#0 | Mark Damian McDonnell (born 28 February 1975) is an Australian electronic engineer and mathematician, notable for his work on stochastic resonance and more specifically suprathreshold stochastic resonance. == Education == McDonnell graduated from the Salesian College, Adelaide. He received a BSc in Mathematical & Computer Sciences (1997), a BE (Hons) in Electrical & Electronic Engineering (1998), and a BSc (Hons) in Applied Mathematics (2001) all from The University of Adelaide, Australia. He received his PhD in Electrical & Electronic Engineering (2006), under Derek Abbott and Charles E. M. Pearce, also from the University of Adelaide, for a thesis entitled Theoretical Aspects of Stochastic Signal Quantisation and Suprathreshold Stochastic Resonance. During the course of his PhD, he was also a visiting scholar at the University of Warwick, UK, under Nigel G. Stocks. == Career == McDonnell worked as a research assistant in electromagnetic propagation, ice-penetrating radar, and as a computer systems engineer, at the University of Adelaide. His main research interests are in the field of nonlinear signal processing, with applications in computational neuroscience, complex systems, and lossy compression, reliable communication, and coding of noisy signals. == Honors == In 2002, McDonnell was awarded a D. R. Stranks Fellowship, and in 2003, he was awarded a Santa Fe Institute Complex Systems Fellowship, as well as the AFUW Doreen MacCarthy Bursary. In 2004 he was the recipient of an Australian Academy of Science Young Researcher's Award. He was awarded the Postgraduate Alumni University Medal for his PhD thesis. In 2007, he won a Fresh Science award, the Gertrude Rohan Prize, and an Australian Postdoctoral Fellowship that he took up at the University of South Australia. == Books by McDonnell == Mark D. McDonnell, Nigel G. Stocks, Charles E. M. Pearce, and Derek Abbott, Stochastic Resonance, Cambridge University Press, 2008, ISBN 978-0-521-88262-0. == See also == Stochastic resonance Suprathreshold stochastic resonance Stochastic Resonance (book) == Notes == == External links == McDonnell's homepage Mark D. McDonnell at the Mathematics Genealogy Project McDonnell's COSnet profile Stochastic Resonance McDonnell's FaceBook profile |
Wikipedia:Mark Ellingham#0 | Mark Norman Ellingham is a professor of mathematics at Vanderbilt University whose research concerns graph theory. With Joseph D. Horton, he is the discoverer and namesake of the Ellingham–Horton graphs, two cubic 3-vertex-connected bipartite graphs that have no Hamiltonian cycle. Ellingham earned his Ph.D. in 1986 from the University of Waterloo under the supervision of Lawrence Bruce Richmond. In 2012, he became one of the inaugural fellows of the American Mathematical Society. == References == |
Wikipedia:Mark Freidlin#0 | Mark Iosifovich Freidlin (Russian: Марк Иосифович Фрейдлин, born 1938) is a Russian-American probability theorist who works as a Distinguished University Professor of Mathematics at the University of Maryland, College Park. He is one of the namesakes of the Freidlin–Wentzell theory, which is an important part of the large deviations theory. Freidlin and Wentzell are the authors of the first monograph on the large deviations theory for stochastic processes (1979). The Freidlin-Wentzell theory describes, in particular, the long-time effects caused by random perturbations. The latest edition of the book was published by Springer in 2012. It contains not just the results on large deviations but also new results on other asymptotic problems, in particular, on the averaging principle for stochastic perturbations. Other works of Mark Freidlin concern perturbations of Hamiltonian systems, wave front propagation in reaction-diffusion equations, non-linear perturbations of partial differential equations. stochasticity in deterministic dynamical systems. Friedlin was born in 1938 in Moscow. He began studying mathematics at Moscow State University at the age of 16, and earned a candidate's degree there in 1962, under the supervision of Eugene Dynkin. In 1970 he completed a doctorate. However, growing anti-semitism in the Soviet Union prevented Friedlin from traveling and forced him to transfer from the Mechanics and Mathematics Department at Moscow State to the Bio-Physics Department (with the assistance of Andrey Kolmogorov in finding him this position). By 1979 he had decided to emigrate to the US, but was denied permission to leave Russia; despite having no permanent employment for the next eight years, he continued to work and publish in mathematics. Finally, in 1987, he was able to move to the University of Maryland. Freidlin was an invited speaker at the 1998 International Congress of Mathematicians. He became a Distinguished Professor at Maryland in 2000. In May 2003, a conference on "Asymptotic Problems in Stochastic Processes and PDE's" was held at the University of Maryland in honor of Freidlin's 65th birthday. In 2012, he became one of the inaugural fellows of the American Mathematical Society. His doctoral students include Jürgen Gärtner. == Selected publications == Functional Integration and Partial Differential Equations. Princeton University Press. 21 August 1985. ISBN 0-691-08362-2. Markov Processes and Differential Equations: Asymptotic Problems. Springer Science & Business Media. 28 March 1996. ISBN 978-3-7643-5392-6. with Alexander D. Wentzell: Random perturbations and dynamical systems. Grundlehren der mathematischen Wissenschaften. Vol. 260 (2nd ed.). Springer. 1998. ISBN 9780387983622; translated by Joseph Szücs; 1st edition 1984{{cite book}}: CS1 maint: postscript (link); 3rd edition 2012 with M. Weber: Random perturbations of nonlinear oscillators, Ann. Probability 26 (1998), no. 3, pp. 925–967. with M. Weber: Random perturbations of dynamical systems and diffusion processes with conservation laws, Probability Theory Related Fields 128 (2004), pp. 441–466. with A.D. Wentzell: On the Neumann problem for PDEs with a small parameter and corresponding diffusion processes, Probab. Theory Relat. Fields 152 (2012), no. 1-2, pp. 101–140. with A.D. Wentzell: Diffusion approximation for noise-induced evolution of first integrals in multi-frequency systems, Journal of Statistical Physics, 182, Article number: 45 (2021). with L. Koralov: Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE's with a small parameter, Probability Theory and Related Fields 147 (2010), pp. 273–301. with W. Hu: On perturbations of generalized Landau-Lifshitz dynamics, Journ. Stat. Phys. 144 (2011), no. 5, pp. 978–1008. Reaction-diffusion equations in incompressible fluid: asymptotic problems. Journal of Differential Equations, 179, pp 44–96 (2002). Large Deviations at Saint-Flour, Springer (2013). == References == |
Wikipedia:Mark Perakh#0 | Mark Perakh (Russian: Марк Пэрах; perach (פֶּ֫רַח) is the Hebrew word for "flower"; born Mark Yakovlevich Popereka in 1924, Kiev, Ukraine, died 7 May 2013 in Escondido, California), was a professor emeritus of Mathematics and statistical mechanics at California State University, Fullerton in Fullerton, California. Perakh taught physics, researched superconductivity, and wrote some 300 scientific papers, but his fame particularly comes from his writing about science and religion on Talk Reason, a website he helped found, and from his regular contributions to the blog The Panda's Thumb. On August 28, 1958 Perakh (then Popereka), who at the time had been the head of a department in Kazakh Agricultural University in Almaty (then Alma-Ata) and K.S.Frusin (department assistant) were sentenced for "badmouthing" the Soviet government and for spreading leaflets calling to vote against candidates in the then forthcoming elections to the Supreme Soviet of the USSR. Some of Perakh's short stories were inspired by his stay in the gulag. In 2003, Perakh published Unintelligent Design (Prometheus Books, ISBN 1-59102-084-0), a book that is critical of Intelligent Design, and he is particularly skeptical of some of the arguments proposed by William Dembski, which he states are pseudomathematical. He also wrote critically of Old Earth creationist astronomer Hugh Ross, and has responded to claims by Jonathan Wells that the lack of published research by creationists contradicting the prevailing scientific consensus is due to a conspiracy he likens to Lysenkoism in the former USSR. Perakh was also interested in Bible codes, which he believed are ridiculous. Perakh's other published books include a technical volume on the subject of thin films, which has been translated into eight languages, and the novel Man in a Wire Cage (originally titled by the author "Train in a Wire Cage" but changed by the publisher) (1988, ISBN 1-55547-257-5). His website also has a section on Russian oral jokes (anekdoty) and short stories he has written in English and Russian. Perakh died of leukemia on May 7, 2013 in his home in Hidden Meadows outside Escondido, California. == References == == Publications == Unintelligent Design (Prometheus Books, 2003) ISBN 1-59102-084-0 Man in a Wire Cage (Critics Choice Paperbacks, August 1988) ISBN 1-55547-257-5 == External links == Mark Perakh's home page Talk Reason website |
Wikipedia:Mark Pinsker#0 | Mark Semenovich Pinsker (Russian: Марк Семено́вич Пи́нскер; April 24, 1925 – December 23, 2003) or Mark Shlemovich Pinsker (Russian: Марк Шлемо́вич Пи́нскер) was a noted Russian mathematician in the fields of information theory, probability theory, coding theory, ergodic theory, mathematical statistics, and communication networks. Pinsker studied stochastic processes under A. N. Kolmogorov in the 1950s, and later worked at the Institute for Information Transmission Problems (IITP), Russian Academy of Sciences, Moscow. His accomplishments included a classic paper on the entropy theory of dynamical systems which introduced the maximal partition with zero entropy, later known as Pinsker's partition. His work in mathematical statistics was devoted mostly to the applications of information theory, including asymptotically sufficient statistics for parameter estimation and nonparametric estimation; Pinsker's inequality is named after him. He also produced notable results in the theory of switching networks and complexity problems in coding theory. Pinsker received the IEEE Claude E. Shannon Award in 1978, and the IEEE Richard W. Hamming Medal in 1996. == Selected works == "Theory of curves in Hilbert space with stationary increments of order " Izv. Akad. Nauk SSSR Ser. Mat., 19, 1955. "Динамические системы с вполне положительной и нулевой энтропией" [Dynamical systems with completely positive and zero entropy]. Doklady Akademii Nauk SSSR. 133 (5): 1025–1026. 1960. Information and information stability of random variables and processes, translated and edited by Amiel Feinstein, Holden-Day, San Francisco, 1964. L. A. Bassalygo and M. S. Pinsker, "The complexity of an optimal non-blocking commutation scheme without reorganization", Problemy Peredaci Informacii, 9(1):84–87, 1973. Translated into English in Problems of Information Transmission, 9 (1974) 64-66. M. S. Pinsker. "On the complexity of a concentrator", 7th International Teletraffic Conference, pages 318/1-318/4, 1973. "Estimation of error-correction complexity of Gallager low-density codes", Problems of Information Transmission, 11:18—28, 1976. "Reflections of Some Shannon Lecturers". == Notes == == References == "Review of Scientific Achievements of M. S. Pinsker", Problems of Information Transmission (translation of Problemy Peredachi Informatsii), Volume 32, Number 1, January–March, 1996, pages 3–14. == External links == "Mark Semenovich Pinsker. In Memoriam", Problems of Information Transmission, MAIK Nauka/Interperiodica, Volume 40, Number 1 / January, 2004, pages 1–4. ISSN 0032-9460. English version Ramesh Rao. "Mark Semenovich Pinsker - On his 70th Birthday", IEEE Information Theory Society Newsletter, September 1995. Sasha Barg. "In Memoriam - Mark Semënovich Pinsker", IEEE Information Theory Society Newsletter, Volume 54, Number 3, September 2004. Pinsker Marks Shlemovich (1925–2003) author page at Math-Net.ru "Reflections of Some Shannon Lecturers" Mark Pinsker at the Mathematics Genealogy Project |
Wikipedia:Mark Stern#0 | Mark Joseph Stern (born 1991) is an American journalist and commentator. He is a senior writer covering courts and the law, especially the Supreme Court, for Slate. He frequently appears on television, especially on MSNBC, and in podcasts, commenting on legal and social issues. In addition to the Supreme Court, his areas of expertise include LGBTQ+ equality, reproductive rights, U.S. territorial law and criminal justice. He has co-authored law review articles about free speech, gay rights, and transgender equality. == Education and career == Stern received a B.A. in history and art history from Georgetown University in 2013 and obtained a J.D. from Georgetown University Law Center in 2016. In 2016 he was admitted to the Maryland Bar. He began working as an intern for Slate in August 2012 and continued there while attending law school at Georgetown. He became a full-time contributor and staff writer in 2016, and in February 2022, he was promoted to his current position as senior writer. At Slate he covers the U.S. Supreme Court, federal appellate and district courts, and state and local courts. He has published articles in The Wall Street Journal, The Week, and The American Prospect. Stern regularly speaks at universities, law schools, law firms, businesses, bar associations, and other non-profits. He has appeared on NPR and his frequent appearances on television include Alex Wagner Tonight, All In with Chris Hayes, The Katie Phang Show, The 11th Hour with Stephanie Ruhle, Katy Tur Reports, The Weekend with Jonathan Capeheart and Deadline: White House with Ali Velshi. He co-hosts weekly bonus episodes of the podcast Amicus with Dahlia Lithwick for Slate Plus members. Other podcasts he has appeared on include The Bulwark Podcast with Tim Miller, The Majority Report with Sam Seder, The Gist with Michelangelo Signorile, and How I Lawyer with Jonah Perlin. == Personal life == Stern was born in Tallahassee, Florida in 1991. He is the son of former Florida State University College of Law professor Nat Stern with whom he sometimes co-authors. His grandfather was a Holocaust survivor. Mark is Jewish and gay. He married his husband Tyler in 2018. They welcomed the birth of their son in October 2023. == Works == American Justice 2019: The Roberts Courts Arrives. University of Pennsylvania Press, 2019. ISBN 9780812252132 == References == == External links == Personal website Mark Joseph Stern at Slate |
Wikipedia:Marko Tadić#0 | Marko Tadić (born 16 November 1953 in Tomislavgrad) is a Croatian mathematician. Tadić does research in the field of noncommutative harmonic analysis, especially the representation theory of classical groups and classification of unitary representations and its interaction with the modern theory of automorphic forms through Langlands program. Tadić graduated from the University of Zagreb with a B.S. in 1976, an M.S. in 1979, and a Ph.D. in 1980. He has been a full professor at the University of Zagreb since 1987. He has served two full-year appointments as a visiting professor at the University of Utah. He is a fellow of the Croatian Academy of Sciences and Arts and a member of Academia Europaea. == References == == External links == Personal web page List of publications |
Wikipedia:Markov brothers' inequality#0 | In mathematics, the Markov brothers' inequality is an inequality, proved in the 1890s by brothers Andrey Markov and Vladimir Markov, two Russian mathematicians. This inequality bounds the maximum of the derivatives of a polynomial on an interval in terms of the maximum of the polynomial. For k = 1 it was proved by Andrey Markov, and for k = 2, 3, ... by his brother Vladimir Markov. == The statement == Let P be a polynomial of degree ≤ n. Then for all nonnegative integers k {\displaystyle k} max − 1 ≤ x ≤ 1 | P ( k ) ( x ) | ≤ n 2 ( n 2 − 1 2 ) ( n 2 − 2 2 ) ⋯ ( n 2 − ( k − 1 ) 2 ) 1 ⋅ 3 ⋅ 5 ⋯ ( 2 k − 1 ) max − 1 ≤ x ≤ 1 | P ( x ) | . {\displaystyle \max _{-1\leq x\leq 1}{\big |}P^{(k)}(x){\big |}\leq {\frac {n^{2}(n^{2}-1^{2})(n^{2}-2^{2})\cdots (n^{2}-(k-1)^{2})}{1\cdot 3\cdot 5\cdots (2k-1)}}\max _{-1\leq x\leq 1}|P(x)|.} This inequality is tight, as equality is attained for Chebyshev polynomials of the first kind. == Related inequalities == Bernstein's inequality (mathematical analysis) Remez inequality == Applications == Markov's inequality is used to obtain lower bounds in computational complexity theory via the so-called "polynomial method". == References == |
Wikipedia:Markov switching multifractal#0 | In financial econometrics (the application of statistical methods to economic data), the Markov-switching multifractal (MSM) is a model of asset returns developed by Laurent E. Calvet and Adlai J. Fisher that incorporates stochastic volatility components of heterogeneous durations. MSM captures the outliers, log-memory-like volatility persistence and power variation of financial returns. In currency and equity series, MSM compares favorably with standard volatility models such as GARCH(1,1) and FIGARCH both in- and out-of-sample. MSM is used by practitioners in the financial industry for different types of forecasts. == MSM specification == The MSM model can be specified in both discrete time and continuous time. === Discrete time === Let P t {\displaystyle P_{t}} denote the price of a financial asset, and let r t = ln ( P t / P t − 1 ) {\displaystyle r_{t}=\ln(P_{t}/P_{t-1})} denote the return over two consecutive periods. In MSM, returns are specified as r t = μ + σ ¯ ( M 1 , t M 2 , t . . . M k ¯ , t ) 1 / 2 ϵ t , {\displaystyle r_{t}=\mu +{\bar {\sigma }}(M_{1,t}M_{2,t}...M_{{\bar {k}},t})^{1/2}\epsilon _{t},} where μ {\displaystyle \mu } and σ {\displaystyle \sigma } are constants and { ϵ t {\displaystyle \epsilon _{t}} } are independent standard Gaussians. Volatility is driven by the first-order latent Markov state vector: M t = ( M 1 , t M 2 , t … M k ¯ , t ) ∈ R + k ¯ . {\displaystyle M_{t}=(M_{1,t}M_{2,t}\dots M_{{\bar {k}},t})\in R_{+}^{\bar {k}}.} Given the volatility state M t {\displaystyle M_{t}} , the next-period multiplier M k , t + 1 {\displaystyle M_{k,t+1}} is drawn from a fixed distribution M with probability γ k {\displaystyle \gamma _{k}} , and is otherwise left unchanged. The transition probabilities are specified by γ k = 1 − ( 1 − γ 1 ) ( b k − 1 ) {\displaystyle \gamma _{k}=1-(1-\gamma _{1})^{(b^{k-1})}} . The sequence γ k {\displaystyle \gamma _{k}} is approximately geometric γ k ≈ γ 1 b k − 1 {\displaystyle \gamma _{k}\approx \gamma _{1}b^{k-1}} at low frequency. The marginal distribution M has a unit mean, has a positive support, and is independent of k. ==== Binomial MSM ==== In empirical applications, the distribution M is often a discrete distribution that can take the values m 0 {\displaystyle m_{0}} or 2 − m 0 {\displaystyle 2-m_{0}} with equal probability. The return process r t {\displaystyle r_{t}} is then specified by the parameters θ = ( m 0 , μ , σ ¯ , b , γ 1 ) {\displaystyle \theta =(m_{0},\mu ,{\bar {\sigma }},b,\gamma _{1})} . Note that the number of parameters is the same for all k ¯ > 1 {\displaystyle {\bar {k}}>1} . === Continuous time === MSM is similarly defined in continuous time. The price process follows the diffusion: d P t P t = μ d t + σ ( M t ) d W t , {\displaystyle {\frac {dP_{t}}{P_{t}}}=\mu dt+\sigma (M_{t})\,dW_{t},} where σ ( M t ) = σ ¯ ( M 1 , t … M k ¯ , t ) 1 / 2 {\displaystyle \sigma (M_{t})={\bar {\sigma }}(M_{1,t}\dots M_{{\bar {k}},t})^{1/2}} , W t {\displaystyle W_{t}} is a standard Brownian motion, and μ {\displaystyle \mu } and σ ¯ {\displaystyle {\bar {\sigma }}} are constants. Each component follows the dynamics: The intensities vary geometrically with k: γ k = γ 1 b k − 1 . {\displaystyle \gamma _{k}=\gamma _{1}b^{k-1}.} When the number of components k ¯ {\displaystyle {\bar {k}}} goes to infinity, continuous-time MSM converges to a multifractal diffusion, whose sample paths take a continuum of local Hölder exponents on any finite time interval. == Inference and closed-form likelihood == When M {\displaystyle M} has a discrete distribution, the Markov state vector M t {\displaystyle M_{t}} takes finitely many values m 1 , . . . , m d ∈ R + k ¯ {\displaystyle m^{1},...,m^{d}\in R_{+}^{\bar {k}}} . For instance, there are d = 2 k ¯ {\displaystyle d=2^{\bar {k}}} possible states in binomial MSM. The Markov dynamics are characterized by the transition matrix A = ( a i , j ) 1 ≤ i , j ≤ d {\displaystyle A=(a_{i,j})_{1\leq i,j\leq d}} with components a i , j = P ( M t + 1 = m j | M t = m i ) {\displaystyle a_{i,j}=P\left(M_{t+1}=m^{j}|M_{t}=m^{i}\right)} . Conditional on the volatility state, the return r t {\displaystyle r_{t}} has Gaussian density f ( r t | M t = m i ) = 1 2 π σ 2 ( m i ) exp [ − ( r t − μ ) 2 2 σ 2 ( m i ) ] . {\displaystyle f(r_{t}|M_{t}=m^{i})={\frac {1}{\sqrt {2\pi \sigma ^{2}(m^{i})}}}\exp \left[-{\frac {(r_{t}-\mu )^{2}}{2\sigma ^{2}(m^{i})}}\right].} === Conditional distribution === === Closed-form Likelihood === The log likelihood function has the following analytical expression: ln L ( r 1 , … , r T ; θ ) = ∑ t = 1 T ln [ ω ( r t ) . ( Π t − 1 A ) ] . {\displaystyle \ln L(r_{1},\dots ,r_{T};\theta )=\sum _{t=1}^{T}\ln[\omega (r_{t}).(\Pi _{t-1}A)].} Maximum likelihood provides reasonably precise estimates in finite samples. === Other estimation methods === When M {\displaystyle M} has a continuous distribution, estimation can proceed by simulated method of moments, or simulated likelihood via a particle filter. == Forecasting == Given r 1 , … , r t {\displaystyle r_{1},\dots ,r_{t}} , the conditional distribution of the latent state vector at date t + n {\displaystyle t+n} is given by: Π ^ t , n = Π t A n . {\displaystyle {\hat {\Pi }}_{t,n}=\Pi _{t}A^{n}.\,} MSM often provides better volatility forecasts than some of the best traditional models both in and out of sample. Calvet and Fisher report considerable gains in exchange rate volatility forecasts at horizons of 10 to 50 days as compared with GARCH(1,1), Markov-Switching GARCH, and Fractionally Integrated GARCH. Lux obtains similar results using linear predictions. == Applications == === Multiple assets and value-at-risk === Extensions of MSM to multiple assets provide reliable estimates of the value-at-risk in a portfolio of securities. === Asset pricing === In financial economics, MSM has been used to analyze the pricing implications of multifrequency risk. The models have had some success in explaining the excess volatility of stock returns compared to fundamentals and the negative skewness of equity returns. They have also been used to generate multifractal jump-diffusions. == Related approaches == MSM is a stochastic volatility model with arbitrarily many frequencies. MSM builds on the convenience of regime-switching models, which were advanced in economics and finance by James D. Hamilton. MSM is closely related to the Multifractal Model of Asset Returns. MSM improves on the MMAR's combinatorial construction by randomizing arrival times, guaranteeing a strictly stationary process. MSM provides a pure regime-switching formulation of multifractal measures, which were pioneered by Benoit Mandelbrot. == See also == Brownian motion Rogemar Mamon Markov chain Multifractal model of asset returns Multifractal Stochastic volatility == References == == External links == Financial Time Series, Multifractals and Hidden Markov Models |
Wikipedia:Markus–Yamabe conjecture#0 | In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. If the Jacobian matrix of a dynamical system at a fixed point is Hurwitz, then the fixed point is asymptotically stable. Markus-Yamabe conjecture asks if a similar result holds globally. Precisely, the conjecture states that if a continuously differentiable map on an n {\displaystyle n} -dimensional real vector space has a fixed point, and its Jacobian matrix is everywhere Hurwitz, then the fixed point is globally stable. The conjecture is true for the two-dimensional case. However, counterexamples have been constructed in higher dimensions. Hence, in the two-dimensional case only, it can also be referred to as the Markus–Yamabe theorem. Related mathematical results concerning global asymptotic stability, which are applicable in dimensions higher than two, include various autonomous convergence theorems. Analog of the conjecture for nonlinear control system with scalar nonlinearity is known as Kalman's conjecture. == Mathematical statement of conjecture == Let f : R n → R n {\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} ^{n}} be a C 1 {\displaystyle C^{1}} map with f ( 0 ) = 0 {\displaystyle f(0)=0} and Jacobian D f ( x ) {\displaystyle Df(x)} which is Hurwitz stable for every x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} . Then 0 {\displaystyle 0} is a global attractor of the dynamical system x ˙ = f ( x ) {\displaystyle {\dot {x}}=f(x)} . The conjecture is true for n = 2 {\displaystyle n=2} and false in general for n > 2 {\displaystyle n>2} . == References == Markus, Lawrence; Yamabe, Hidehiko (1960). "Global Stability Criteria for Differential Systems". Osaka Mathematical Journal. 12 (2): 305–317. Meisters, Gary (1996). "A Biography of the Markus–Yamabe Conjecture" (PDF). Retrieved October 20, 2023. Gutierrez, Carlos (1995). "A solution to the bidimensional Global Asymptotic Stability Conjecture". Annales de l'Institut Henri Poincaré C. 12 (6): 627–671. Bibcode:1995AIHPC..12..627G. doi:10.1016/S0294-1449(16)30147-0. Feßler, Robert (1995). "A proof of the two-dimensional Markus–Yamabe stability conjecture and a generalisation". Annales Polonici Mathematici. 62: 45–74. doi:10.4064/ap-62-1-45-74. Cima, Anna; van den Essen, Arno; Gasull, Armengol; Hubbers, Engelbert; Mañosas, Francesc (1997). "A Polynomial Counterexample to the Markus–Yamabe Conjecture". Advances in Mathematics. 131 (2): 453–457. doi:10.1006/aima.1997.1673. hdl:2066/112453. Bernat, Josep; Llibre, Jaume (1996). "Counterexample to Kalman and Markus–Yamabe Conjectures in dimension larger than 3". Dynamics of Continuous, Discrete & Impulsive Systems. 2 (3): 337–379. Bragin, V. O.; Vagaitsev, V.I.; Kuznetsov, N. V.; Leonov, G.A. (2011). "Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits". Journal of Computer and Systems Sciences International. 50 (5): 511–543. doi:10.1134/S106423071104006X. S2CID 21657305. Leonov, G. A.; Kuznetsov, N. V. (2013). "Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits". International Journal of Bifurcation and Chaos. 23 (1): 1330002–1330219. Bibcode:2013IJBC...2330002L. doi:10.1142/S0218127413300024. |
Wikipedia:Marlyn Meltzer#0 | Marlyn Wescoff Meltzer (1922 – December 7, 2008) was an American mathematician and computer programmer, and one of the six original programmers of ENIAC, the first general-purpose electronic digital computer. == Early life == Meltzer was born Marlyn Wescoff in Philadelphia in 1922. She graduated from Temple University in 1942. == Career == Meltzer was hired by the Moore School of Engineering after graduating to perform weather calculations, mainly because she knew how to operate an adding machine; in 1943, she was hired to perform calculations for ballistics trajectories. At the time, this was accomplished by using manual desktop mechanical calculators. In 1945, she was selected to become one of the 6 original programmers of Electronic Numerical Integrator and Computer. === ENIAC === Meltzer, alongside Kathleen Antonelli, Jean Jennings Bartik, Frances Elizabeth Holberton, Frances Spence and Ruth Teitelbaum, were the original six programmers of ENIAC, a project that originally began in secret at the Moore School of Electrical Engineering at the University of Pennsylvania in 1943. ENIAC was a huge machine full of black panels and switches, containing 17,468 vacuum tubes, 7200 crystal diodes, 1500 relays, 70000 resistors, 10000 capacitors and approximately 5000000 hand-soldered joints. It weighed more than 30 short tons, occupied 167m2 and consumed 150 kW of electricity. Its huge power requirement led to a rumor that the lights across Philadelphia would dim every time it was switched on. ENIAC was unveiled to the public on February 14, 1946, making headlines across the country. Although mentioned in Woman of the ENIAC at the time, little recognition was attributed to the women working on the computer, with attention focused on the male engineers who built the machine. She resigned from the team in 1947 to get married before ENIAC was relocated to the Aberdeen Proving Grounds. In 1997, Meltzer was inducted into the Women in Technology International Hall of Fame, along with the other original ENIAC programmers. This award was established in 1996 by WITI to "recognize, honor, and promote the outstanding contributions women make to the scientific and technological communities that improve and evolve our society". === Volunteer work === Meltzer enjoyed volunteering at Shir Ami Library and Sunday school story hour. She also delivered Meals on Wheels for more than 10 years for the Greenwood House in Ewing, NJ. She was the treasurer of the Trenton/Lawrenceville chapter of Hadassah and an active member of Women for Greenwood House. During her last four years, she had knitted more than 500 chemotherapy hats for Susan B. Komen For the Cure, a non-profit organization in Philadelphia. == Death == Meltzer died on December 7, 2008, in Yardley, Bucks County, Pennsylvania, United States. == Legacy == In 1997 she was inducted into the Women in Technology International Hall of Fame, along with the other original ENIAC programmers. Her work on ENIAC and at the University of Pennsylvania was later recognized in the 2010 documentary film Top Secret Rosies: The Female "Computers" of WWII. The ENIAC team is also the inspiration behind the award-winning 2013 documentary The Computers. This documentary, created by Kathy Kleiman and the ENIAC Programmers Project, combines actual footage of the ENIAC team from the 1940s with interviews with the female team members as they reflect on their time working together on the ENIAC. == See also == Timeline of women in science == References == == External links == ENIAC Programmers at witi.com The Women of ENIAC at ieeecomputersociety.org |
Wikipedia:Mars Cramer#0 | Jan Salomon (Mars) Cramer (28 April 1928 – 15 March 2014) was a Dutch economist, Professor of Statistics and Econometrics at the University of Amsterdam, known for his work of empirical econometrics. == Biography == Born in The Hague, Mars Cramer was the son of biologist and Professor P. J. S. Cramer (1879–1952) He received his PhD in Mathematics in 1961 at the University of Amsterdam with a thesis entitled "A Statistical Model of the Ownership of Major Consumer Durables with an Application to some Findings of the 1953 Oxford Savings Survey" under supervision of Pieter de Wolff. In the 1950s Cramer started his career as researcher for the Bureau for Economic Policy Analysis. After graduation in 1961 at the University of Amsterdam he was appointed Professor of Econometrics, a newly established chair. He was Director of the SEO Economic Research from 1985 to 1992 as successor of Wim Driehuis. Among his doctoral students were Arnold Merkies (1972), Geert Ridder (1987) and Mirjam van Praag (2005). In 1980 Cramer was elected member of the Royal Netherlands Academy of Arts and Sciences, and later Fellow of the Tinbergen Institute. Cramer died on 15 March 2014 in Amsterdam The University of Amsterdam's Faculty of Economics and Business (2014) recalled that "Mars was known for his originality and his wit. He possessed a genuine academic curiosity and a rather characteristic style of writing. For example, his research into the velocity of money led him to study the velocity of particular coins. As a student he served as editor of the literary student periodical Propria Cures, and he continued to intermittently publish short stories and opinion pieces. In 2012, the Washington Post published his moving account of his wife Til’s euthanasia four years earlier." Cramer "continued working on new research projects and contributing to the supervision of students until the very last day before his passing." == Publications == Cramer authored and co-authored numerous publications in the field of econometrics. Books, a selection: 1958. Economic forecasts and policy. With Henri Theil assisted by J.S. Cramer, H. Moerman, and A. Russchen. 1961. A Statistical Model of the Ownership of Major Consumer Durables with an Application to some Findings of the 1953 Oxford Savings Survey. 1969. Empirical econometrics. Amsterdam : North-Holland Pub. Co. 1991. The logit model: an introduction for economists. London: Edward Arnold. 2003. Logit models from economics and other fields. Cambridge University Press, 2003. Articles, a selection: Cramer, Jan Salomon (1987). "Mean and variance of R 2 {\displaystyle R^{2}} in small and moderate samples". Journal of Econometrics. 35 (2): 253–266. doi:10.1016/0304-4076(87)90027-3. Cramer, Jan Salomon; Ridder, Geert (1991). "Pooling states in the multinomial logit model". Journal of Econometrics. 47 (2): 267–272. doi:10.1016/0304-4076(91)90102-J. Van Praag, C. Mirjam; Cramer, Jan S. (2001). "The roots of entrepreneurship and labour demand: Individual ability and low risk aversion" (PDF). Economica. 68 (269): 45–62. doi:10.1111/1468-0335.00232. Cramer, J. S.; Hartog, J.; Jonker, N.; Van Praag, C. M. (2002). "Low risk aversion encourages the choice for entrepreneurship: an empirical test of a truism" (PDF). Journal of Economic Behavior & Organization. 48 (1): 29–36. doi:10.1016/S0167-2681(01)00222-0. S2CID 154481271. == References == == External links == In memoriam: Mars Cramer on uva.nl |
Wikipedia:Marta Bunge#0 | Marta Cavallo Bunge (née Cavallo; 1938 – 25 October 2022) was an Argentine-Canadian mathematician specializing in category theory, and known for her work on synthetic calculus of variations and synthetic differential topology. She was a professor emeritus at McGill University. == Early life and career == Bunge was a student at a teacher's college in Buenos Aires, the daughter of Ricardo and María Teresa Cavallo. She met Argentine philosopher Mario Bunge while auditing one of his courses, and they eloped in late 1958 (as his second marriage). Bunge earned her Ph.D. from the University of Pennsylvania in 1966. Her dissertation, Categories of Set Valued Functors, was jointly supervised by Peter J. Freyd and William Lawvere. When she was offered a postdoctoral research position at McGill in 1966, her husband followed her there, and they remained in Canada afterwards. She became an assistant professor at McGill in 1969, was promoted to full professor in 1985, and retired as a professor emeritus in 2003. == Books == With her doctoral student Jonathon Funk, Bunge is the co-author of Singular Coverings of Toposes (Lecture Notes in Mathematics 1890, Springer, 2006). With Felipe Gago and Ana María San Luis, Bunge is the co-author of Synthetic Differential Topology (London Mathematical Society Lecture Note Series 448, Cambridge University Press, 2018). == References == == External links == Home page Marta Bunge publications indexed by Google Scholar |
Wikipedia:Martha Guzmán Partida#0 | Martha Dolores Guzmán Partida is a Mexican mathematician specializing in functional analysis, including Fourier analysis, harmonic analysis, and the theory of distributions. She is a professor of mathematics at the Universidad de Sonora. == Education == Guzmán Partida was an undergraduate at the Meritorious Autonomous University of Puebla. She completed her doctorate in 1995 at the National Autonomous University of Mexico. Her dissertation, Hardy Spaces of Conjugates Temperatures, was supervised by Salvador Pérez Esteva. == Recognition == Guzmán was elected to the Mexican Academy of Sciences in 2013. == Selected publications == Source: Alvarez, J; Lakey, J.; Guzmán–Partida, Martha. "Spaces of bounded lambda–central mean oscillation, Morrey spaces, and lambda–central Carleson measures." Collectanea Mathematica, 51 (1), 2000, pp. 1–47. Alvarez, J; Guzmán–Partida, Martha; Pérez–Esteva, S. "Harmonic extensions of distributions." Mathematische Nachrichten, 280 (13–14), 2007, pp.1443–1466. Alvarez, J; Guzmán–Partida, Martha; Skórnik, U. "S'–convolvability with the Poisson kernel in the Euclidean case and the product domain case." Studia Mathematica, 2 (156), 2003, pp.143–163. == References == == External links == Martha Guzmán Partida publications indexed by Google Scholar |
Wikipedia:Martha Helen Barton#0 | Martha Helen Barton (1891–1971), also known as Helen Barton, was an American physicist and mathematician. She was one of the few women to earn a doctorate in the United States in mathematics before World War II. == Biography == Martha Helen Barton was born August 9, 1891, in Baltimore, Maryland, the daughter of Mary Irene Eichelberger and James Sheridan Barton. She attended Western High School graduating with honors and then completed her bachelor's degree from nearby Goucher College in 1913, a member of Phi Beta Kappa. By then she was known as Helen Barton. She worked for one year as an assistant in physics at Goucher and the following year, 1914–1915, began graduate studies in mathematics and physics as a Goucher alumnae fellow at the Johns Hopkins University in Baltimore. === Educator === For four years beginning in 1915, Barton headed the department of chemistry and physics at Salem College, a private college for women in Winston-Salem, North Carolina. She spent the next two years as a math instructor at Wellesley College in Massachusetts. Returning to her graduate study at Johns Hopkins during the summers of 1920 and 1921, she also pursued graduate work at Harvard University in the winter of 1921 even as she taught at Wellesley. Johns Hopkins awarded her a master's degree in June 1922. Her master's thesis was titled: The fundamental theorem of algebra. In 1921, she relocated to teach at a private institution in Michigan, Albion College, where Barton was named associate professor of mathematics. Johns Hopkins awarded her a doctorate in 1926 for mathematics with physics as her first subordinate subject and applied mathematics as the second. Her research was titled: A Modern Presentation of Grassman's Tensor Analysis Mathematics Subject Classification: 01—History and biography. Barton's work inspired her supervisor Frank Morley and Francis D. Murnaghan to note that, "she has considerably simplified the exposition of Grassmann's theory of extensive magnitudes by the use of [the generalized Kronecker symbol]." === Professor === Barton taught for a year as a professor and department head at Alabama College, a rural college for women in Montevallo, Alabama, (today’s University of Montevallo). In 1927, she joined the faculty of the North Carolina College for Women (later known as the Woman's College of the University of North Carolina and now called the University of North Carolina at Greensboro), and she taught as an associate professor and was then named the acting head of the department. In 1928, she was named professor and department head. Although she retired at 68 in 1960 as professor emeritus, she continued her role there part-time as an educator. Helen Barton died March 19, 1971, after a long illness in Greensboro at age 79. She was buried in Baltimore. == Memberships == According to Green, Barton was active in several professional organizations. American Mathematical Society American Association of University Professors Mathematical Association of America Phi Beta Kappa American Association of University Women Sigma Xi == Legacy == The Helen Barton Mathematics and Statistics scholarship at the University of North Carolina at Greensboro is awarded to both undergraduate and graduate students. The Helen Barton Lecture Series in Mathematical Sciences has been held at UNC-Greensboro. In 1960 the Barton faculty area in the McIver classroom building at UNC-Greensboro was named in her honor. == References == == External links == Photograph of Martha Helen Barton at Johns Hopkins University Grassmann's theory of extensive magnitudes |
Wikipedia:Martin Liebeck#0 | Martin Liebeck (born 23 September 1954) is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics. == Career and research == Martin Liebeck studied mathematics at the University of Oxford earning a First Class BA in 1976, an MSc in 1977, and a D.Phil. in 1979, with the Dissertation Finite Permutation Groups under Peter M. Neumann. In January 1991 he was appointed Professor at Imperial College London and became Head of the Pure Mathematics section there in 1997. Liebeck has published over 150 research articles and 10 books. His research interests include algebraic combinatorics, algebraic groups, permutation groups, and finite simple groups. He was elected Fellow of the American Mathematical Society (AMS) in 2019, and was awarded the London Mathematical Society’s Pólya Prize in 2020. In February of 2020 he and Colva Roney-Dougal organized a programme titled "Groups, Representations and Applications" at the Isaac Newton Institute for Mathematical Sciences. == Personal life == Martin is the son of mathematician Hans Liebeck and mathematics educationalist Pamela Liebeck. His wife Ann is a professional musician, and they have two sons Jonathan and Matthew. Martin's main hobbies are playing tennis, especially doubles, and the violin, particularly chamber music. == Selected publications == === Papers === 1990: "The maximal factorizations of the finite simple groups and their automorphism groups", Memoirs Amer. Math. Soc. 86, pp. 1–151 (with C.E. Praeger and Jan Saxl) 1995: "The probability of generating a finite simple group", Geom. Dedicata 56, 103-113 (with A. Shalev) 1998: "On the subgroup structure of classical groups", Invent. Math. 134, 427-453 (with G.M. Seitz) 1999: "Simple groups, permutation groups, and probability", J. Amer. Math. Soc. 12, 497-520 (with A. Shalev) 2001: "Diameters of finite simple groups: sharp bounds and applications", Annals of Math. 154, 383-406 (with A. Shalev) 2004: "The maximal subgroups of positive dimension in exceptional algebraic groups", Memoirs Amer. Math. Soc. 169, no. 802, pp. 1–227 (with G.M. Seitz) 2010: "The Ore Conjecture", J. European Math. Soc., 12, 939–1008 (with E. O’Brien, A. Shalev, P. Tiep) 2018: "Character bounds for finite groups of Lie type", Acta Math. 221, 1–57 (with R. Bezrukavnikov, A. Shalev and P. Tiep) 2019: "Algorithms determining finite simple images of finitely presented groups", Inventiones Math. 218, 623–648 (with M. Bridson, D.M. Evans and D. Segal) === Books === 1990: The Subgroup Structure of the Finite Classical Groups, London Math. Soc. Lecture Note Series No. 129, Cambridge Univ. Press, 303pp. (with P. Kleidman) 2000: A Concise Introduction to Pure Mathematics, CRC Press, 2000; Second Edition, 2005; Third Edition, 2010; Fourth Edition, 2015 2012: Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, Math. Surveys and Monographs Series, Vol. 180, American Math. Soc., 380pp. (with G.M. Seitz) == Awards and distinctions == Johnson University Prize, Oxford University, 1979 Senior Mathematical Prize, Oxford University, 1979 ISI Highly Cited Researcher, 2011 Simons Research Professor, MSRI 2018 The President's Award for Excellence in Leadership, 2019 Fellow of the American Mathematical Society, 2019 London Mathematical Society (LMS) Pólya Prize in 2020 == See also == O'Nan–Scott theorem Rank 3 permutation group == References == == External links == Martin Liebeck at the Mathematics Genealogy Project Personal web page |
Wikipedia:Martin Nowak#0 | Martin Andreas Nowak (born April 7, 1965) is an Austrian-born professor of mathematics and biology at Harvard University. He is a researcher in evolutionary dynamics, and has made contributions to the fields of evolutionary theory and viral dynamics. He held faculty positions at Oxford University and the Institute for Advanced Study in Princeton, before being recruited by Harvard in 2003. During this time, Jeffrey Epstein funded a portion of Nowak's work, helping to set up a center for studying cooperation in evolution. He was the director of Harvard's Program for Evolutionary Dynamics (PED) from 2003 until 2020, when he was suspended from supervising undergraduate research for two years, and had his institute permanently closed down, due to Epstein continuing to have a personal office in the PED building and having unlimited access to the building for over ten years after his conviction for sex crimes. == Early life and education == Nowak was born in Vienna, Austria, on April 7, 1965. He studied at Albertus Magnus Gymnasium and the University of Vienna, earning a doctorate in biochemistry and mathematics in 1989. He worked with Peter Schuster on quasispecies theory, and with Karl Sigmund on evolution of cooperation. Nowak received the highest Austrian honors (Sub auspiciis Praesidentis) when awarded his degree. In 1993, he received his Habilitation at the Institute of Mathematics, University of Vienna. In 2001, he was elected into the Austrian Academy of Sciences. == Career == From 1989 to 1998, Nowak worked at the University of Oxford with Robert May. First, he was an Erwin Schrödinger Postdoctoral Scholar, then a Junior Research Fellow at Wolfson College, and at Keble College. From 1992, he was a Welcome Trust Senior Research Fellow. From 1997 to 1998, Nowak was a professor of mathematical biology. In 1998, Martin Nowak was recruited by the Institute for Advanced Study in Princeton, and was Head of the Institute's first Initiative in Theoretical Biology from 1998 until 2003. In 2003, Nowak joined Harvard University as a Professor of Mathematics and Biology. Nowak was also co-director, with Sarah Coakley, of the Evolution and Theology of Cooperation project at Harvard University, sponsored by the Templeton Foundation, where he was also a member of their Board of Advisors. He was appointed Director of the Program for Evolutionary Dynamics (PED). The PED was funded with a large sum of money from the Jeffrey Epstein VI Foundation. In 2003, Epstein had introduced himself as a science philanthropist, cementing the initial interaction with a large donation to Harvard. Scientific American reported that Nowak's team received US$6.5 million initially. However, he did not receive any funds after 2007, and a couple of hundred thousand dollars remained unspent from his previous funding. After Epstein's 2008 conviction, Harvard president Drew Faust decided that the university would no longer accept his donations. A report, commissioned by the university, found that Nowak allowed Epstein to visit the PED offices more than 40 times after his conviction, to maintain an office with a phone line and webpage, and to interact with students at PED. In 2020, the university placed Nowak on paid academic leave for violation of campus policies including professional conduct and campus access. In 2021, Harvard decided a proportionate response to the severity of Nowak's failure to follow Harvard policies, closing the institute founded with Epstein's money, and donating the remaining money to a foundation helping victims of sexual assault. Harvard also imposed a two year ban on Nowak to supervise undergraduate research, to act as the principal investigator of new grants, and to further supervise new graduate students or postdoctoral fellows. Nowak said he would "take the lessons from this time with me as I move forward". The sanctions against Nowak were lifted in 2023. == Academic research == Martin Nowak contributed to various scientific disciplines, including evolutionary game theory, virology, cancer dynamics, the evolution of cooperation, and the origins of language. Throughout his career, Nowak has collaborated with notable figures such as Robert May, Karl Sigmund, and John Maynard Smith. Nowak has authored books and scientific papers on topics in evolutionary game theory, cancer, viruses, infectious disease, the evolution of language, and the evolution of cooperation. At Oxford, he helped to establish the fields of virus dynamics and spatial games (which later became evolutionary graph theory). He maintained a collaboration with Karl Sigmund in game theory. He collaborated with John Maynard Smith on genetic redundancy, with Baruch Blumberg on hepatitis B virus, and with Robert May as well as George Shaw and Andrew McMichael on HIV. In 1990, Nowak and Robert May proposed a mathematical model which aimed to explain the delay between HIV infection and AIDS. in terms of the evolution of different strains of the virus during individual infections, to the point where the genetic diversity of the virus reaches a threshold whereby the immune system can no longer control it. This detailed quantitative approach depended on assumptions about the biology of HIV which were subsequently confirmed by experiment. At Harvard, Nowak continued his work on virus dynamics, cancer dynamics, and evolutionary game theory. In 2004, he established evolutionary game dynamics in finite populations. In 2005 and 2006 he wrote key papers establishing evolutionary graph theory. In 2006, he suggested that cooperation was a third fundamental principle of evolution beside mutation and selection. In 2007, he proposed prelife - a theory for the origin of life. In 2008 and 2009 he suggested that positive interaction, but not punishment, promotes evolution of cooperation. In 2006, Nowak enunciated and unified the mathematical rules for the five understood bases of the evolution of cooperation (kin selection, direct reciprocity, indirect reciprocity, network reciprocity, and group selection) which published as a paper in Science. Nowak suggests that evolution is constructive because of cooperation, and that we might add “natural cooperation” as a third fundamental principle of evolution beside mutation and natural selection. In 2007, Nowak and colleagues demonstrated that the transition of irregular verbs to regular verbs in English over time obeys a simple inverse-square law, thus providing one of the first quantitative laws in the evolution of language which featured on the front cover of Nature. In 2010, Nowak, with E. O. Wilson, and Corina Tarnita, in Nature, argued that standard natural selection theory represents a simpler and superior approach to kin selection theory in the evolution of eusociality. This work has led to many comments including strong criticism from proponents of inclusive fitness theory. Nowak maintains that the findings of the paper are conclusive and that the field of social evolution should move beyond inclusive fitness theory. He has over 300 scientific publications, of which 40 are in Nature and 15 in Science. Nowak's research interests include: Somatic evolution of cancer, genetic instability, tumor suppressor genes Stem cells, tissue architecture Viruses, infectious diseases, immunology Dynamics of prion infections Quasispecies Genetic redundancy Evolution of language Evolutionary game theory Evolutionary graph theory Evolution of cooperation Prelife and origins of life == Published books == Aside from his scientific career, Nowak has also authored five books. His 2006 work Evolutionary Dynamics: Exploring the Equation of Life received praise for its unique perspective on theoretical biology and won the R.R. Hawkins Award. In 2011, he co-authored SuperCooperators, which argues for cooperation as a fundamental principle of evolution and garnered positive reviews. Additionally, Nowak has edited books, including Evolution, Games, and God, which examines the relationship between theology and evolutionary theory. Nowak identifies himself as a Roman Catholic, advocating for the compatibility of science and religion in the pursuit of truth. His 2024 book, Beyond, is a poetic exploration of the connection between religion and science. In 2015, he received the honorary degree Doctor of Humane Letters from the Dominican School of Philosophy & Theology at Berkeley. Nowak's first book Virus Dynamics: Mathematical Principles of Immunology and Virology, written with Robert May, was published by Oxford University Press in 2001. Nowak's 2006 book Evolutionary Dynamics: Exploring the Equations of Life discusses the evolution of various biological processes. Reviewing Evolutionary Dynamics in Nature, Sean Nee called it a "unique book" that "should be on the shelf of anyone who has, or thinks they might have, an interest in theoretical biology." The book received the Association of American Publishers' R.R. Hawkins Award for the Outstanding Professional, Reference or Scholarly Work of 2006. Nowak's book SuperCooperators: The Mathematics of Evolution, Altruism and Human Behaviour (Or, Why We Need Each Other to Succeed), co-authored with Roger Highfield, was published in 2011. SuperCooperators is both an autobiography of Nowak and a popular presentation of his work in mathematical biology on the evolution of cooperation, the origin of life, and the evolution of language. In the book, Nowak argues that cooperation is the third fundamental principle of evolution, next to mutation and natural selection. SuperCooperators received positive reviews in The New York Times, Nature, and the Financial Times. With Sarah Coakley, Nowak edited the 2013 book Evolution, Games, and God: The Principle of Cooperation, published by Harvard University Press. The volume features articles from experts in multiple fields who explore the interplay between theology and evolutionary theory as pertaining to cooperation and altruism. == Awards == Nowak is a corresponding member of the Austrian Academy of Sciences. He won the Weldon Memorial Prize, the Albert Wander Prize, the Akira Okubo Prize, the David Starr Jordan Prize and the Henry Dale Prize. == Personal life == Nowak is a Roman Catholic. In a 2007 lecture at Harvard, he argued that science and religion occupied different but complementary roles in humans' search for meaning, stating: "Science and religion are two essential components in the search for truth. Denying either is a barren approach." == References == == External links == Official website Martin Nowak: Extended film interview with transcript for the 'Why Are We Here?' documentary series. |
Wikipedia:Martine Deprez#0 | Martine Deprez (born 26 April 1969 in Wiltz) is a Luxembourgish politician who serves as Minister of Health and Social Security in the Frieden-Bettel government since 17 November 2023. She is a member of the CSV. == Early life == Deprez completed her high-school studies in 1988. Afterwards, she studied Mathematics at the Cours universitaires du Luxembourg and later at the University of Liège, Belgium. She obtained her degree (licence) in 1992. Her first job was at the General Inspectorate of Social Security, where she worked as researcher on the Luxembourgish pension system. In 2004, she changed jobs after having completed a training as secondary school teacher and worked as mathematics teacher at Lycée Aline Mayrisch. In 2011, she started teaching at Lycée Hubert Clément. She held this position until her appointment as Minister in November 2023. == Political career == Deprez became member of the Christian Social People's Party in 1986. From 1992 on, she held was active in her local section in Dudelange and the youth department of the party, CSJ. She was also member of the national committee of the CSG, the organization of local politicians in the CSV, in 2000. In 2006, she became a member of the executive committee of the southern district. She also worked in party structures on a national level, becoming deputy secretary general in 2008, working as a contact person for new members. Deprez he was a candidate for the general election in 2009, but did not get elected to the Chamber of Deputies. On 14 November 2009, she was elected as delegate from her district to the national executive board. === Council of State === As the term of Council of State president Georges Schroeder came to an end on 12 June 2012, a new member was needed and Deprez was proposed. On 31 October 2012, she was officially nominated and was sworn-in on 4 November. She worked in the commission for education, research and higher studies as well as the commission for social security and work, using her experience in the Luxembourgish social security system. As membership in the Council of State is incompatible with being a minister, she resigned on 17 November 2023. Her replacement was Alex Penning. === Minister of Health and Social Security === As she was a member of the Council of State, Deprez wasn't a candidate in the 2023 general election. Her nomination as member of the government was a surprise, as she was perceived as newcomer. During coalition talks, newly elected DP member of parliament and virologist Gérard Schockmel had proposed himself for Minister of Health, which added further surprise to Deprez' nomination. She was sworn in together with every other member of the government on 17 November 2023. When asked about her political priorities, she stated that she wanted to implement the coalition agreement, which she had been involved in negotiating. In an interview with Radio 100,7 on 28 November 2023, Deprez gave a first insight into her views on the overhaul of the Luxembourgish pension system. She stated needs for consultations with the civil society if prognoses showed that the pension system would turn out to be in an imbalance in a few years. She stated she was against a higher cap on deposits, as this would mean the payoffs would need to grow in the same manner. After a meeting with the respective parliamentary commission, she was criticized, having stated wanting to cut pensions and incentivizing occupational and private pension insurances. In interviews, Deprez emphasised that she only wanted to "strengthen" the so-called second and third pillars of the pension system without reducing the compulsory state pension. Trade union leaders condemned these announcements, criticizing Deprez for talking with the press about her plans before bringing them up with the social partners and for wanting to "privatize" the pension system. A new report on the status of the pension system was announced for June 2024, with formal discussions about reforms beginning in autumn. In January 2024, it was reported that, from 2022 to 2023, the sales of cigarettes in Luxembourg had gone up by 400 million. Deprez stated that this was only alarming if it meant that people in Luxembourg would smoke more. A lot of cigarette in Luxembourg would be bought by people not living in the country, due to lower prices compared to neighbouring countries. Although she was aware of the risks of nicotine pouches and emphasised that they could tempt young people to start smoking, she was not in favour of a ban. Due to the small size of the country and the open borders, young people would then travel to neighbouring countries to buy nicotine pouches. After their petition reached the necessary quorum, a group of activists demanded a ban on so-called "virginity certificates" in a public hearing in the Chamber of Deputies on 18 April 2024. Deprez emphasised that such a ban was part of the government agreement, although no timeline for the introduction of a corresponding law had been worked out yet. She stated that a possible ban on hymen reconstruction should be part of the discussions. == Voluntary activities == Between 2008 and 2012, Deprez was Secretary General of the Union Grand-Duc Adolphe (UGDA), an umbrella organization for music interests in Luxembourg. After an internal dispute over the management styles, Deprez became interim president of the UGDA after an extraordinary congress on 29 October 2015. This position was confirmed on 28 February 2016. Deprez vowed to renew the statues of the UGDA and to intensify the relations with member associations. In July 2016, she was confronted with accusations from the Fédération générale de la fonction communale, the municipal employees' union about poor working conditions and insecure employment relationships for music school teachers with temporary employment contracts, for which the UGDA was responsible. Deprez denied these accusations. She resigned in January 2019, citing time constraints. == Personal life == Deprez is married to a man and has three children. == References == |
Wikipedia:Martyn Cundy#0 | Henry Martyn Cundy (23 December 1913 – 25 February 2005) was a mathematics teacher and professor in Britain and Malawi as well as a singer, musician and poet. He was one of the founders of the School Mathematics Project to reform O level and A level teaching. Through this he had a big effect on maths teaching in Britain and especially in Africa. == Education and career == Cundy attended Monkton Combe School and then read mathematics at Trinity College, Cambridge, where he earned a PhD in quantum theory in 1938. In 1937, Cundy was awarded the Cambridge University Rayleigh Prize for Mathematical Physics (now known as the Rayleigh-Knight Prize) for an essay entitled "Motion in a Tetrahedral Field". Others awarded the Rayleigh Prize include Royal Society Fellows Alan Turing and Fred Hoyle; instead of acquiring a University position, Cundy initially chose work at the secondary school level. He taught at the Sherborne School from 1938 to 1966 and became prominently involved in the reform of school mathematics teaching in Great Britain. Secondary school Mathematics teachers became aware of Cundy after the appearance of his and his co-author A.P. Rollett's Mathematical Models, in continuous publication since 1952. A book focusing on the model construction of many of the regular polyhedra and other mathematical objects, Mathematical Models has remained "an inspiration for generations of mathematics teachers". Cundy was Deputy Director of the School Mathematics Project between 1967 and 1968. In 1968 he became Chair of Mathematics at the University of Malawi, and held the post until 1975. Cundy spent many years publishing dozens of articles in The Mathematical Gazette, including at age 89 the "Article of the Year" for 2003, entitled "A Journey round the Triangle: Lester's Circle, Kiepert's Hyperbola and a Configuration from Morley". == Personal life == He married Kathleen Ethel ("Kittie") Hemmings in 1939 and had three children, including Ian Cundy, successively Bishop of Lewes and of Peterborough. Martyn Cundy was a devout Christian and especially notable for his ecumenical views toward worship. In 1932 he was secretary of the Cambridge University Prayer Fellowship. Subsequently he served as a Methodist lay preacher and after taking up his position at the University of Malawi, an elder in the Malawi Presbyterian Church. In Malawi Cundy learned to speak the Chewa language and he and his wife Kittie were active members of the university community there. The Cundys were enthusiastic trekkers and together they contributed a walking guide to the Zomba Massif. On returning to the U.K. in 1975, the Cundys settled in Kendal and became active in the church community there. Martyn Cundy continued with his contributions to mathematics, religion and pedagogy for the remainder of his life. == Publications == The Faith of a Christian (London: Inter-Varsity Press, 1950). Mathematical Models, with A.P. Rollett (London: Oxford University Press, 1952). More than fifty articles in the Mathematical Gazette, including "Article of the Year" in 2003. == References == |
Wikipedia:Mary Beisiegel#0 | Mary D. Beisiegel is a Professor in the Department of Mathematics at Oregon State University. She is a Whiteley Faculty scholar for Teaching Excellence. Her research is in mathematics education. == Education and career == Beisiegel received her PhD in Mathematics from the University of Alberta in 2009. Her dissertation, Being (Almost) a Mathematician: Teacher Identity Formation in Post-Secondary Mathematics, was supervised by Elaine Simmt, David Pimm, and Terrance Ronald Carson. == Awards and honors == Beisiegel received the Mathematical Association of America's Henry L. Adler Award in 2017. == References == |
Wikipedia:Mary Bradburn#0 | Mary Bradburn (1918–2000) was a British mathematics educator who became president of the Mathematical Association for the 1994–1995 term. == Education and career == Bradburn was born on 17 March 1918 in Normanby in North Yorkshire, the daughter of a marine engineer and a Scotswoman. She attended a school that didn't approve of girls studying mathematics, but allowed her to progress through the mathematics curriculum at her own rate, several years ahead of the other students. She earned a state scholarship, but at 17, she was below the required age for Oxford and Cambridge, so she ended up going to Royal Holloway College. She was a student there beginning in 1935 and, despite multiple extracurricular activities, earned first class honours in mathematics in 1938, and completed a master's degree there in 1940. With another scholarship from the University of London, she went to the University of Edinburgh for graduate study with Max Born, beginning in 1941; her dissertation was The Statistical Thermodynamics of Crystal Lattices. She taught briefly at Edinburgh and the University of Dundee before returning to Royal Holloway as an instructor in 1945. She remained at Royal Holloway through its 1965 transition from a women's college to a coeducational one (a change that she supported), until her retirement in 1980. == Recognition and legacy == She became a Fellow of the Royal Astronomical Society in 1955. The mathematics department of Royal Holloway offers an annual prize to undergraduates, the Mary Bradburn Prize, named in her memory. The British Federation of Women Graduates also offers a Mary Bradburn Prize, from a bequest left by Bradburn. == References == |
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