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https://en.wikipedia.org/wiki/Canonical%20analysis | In statistics, canonical analysis (from bar, measuring rod, ruler) belongs to the family of regression methods for data analysis. Regression analysis quantifies a relationship between a predictor variable and a criterion variable by the coefficient of correlation r, coefficient of determination r2, and the standard re... |
https://en.wikipedia.org/wiki/Eigenvalues%20and%20eigenvectors | In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor.
Geometrically, a transformation matrix... |
https://en.wikipedia.org/wiki/Padovan%20sequence | In number theory, the Padovan sequence is the sequence of integers P(n) defined by the initial values
and the recurrence relation
The first few values of P(n) are
1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ...
A Padovan prime is a Padovan number that is prime. The first Padov... |
https://en.wikipedia.org/wiki/Dini%20derivative | In mathematics and, specifically, real analysis, the Dini derivatives (or Dini derivates) are a class of generalizations of the derivative. They were introduced by Ulisse Dini, who studied continuous but nondifferentiable functions.
The upper Dini derivative, which is also called an upper right-hand derivative, of a c... |
https://en.wikipedia.org/wiki/Sieve%20%28category%20theory%29 | In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection of open subsets of a fixed open set in topology. In a Grothendieck topology, certain sieves become categorical analogues of open covers in topology. Sieves were introdu... |
https://en.wikipedia.org/wiki/List%20of%20busiest%20airports%20by%20international%20passenger%20traffic | The following is a list of the world's largest airports by international passenger traffic.
2022 statistics
Airports Council International's preliminary figures are as follows.
2021 statistics
Airports Council International's preliminary figures are as follows.
2020 statistics
Airports Council International's preli... |
https://en.wikipedia.org/wiki/Rosser%27s%20theorem | In number theory, Rosser's theorem states that the th prime number is greater than , where is the natural logarithm function. It was published by J. Barkley Rosser in 1939.
Its full statement is:
Let be the th prime number. Then for
In 1999, Pierre Dusart proved a tighter lower bound:
See also
Prime number theo... |
https://en.wikipedia.org/wiki/Vital%20rates | Vital rates refer to how fast vital statistics change in a population (usually measured per 1000 individuals). There are 2 categories within vital rates: crude rates and refined rates.
Crude rates measure vital statistics in a general population (overall change in births and deaths per 1000).
Refined rates measure th... |
https://en.wikipedia.org/wiki/Choice%20%28disambiguation%29 | Choice consists of the mental process of thinking involved with the process of judging the merits of multiple options and selecting one of them for action.
Choice may also refer to:
Mathematics
Binomial coefficient, a mathematical function describing number of possible selections of subsets ('seven choose two')
Axi... |
https://en.wikipedia.org/wiki/Gertrude%20Mary%20Cox | Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Resea... |
https://en.wikipedia.org/wiki/F-algebra | In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature... |
https://en.wikipedia.org/wiki/Algebra%20%28disambiguation%29 | The word 'algebra' is used for various branches and structures of mathematics. For their overview, see Algebra.
The bare word "algebra"
The bare word "algebra" may refer to:
Elementary algebra
Abstract algebra
Algebra over a field
In universal algebra, algebra has an axiomatic definition, roughly as an instance o... |
https://en.wikipedia.org/wiki/Evert%20Willem%20Beth | Evert Willem Beth (7 July 1908 – 12 April 1964) was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics. He was a member of the Significs Group.
Biography
Beth was born in Almelo, a small town in the eastern Netherlands. His father had studied mathematics and physics at ... |
https://en.wikipedia.org/wiki/David%20Masser | David William Masser (born 8 November 1948) is Professor Emeritus in the Department of Mathematics and Computer Science at the University of Basel. He is known for his work in transcendental number theory, Diophantine approximation, and Diophantine geometry. With Joseph Oesterlé in 1985, Masser formulated the abc conj... |
https://en.wikipedia.org/wiki/Piecewise%20linear%20manifold | In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined by means of an atlas, such that one can pass from chart to chart in it by piecewise linear functions. This is slightly stronger than the topological notion of a tr... |
https://en.wikipedia.org/wiki/Reduced%20product | In model theory, a branch of mathematical logic, and in algebra, the reduced product is a construction that generalizes both direct product and ultraproduct.
Let {Si | i ∈ I} be a nonempty family of structures of the same signature σ indexed by a set I, and let U be a proper filter on I. The domain of the reduced prod... |
https://en.wikipedia.org/wiki/Loop%20space | In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, i.e. continuous pointed maps from the pointed circle S1 to X, equipped with the compact-open topology. Two loops can be multiplied by concatenation. With this operation, the loop space is an A∞-s... |
https://en.wikipedia.org/wiki/Sylvester%20matrix | In mathematics, a Sylvester matrix is a matrix associated to two univariate polynomials with coefficients in a field or a commutative ring. The entries of the Sylvester matrix of two polynomials are coefficients of the polynomials. The determinant of the Sylvester matrix of two polynomials is their resultant, which is ... |
https://en.wikipedia.org/wiki/Method%20of%20moments%20%28statistics%29 | In statistics, the method of moments is a method of estimation of population parameters. The same principle is used to derive higher moments like skewness and kurtosis.
It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the pa... |
https://en.wikipedia.org/wiki/Interval%20arithmetic | [[File:Set of curves Outer approximation.png|345px|thumb|right|Tolerance function (turquoise) and interval-valued approximation (red)]]
Interval arithmetic (also known as interval mathematics; interval analysis or interval computation) is a mathematical technique used to mitigate rounding and measurement errors in math... |
https://en.wikipedia.org/wiki/Michael%20Resnik | Michael David Resnik (; born March 20, 1938) is a leading contemporary American philosopher of mathematics.
Biography
Resnik obtained his B.A. in mathematics and philosophy at Yale University in 1960, and his PhD in Philosophy at Harvard University in 1964. He wrote his thesis on Frege. He was appointed Associate Prof... |
https://en.wikipedia.org/wiki/Conical%20intersection | In quantum chemistry, a conical intersection of two or more potential energy surfaces is the set of molecular geometry points where the potential energy surfaces are degenerate (intersect) and the non-adiabatic couplings between these states are non-vanishing. In the vicinity of conical intersections, the Born–Oppenhei... |
https://en.wikipedia.org/wiki/Airport%20problem | In mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport runway among different players who need runways of different lengths. The problem was introduced by S. C. Littlechild and G. Owen in 1973. Their proposed sol... |
https://en.wikipedia.org/wiki/Universal%20bundle | In mathematics, the universal bundle in the theory of fiber bundles with structure group a given topological group , is a specific bundle over a classifying space , such that every bundle with the given structure group over is a pullback by means of a continuous map .
Existence of a universal bundle
In the CW compl... |
https://en.wikipedia.org/wiki/Obstruction%20theory | In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants.
In the original work of Stiefel and Whitney, characteristic classes were defined as obstructions to the existence of certain fields of linear independent vectors. Obstruction theory ... |
https://en.wikipedia.org/wiki/Hauptvermutung | The Hauptvermutung of geometric topology is a now refuted conjecture asking whether any two triangulations of a triangulable space have subdivisions that are combinatorially equivalent, i.e. the subdivided triangulations are built up in the same combinatorial pattern. It was originally formulated as a conjecture in 190... |
https://en.wikipedia.org/wiki/Kirby%E2%80%93Siebenmann%20class | In mathematics, more specifically in geometric topology, the Kirby–Siebenmann class is an obstruction for topological manifolds to allow a PL-structure.
The KS-class
For a topological manifold M, the Kirby–Siebenmann class is an element of the fourth cohomology group of M that vanishes if M admits a piecewise linear ... |
https://en.wikipedia.org/wiki/Exotic%20R4 | {{DISPLAYTITLE:Exotic R4}}
In mathematics, an exotic is a differentiable manifold that is homeomorphic (i.e. shape preserving) but not diffeomorphic (i.e. non smooth) to the Euclidean space The first examples were found in 1982 by Michael Freedman and others, by using the contrast between Freedman's theorems about to... |
https://en.wikipedia.org/wiki/Donaldson%27s%20theorem | In mathematics, and especially differential topology and gauge theory, Donaldson's theorem states that a definite intersection form of a compact, oriented, smooth manifold of dimension 4 is diagonalisable. If the intersection form is positive (negative) definite, it can be diagonalized to the identity matrix (negative ... |
https://en.wikipedia.org/wiki/Tarski%27s%20axioms | Tarski's axioms, due to Alfred Tarski, are an axiom set for the substantial fragment of Euclidean geometry that is formulable in first-order logic with identity, and requiring no set theory (i.e., that part of Euclidean geometry that is formulable as an elementary theory). Other modern axiomizations of Euclidean geome... |
https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck%20process | In mathematics, the Ornstein–Uhlenbeck process is a stochastic process with applications in financial mathematics and the physical sciences. Its original application in physics was as a model for the velocity of a massive Brownian particle under the influence of friction. It is named after Leonard Ornstein and George E... |
https://en.wikipedia.org/wiki/Serre%27s%20property%20FA | In mathematics, Property FA is a property of groups first defined by Jean-Pierre Serre.
A group G is said to have property FA if every action of G on a tree has a global fixed point.
Serre shows that if a group has property FA, then it cannot split as an amalgamated product or HNN extension; indeed, if G is contained... |
https://en.wikipedia.org/wiki/Uniformization | Uniformization may refer to:
Uniformization (set theory), a mathematical concept in set theory
Uniformization theorem, a mathematical result in complex analysis and differential geometry
Uniformization (probability theory), a method to find a discrete-time Markov chain analogous to a continuous-time Markov chain
U... |
https://en.wikipedia.org/wiki/List%20of%20University%20of%20G%C3%B6ttingen%20people | This is a list of people who have taught or studied at the University of Göttingen:
Natural sciences and mathematics
A
Wilhelm Ackermann — Mathematics
Immo Appenzeller — Astrophysics
Cahit Arf — (Doctorate in Mathematics)
B
Heinrich Behmann — Mathematical Logic
Paul Bernays — Mathematics, mathematical logic — (Stu... |
https://en.wikipedia.org/wiki/Karl%20Georg%20Christian%20von%20Staudt | Karl Georg Christian von Staudt (24 January 1798 – 1 June 1867) was a German mathematician who used synthetic geometry to provide a foundation for arithmetic.
Life and influence
Karl was born in the Free Imperial City of Rothenburg, which is now called Rothenburg ob der Tauber in Germany. From 1814 he studied in Gymna... |
https://en.wikipedia.org/wiki/S.%20K.%20Gurunathan | S. K. Gurunathan (1 August 1908 – 5 May 1966) was a sports journalist and one of the pioneers of cricket statistics in India.
Gurunathan studied in the Hindu High School in Triplicane, Madras. He started his journalistic career in the advertisement section of The Hindu in 1928. He became a reporter in 1938 and from 19... |
https://en.wikipedia.org/wiki/Complex%20Lie%20group | In geometry, a complex Lie group is a Lie group over the complex numbers; i.e., it is a complex-analytic manifold that is also a group in such a way is holomorphic. Basic examples are , the general linear groups over the complex numbers. A connected compact complex Lie group is precisely a complex torus (not to be c... |
https://en.wikipedia.org/wiki/Love%2C%20Hell%20or%20Right | Love Hell or Right (Da Come Up) is an album by the hip hop producer DJ Mathematics, who is a DJ with Wu-Tang Clan.
Completely mixed, arranged and produced by Mathematics himself, Love, Hell or Right was released August 26, 2003, on his own Quewisha Records label in conjunction with High Times Records, and it went on t... |
https://en.wikipedia.org/wiki/Corner%20solution | In mathematics and economics, a corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a corner solution is when the chooser is either unwilling or unable to make a trade-off between goods.
In eco... |
https://en.wikipedia.org/wiki/Tree%20%28descriptive%20set%20theory%29 | In descriptive set theory, a tree on a set is a collection of finite sequences of elements of such that every prefix of a sequence in the collection also belongs to the collection.
Definitions
Trees
The collection of all finite sequences of elements of a set is denoted .
With this notation, a tree is a nonempty su... |
https://en.wikipedia.org/wiki/Decagram | Decagram may refer to:
10 gram, or 0.01 kilogram, a unit of mass, in SI referred to as a dag
Decagram (geometry), geometric figure |
https://en.wikipedia.org/wiki/Rectification%20%28geometry%29 | In Euclidean geometry, rectification, also known as critical truncation or complete-truncation, is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points. The resulting polytope will be bounded by vertex figure facets and the rectified facets of the ... |
https://en.wikipedia.org/wiki/Resultant | In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also call... |
https://en.wikipedia.org/wiki/Rational%20zeta%20series | In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function. Specifically, given a real number x, the rational zeta series for x is given by
where qn is a rational number, the va... |
https://en.wikipedia.org/wiki/Gauss%E2%80%93Kuzmin%20distribution | In mathematics, the Gauss–Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1). The distribution is named after Carl Friedrich Gauss, who derived it around... |
https://en.wikipedia.org/wiki/SYSTAT%20%28statistics%20package%29 | SYSTAT is a statistics and statistical graphics software package, developed by Leland Wilkinson in the late 1970s, who was at the time an assistant professor of psychology at the University of Illinois at Chicago. Systat Software Inc. was incorporated in 1983 and grew to over 50 employees.
In 1995, SYSTAT was sold to ... |
https://en.wikipedia.org/wiki/Zeta%20function%20universality | In mathematics, the universality of zeta functions is the remarkable ability of the Riemann zeta function and other similar functions (such as the Dirichlet L-functions) to approximate arbitrary non-vanishing holomorphic functions arbitrarily well.
The universality of the Riemann zeta function was first proven by in ... |
https://en.wikipedia.org/wiki/Cross-covariance | In probability and statistics, given two stochastic processes and , the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation for the expectation operator, if the processes have the mean functions and , then the cross-covariance is giv... |
https://en.wikipedia.org/wiki/Front%20velocity | In physics, front velocity is the speed at which the first rise of a pulse above zero moves forward.
In mathematics, it is used to describe the velocity of a propagating front in the solution of hyperbolic partial differential equation.
Various velocities
Associated with propagation of a disturbance are several diff... |
https://en.wikipedia.org/wiki/Selberg%20class | In mathematics, the Selberg class is an axiomatic definition of a class of L-functions. The members of the class are Dirichlet series which obey four axioms that seem to capture the essential properties satisfied by most functions that are commonly called L-functions or zeta functions. Although the exact nature of th... |
https://en.wikipedia.org/wiki/Stickelberger%27s%20theorem | In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class groups of cyclotomic fields. A special case was first proven by Ernst Kummer (1847) while the general result is due to Ludwig Stickelberger (1890).
The Stickelberger e... |
https://en.wikipedia.org/wiki/David%20Blackwell | David Harold Blackwell (April 24, 1919 – July 8, 2010) was an American statistician and mathematician who made significant contributions to game theory, probability theory, information theory, and statistics. He is one of the eponyms of the Rao–Blackwell theorem. He was the first African American inducted into the Nati... |
https://en.wikipedia.org/wiki/Explicit%20formulae%20for%20L-functions | In mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function. Such explicit formulae have been applied also to questions on bounding the discriminant of an algebraic number fi... |
https://en.wikipedia.org/wiki/Concurrent%20lines | In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point. They are in contrast to parallel lines.
Examples
Triangles
In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors:
A triangle's alt... |
https://en.wikipedia.org/wiki/Einstein%20coefficients | Einstein coefficients are quantities describing the probability of absorption or emission of a photon by an atom or molecule. The Einstein A coefficients are related to the rate of spontaneous emission of light, and the Einstein B coefficients are related to the absorption and stimulated emission of light. Throughout t... |
https://en.wikipedia.org/wiki/Calculus%20%28medicine%29 | A calculus (: calculi), often called a stone, is a concretion of material, usually mineral salts, that forms in an organ or duct of the body. Formation of calculi is known as lithiasis (). Stones can cause a number of medical conditions.
Some common principles (below) apply to stones at any location, but for specifics... |
https://en.wikipedia.org/wiki/Lov%C3%A1sz%20local%20lemma | In probability theory, if a large number of events are all independent of one another and each has probability less than 1, then there is a positive (possibly small) probability that none of the events will occur. The Lovász local lemma allows one to relax the independence condition slightly: As long as the events are ... |
https://en.wikipedia.org/wiki/Johann%20Gottlieb%20N%C3%B6rremberg | Johann Gottlieb Christian Nörremberg (11 August 1787, in Pustenbach – 20 July 1862) was a German physicist who worked on the polarization of light.
From 1823 he taught classes in mathematics and physics at the military school in Darmstadt. In 1833 he became a professor of mathematics, physics and astronomy at the Univ... |
https://en.wikipedia.org/wiki/Generic%20filter | In the mathematical field of set theory, a generic filter is a kind of object used in the theory of forcing, a technique used for many purposes, but especially to establish the independence of certain propositions from certain formal theories, such as ZFC. For example, Paul Cohen used forcing to establish that ZFC, if ... |
https://en.wikipedia.org/wiki/Poisson%20kernel | In mathematics, and specifically in potential theory, the Poisson kernel is an integral kernel, used for solving the two-dimensional Laplace equation, given Dirichlet boundary conditions on the unit disk. The kernel can be understood as the derivative of the Green's function for the Laplace equation. It is named for Si... |
https://en.wikipedia.org/wiki/Geometry%20processing | Geometry processing, or mesh processing, is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation and transmission of complex 3D models. As the name implies, many of the co... |
https://en.wikipedia.org/wiki/Dirichlet%20beta%20function | In mathematics, the Dirichlet beta function (also known as the Catalan beta function) is a special function, closely related to the Riemann zeta function. It is a particular Dirichlet L-function, the L-function for the alternating character of period four.
Definition
The Dirichlet beta function is defined as
or, equi... |
https://en.wikipedia.org/wiki/Term%20algebra | In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X. Other synonyms for the notion include ab... |
https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s%20constant | In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number
where is the Riemann zeta function. It has an approximate value of
.
The constant is named after Roger Apéry. It arises naturally in a number of physical problems, including in the second-... |
https://en.wikipedia.org/wiki/Covariance%20and%20correlation | In probability theory and statistics, the mathematical concepts of covariance and correlation are very similar. Both describe the degree to which two random variables or sets of random variables tend to deviate from their expected values in similar ways.
If X and Y are two random variables, with means (expected values... |
https://en.wikipedia.org/wiki/Circular%20symmetry | In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself.
Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal group SO(2), and unitary group U(1). Reflective circular ... |
https://en.wikipedia.org/wiki/Solenoid%20%28mathematics%29 | This page discusses a class of topological groups. For the wrapped loop of wire, see Solenoid.
In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms
where each is a circl... |
https://en.wikipedia.org/wiki/Blum%20integer | In mathematics, a natural number n is a Blum integer if is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form , for some integer t. Integers of this form are referred to as Blum primes. This means that the factors of a Blum integer are Gaussian primes wi... |
https://en.wikipedia.org/wiki/Bishop%20Stopford%27s%20School | Bishop Stopford's School, commonly known as Bishop Stopford's, or (simply) just Bishop's, is a voluntary aided co-educational secondary school specialising in mathematics, computing and engineering, with a sixth form. It is a London Diocesan Church of England school with worship in a relatively High Church Anglo-Catho... |
https://en.wikipedia.org/wiki/Cycles%20and%20fixed%20points | In mathematics, the cycles of a permutation of a finite set S correspond bijectively to the orbits of the subgroup generated by acting on S. These orbits are subsets of S that can be written as , such that
for , and .
The corresponding cycle of is written as ( c1 c2 ... cn ); this expression is not unique since ... |
https://en.wikipedia.org/wiki/Perfect%20set%20property | In descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty perfect subset (Kechris 1995, p. 150). Note that having the perfect set property is not the same as being a perfect set.
As nonempty perfect sets in a Polish space always have the cardinality ... |
https://en.wikipedia.org/wiki/Somos%27%20quadratic%20recurrence%20constant | In mathematics, Somos' quadratic recurrence constant, named after Michael Somos, is the number
This can be easily re-written into the far more quickly converging product representation
which can then be compactly represented in infinite product form by:
The constant σ arises when studying the asymptotic behaviour o... |
https://en.wikipedia.org/wiki/Bartlett%27s%20test | In statistics, Bartlett's test, named after Maurice Stevenson Bartlett, is used to test homoscedasticity, that is, if multiple samples are from populations with equal variances. Some statistical tests, such as the analysis of variance, assume that variances are equal across groups or samples, which can be verified with... |
https://en.wikipedia.org/wiki/William%20Gemmell%20Cochran | William Gemmell Cochran (15 July 1909 – 29 March 1980) was a prominent statistician. He was born in Scotland but spent most of his life in the United States.
Cochran studied mathematics at the University of Glasgow and the University of Cambridge. He worked at Rothamsted Experimental Station from 1934 to 1939, when he... |
https://en.wikipedia.org/wiki/Australian%20Science%20and%20Mathematics%20School | The Australian Science and Mathematics School (ASMS) is a coeducational public senior high school for Years 10–12 located on the Sturt campus of Flinders University in Bedford Park, a southern suburb of Adelaide, the capital of South Australia. As the school is unzoned, it attracts students from all across the Adelaide... |
https://en.wikipedia.org/wiki/Augmentation%20ideal | In algebra, an augmentation ideal is an ideal that can be defined in any group ring.
If G is a group and R a commutative ring, there is a ring homomorphism , called the augmentation map, from the group ring to , defined by taking a (finite) sum to (Here and .) In less formal terms, for any element , for any e... |
https://en.wikipedia.org/wiki/Join%20Java | Join Java is a programming language based on the join-pattern that extends the standard Java programming language with the join semantics of the join-calculus. It was written at the University of South Australia within the Reconfigurable Computing Lab by Dr. Von Itzstein.
Language characteristics
The Join Java exten... |
https://en.wikipedia.org/wiki/J%C3%BAlio%20C%C3%A9sar%20de%20Mello%20e%20Souza | Júlio César de Mello e Souza (Rio de Janeiro, May 6, 1895 – Recife, June 18, 1974), was a Brazilian writer and mathematics teacher. He was well known in Brazil and abroad for his books on recreational mathematics, most of them published under the pen names of Malba Tahan and Breno de Alencar Bianco.
He wrote 69 novels... |
https://en.wikipedia.org/wiki/Stirling%20numbers%20of%20the%20second%20kind | In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by or . Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the st... |
https://en.wikipedia.org/wiki/Stirling%20numbers%20of%20the%20first%20kind | In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers of the first kind count permutations according to their number of cycles (counting fixed points as cycles of length one).
The Stirling numbers of the first and second... |
https://en.wikipedia.org/wiki/Fr%C3%B6licher%20space | In mathematics, Frölicher spaces extend the notions of calculus and smooth manifolds. They were introduced in 1982 by the mathematician Alfred Frölicher.
Definition
A Frölicher space consists of a non-empty set X together with a subset C of Hom(R, X) called the set of smooth curves, and a subset F of Hom(X, R) called ... |
https://en.wikipedia.org/wiki/List%20of%20computer%20algebra%20systems | The following tables provide a comparison of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language. A CAS may include a user interface and graphics capabi... |
https://en.wikipedia.org/wiki/Universally%20measurable%20set | In mathematics, a subset of a Polish space is universally measurable if it is measurable with respect to every complete probability measure on that measures all Borel subsets of . In particular, a universally measurable set of reals is necessarily Lebesgue measurable (see below).
Every analytic set is universally... |
https://en.wikipedia.org/wiki/Distribution%20ensemble | In cryptography, a distribution ensemble or probability ensemble is a family of distributions or random variables where is a (countable) index set, and each is a random variable, or probability distribution. Often and it is required that each have a certain property for n sufficiently large.
For example, a unifor... |
https://en.wikipedia.org/wiki/Basic%20hypergeometric%20series | In mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series.
A series xn is called hypergeometric if the ratio of successive terms xn+1/xn is a rational function of n. If th... |
https://en.wikipedia.org/wiki/Richard%20Rusczyk | Richard Rusczyk (; ; born September 21, 1971) is the founder and chief executive officer of Art of Problem Solving Inc. (as well as the website, which serves as a mathematics forum and place to hold online classes) and a co-author of the Art of Problem Solving textbooks. Rusczyk was a national Mathcounts participant in... |
https://en.wikipedia.org/wiki/Infinity-Borel%20set | In set theory, a subset of a Polish space is ∞-Borel if it
can be obtained by starting with the open subsets of , and transfinitely iterating the operations of complementation and wellordered union. This concept is usually considered without the assumption of the axiom of choice, which means that the ∞-Borel sets may ... |
https://en.wikipedia.org/wiki/Octahedral%20molecular%20geometry | In chemistry, octahedral molecular geometry, also called square bipyramidal, describes the shape of compounds with six atoms or groups of atoms or ligands symmetrically arranged around a central atom, defining the vertices of an octahedron. The octahedron has eight faces, hence the prefix octa. The octahedron is one of... |
https://en.wikipedia.org/wiki/List%20of%20properties%20of%20sets%20of%20reals | This article lists some properties of sets of real numbers. The general study of these concepts forms descriptive set theory, which has a rather different emphasis from general topology.
Definability properties
Borel set
Analytic set
C-measurable set
Projective set
Inductive set
Infinity-Borel set
S... |
https://en.wikipedia.org/wiki/Exponential%20object | In mathematics, specifically in category theory, an exponential object or map object is the categorical generalization of a function space in set theory. Categories with all finite products and exponential objects are called cartesian closed categories. Categories (such as subcategories of Top) without adjoined product... |
https://en.wikipedia.org/wiki/Association%20scheme | The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. In algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial des... |
https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Italy | In the NUTS (Nomenclature of Territorial Units for Statistics) codes of Italy (IT), the three levels are:
NUTS codes
The following codes have been discontinued:
ITC45 (Milano) was split into ITC4C and ITC4D.
ITD (Northeast Italy) became ITH.
ITE (Central Italy) became ITI.
ITF41 (Foggia) and ITF42 (Bari) were spl... |
https://en.wikipedia.org/wiki/Mathematical%20Tripos | The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. It is the oldest Tripos examined at the university.
Origin
In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate students of the Universit... |
https://en.wikipedia.org/wiki/Fermionic%20field | In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics. Fermionic fields obey canonical anticommutation relations rather than the canonical commutation relations of bosonic fields.
The most prominent example of a fermionic field is the Dirac f... |
https://en.wikipedia.org/wiki/Generalized%20arithmetic%20progression | In mathematics, a generalized arithmetic progression (or multiple arithmetic progression) is a generalization of an arithmetic progression equipped with multiple common differences – whereas an arithmetic progression is generated by a single common difference, a generalized arithmetic progression can be generated by mu... |
https://en.wikipedia.org/wiki/Zone%20d%27%C3%A9tudes%20et%20d%27am%C3%A9nagement%20du%20territoire | In 1967 the (French National Institute for Statistics and Economic Studies, INSEE), together with the French Commissariat général and DATAR () declared the nominal division of France into eight large regions. These were named (Research and National Development Zones) or ZEAT.
Until 2016, the ZEAT corresponded to the... |
https://en.wikipedia.org/wiki/Mathematics%20%28producer%29 | Ronald Maurice Bean, better known professionally as Mathematics (also known as Allah Mathematics) (born October 21, 1971), is a hip hop producer and DJ for the Wu-Tang Clan and its solo and affiliate projects. He designed the Wu-Tang Clan logo.
Biography
Born and raised in Jamaica, Queens, New York, Mathematics was in... |
https://en.wikipedia.org/wiki/Continuity | Continuity or continuous may refer to:
Mathematics
Continuity (mathematics), the opposing concept to discreteness; common examples include
Continuous probability distribution or random variable in probability and statistics
Continuous game, a generalization of games used in game theory
Law of continuity, a heuris... |
https://en.wikipedia.org/wiki/Frobenius%20pseudoprime | In number theory, a Frobenius pseudoprime is a pseudoprime, whose definition was inspired by the quadratic Frobenius test described by Jon Grantham in a 1998 preprint and published in 2000. Frobenius pseudoprimes can be defined with respect to polynomials of degree at least 2, but they have been most extensively studie... |
https://en.wikipedia.org/wiki/L%28R%29 | In set theory, L(R) (pronounced L of R) is the smallest transitive inner model of ZF containing all the ordinals and all the reals.
Construction
It can be constructed in a manner analogous to the construction of L (that is, Gödel's constructible universe), by adding in all the reals at the start, and then iterating th... |
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