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https://en.wikipedia.org/wiki/Parabigyrate%20rhombicosidodecahedron | In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.
Alternative Johnson solids, constructed by rotating different cupolae of a rhombico... |
https://en.wikipedia.org/wiki/Paragyrate%20diminished%20rhombicosidodecahedron | In geometry, the paragyrate diminished rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and the opposing pentagonal cupola removed.
External links
Johnson solids |
https://en.wikipedia.org/wiki/Metagyrate%20diminished%20rhombicosidodecahedron | In geometry, the metagyrate diminished rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola () rotated through 36 degrees, and a non-opposing pentagonal cupola removed. (The cupolae cannot be adjacent.)
External links
Johnson solids |
https://en.wikipedia.org/wiki/Bigyrate%20diminished%20rhombicosidodecahedron | In geometry, the bigyrate diminished rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with two pentagonal cupolae rotated through 36 degrees, and a third pentagonal cupola removed. (None of the cupolae can be adjacent.)
External links
Johnson solids |
https://en.wikipedia.org/wiki/Gyrate%20bidiminished%20rhombicosidodecahedron | In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids ().
It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae () removed and a third is rotated 36 degrees. Related Johnson solids are:
The diminished rhombicosidodecahedron () where one cupola is... |
https://en.wikipedia.org/wiki/Metabigyrate%20rhombicosidodecahedron | In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids (). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.
Alternative Johnson solids, constructed by rotating different cupolae of a rhom... |
https://en.wikipedia.org/wiki/Gyroelongated%20pentagonal%20bicupola | In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids (). As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola ( or ) by inserting a decagonal antiprism between its congruent halves.
The gyroelongated pentagonal bicupola is one of five Johnson solids which are c... |
https://en.wikipedia.org/wiki/Classical%20mathematics | In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive mathematics or predicative mathematics. In practice, the most common non-c... |
https://en.wikipedia.org/wiki/Change%20of%20basis | In mathematics, an ordered basis of a vector space of finite dimension allows representing uniquely any element of the vector space by a coordinate vector, which is a sequence of scalars called coordinates. If two different bases are considered, the coordinate vector that represents a vector on one basis is, in gene... |
https://en.wikipedia.org/wiki/Dendroid | The word Dendroid derives from the Greek word "dendron" meaning ( "tree-like")
Dendroid may refer to:
Dendroid (topology), in mathematics
Dendroid (malware), Android malware
See also
Dendrite (disambiguation) |
https://en.wikipedia.org/wiki/Ancient%20Egyptian%20mathematics | Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c. , from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplicatio... |
https://en.wikipedia.org/wiki/Small%20set | In mathematics, the term small set may refer to:
Small set (category theory)
Small set (combinatorics), a set of positive integers whose sum of reciprocals converges
Small set, an element of a Grothendieck universe
See also
Ideal (set theory)
Natural density
Large set (disambiguation) |
https://en.wikipedia.org/wiki/Large%20set | In mathematics, the term large set is sometimes used to refer to any set that is "large" in some sense. It has specialized meanings in three branches of mathematics:
Large set (category theory), a set that does not belong to a fixed universe of sets
Large set (combinatorics), a set of integers whose sum of reciprocals... |
https://en.wikipedia.org/wiki/Complex%20algebra | Complex algebra may refer to:
A complex algebra (set theory), also known as field of sets
Algebra over the complex numbers
Algebra involving complex numbers |
https://en.wikipedia.org/wiki/Carmichael%20function | In number theory, a branch of mathematics, the Carmichael function of a positive integer is the smallest positive integer such that
holds for every integer coprime to . In algebraic terms, is the exponent of the multiplicative group of integers modulo .
The Carmichael function is named after the American mathema... |
https://en.wikipedia.org/wiki/Andrea%20diSessa | Andrea A. diSessa (born June 3, 1947) is an education researcher and author of the book Turtle Geometry about Logo. He has also written highly cited research papers on the epistemology of physics, educational experimentation, and constructivist analysis of knowledge. He also created, with Hal Abelson, the Boxer Program... |
https://en.wikipedia.org/wiki/Dual%20basis%20in%20a%20field%20extension | In mathematics, the linear algebra concept of dual basis can be applied in the context of a finite extension L/K, by using the field trace. This requires the property that the field trace TrL/K provides a non-degenerate quadratic form over K. This can be guaranteed if the extension is separable; it is automatically tr... |
https://en.wikipedia.org/wiki/Dual%20basis | In linear algebra, given a vector space with a basis of vectors indexed by an index set (the cardinality of is the dimension of ), the dual set of is a set of vectors in the dual space with the same index set I such that and form a biorthogonal system. The dual set is always linearly independent but does not n... |
https://en.wikipedia.org/wiki/Quadratic%20residuosity%20problem | The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers and , whether is a quadratic residue modulo or not.
Here for two unknown primes and , and is among the numbers which are not obviously quadratic non-residues (see below).
The problem was first described by Gauss i... |
https://en.wikipedia.org/wiki/Islam%20in%20Thailand | Islam is a minority faith in Thailand, with statistics suggesting 4.9% of the population are Muslim. Figures as high as 5% of Thailand's population have also been mentioned. A 2023 Pew Research Center survey gave 7%.
Most Thai Muslims are Sunni Muslims, although Thailand has a diverse population that includes immigra... |
https://en.wikipedia.org/wiki/Islam%20in%20the%20United%20Arab%20Emirates | Islam is the official religion of the United Arab Emirates. Of the total population, 76.9% are Muslims as of a 2010 estimate by the Pew Research Center. Although no official statistics are available for the breakdown between Sunni and Shia Muslims among noncitizen residents, media estimates suggest less than 20 percent... |
https://en.wikipedia.org/wiki/Initial%20condition | In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t = 0). For a system of order k (the number of time lags in discrete time, or the order of the larges... |
https://en.wikipedia.org/wiki/Linear%20system%20of%20divisors | In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.
These arose first in the form of a linear system of algebraic curves in the projective plane. It ass... |
https://en.wikipedia.org/wiki/Ample%20line%20bundle | In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative" (or a mixture of the two). The most important notion of positivity is that of an ample line bundle, although there are several related classes of line b... |
https://en.wikipedia.org/wiki/Algebroid | In mathematics, algebroid may refer to several distinct notions, which nevertheless all arise from generalising certain aspects of the theory of algebras or Lie algebras.
Algebroid branch, a formal power series branch of an algebraic curve
Algebroid cohomology
Algebroid multifunction
Courant algebroid, an object gener... |
https://en.wikipedia.org/wiki/Block%20design | In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such that frequency of the elements satisfies certain conditions making the collection of blocks exhibit symmetry (balance). Block designs have applications in many areas,... |
https://en.wikipedia.org/wiki/Path%20%28topology%29 | In mathematics, a path in a topological space is a continuous function from the closed unit interval into
Paths play an important role in the fields of topology and mathematical analysis.
For example, a topological space for which there exists a path connecting any two points is said to be path-connected. Any spa... |
https://en.wikipedia.org/wiki/Loop%20%28topology%29 | In mathematics, a loop in a topological space is a continuous function from the unit interval to such that In other words, it is a path whose initial point is equal to its terminal point.
A loop may also be seen as a continuous map from the pointed unit circle into , because may be regarded as a quotient of u... |
https://en.wikipedia.org/wiki/Proper%20map | In mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism.
Definition
There are several competing definitions of a "proper function".
Some authors call a function between two topol... |
https://en.wikipedia.org/wiki/Pl%C3%BCcker%20embedding | In mathematics, the Plücker map embeds the Grassmannian , whose elements are k-dimensional subspaces of an n-dimensional vector space V, either real or complex, in a projective space, thereby realizing it as a projective algebraic variety. More precisely, the Plücker map embeds into the projectivization of the -th e... |
https://en.wikipedia.org/wiki/Splitting%20of%20prime%20ideals%20in%20Galois%20extensions | In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one of the richest parts of algebraic number theory. The splitting of prime ideals in Galois extensions is... |
https://en.wikipedia.org/wiki/Manifold%20%28disambiguation%29 | A manifold is an abstract mathematical space which, in a close-up view, resembles the spaces described by Euclidean geometry.
Manifold may also refer to:
Arts and music
Manifold (comics), a fictional character in Marvel Comics publications
Manifold Records, a record label
Manifold Trilogy, by science fiction autho... |
https://en.wikipedia.org/wiki/Pairing | In mathematics, a pairing is an R-bilinear map from the Cartesian product of two R-modules, where the underlying ring R is commutative.
Definition
Let R be a commutative ring with unit, and let M, N and L be R-modules.
A pairing is any R-bilinear map . That is, it satisfies
,
and
for any and any and any . Equi... |
https://en.wikipedia.org/wiki/Green%27s%20relations | In mathematics, Green's relations are five equivalence relations that characterise the elements of a semigroup in terms of the principal ideals they generate. The relations are named for James Alexander Green, who introduced them in a paper of 1951. John Mackintosh Howie, a prominent semigroup theorist, described this ... |
https://en.wikipedia.org/wiki/Whitehead%20manifold | In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to discovered this puzzling object while he was trying to prove the Poincaré conjecture, correcting an error in an earlier paper where he incorrectly claimed that no such manifold exists.
A contractible manifold ... |
https://en.wikipedia.org/wiki/Skellam%20distribution | The Skellam distribution is the discrete probability distribution of the difference of two statistically independent random variables and each Poisson-distributed with respective expected values and . It is useful in describing the statistics of the difference of two images with simple photon noise, as well as desc... |
https://en.wikipedia.org/wiki/Nottingham%20Urban%20Area | The Nottingham Built-up Area (BUA), Nottingham Urban Area, or Greater Nottingham is an area of land defined by the Office for National Statistics as which is built upon, with nearby areas linked if within 200 metres. It consists of the city of Nottingham and the adjoining urban areas of Nottinghamshire and Derbyshire, ... |
https://en.wikipedia.org/wiki/Jacobian%20conjecture | In mathematics, the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables. It states that if a polynomial function from an n-dimensional space to itself has Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse. It was first conjectured in 1... |
https://en.wikipedia.org/wiki/Ott-Heinrich%20Keller | Eduard Ott-Heinrich Keller (22 June 1906 in Frankfurt – 5 December 1990 in Halle) was a German mathematician who worked in the fields of geometry, topology and algebraic geometry. He formulated the celebrated problem which is now called the Jacobian conjecture in 1939.
He was born in Frankfurt–am-Main, and studied at ... |
https://en.wikipedia.org/wiki/Poisson%20formula | In mathematics, the Poisson formula, named after Siméon Denis Poisson, may refer to:
Poisson distribution in probability
Poisson summation formula in Fourier analysis
Poisson kernel in complex or harmonic analysis
Poisson–Jensen formula in complex analysis |
https://en.wikipedia.org/wiki/Heine%E2%80%93Cantor%20theorem | In mathematics, the Heine–Cantor theorem, named after Eduard Heine and Georg Cantor, states that if is a continuous function between two metric spaces and , and is compact, then is uniformly continuous. An important special case is that every continuous function from a closed bounded interval to the real numbers is... |
https://en.wikipedia.org/wiki/P.%20K.%20Srinivasan | P.K. Srinivasan (PKS) (4 November 1924 – 20 June 2005) was a well known mathematics teacher in India. He taught mathematics at the Muthialpet High School in Chennai, India until his retirement. His singular dedication to education of mathematics would bring him to the United States, where he worked for a year, and then... |
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt | In mathematics, Hilbert–Schmidt may refer to
a Hilbert–Schmidt operator;
a Hilbert–Schmidt integral operator;
the Hilbert–Schmidt theorem. |
https://en.wikipedia.org/wiki/American%20Regions%20Mathematics%20League | The American Regions Mathematics League (ARML), is an annual, national high school mathematics team competition held simultaneously at four locations in the United States: the University of Iowa, Penn State, University of Nevada, Reno, and the University of Alabama in Huntsville. Past sites have included San Jose Stat... |
https://en.wikipedia.org/wiki/List%20of%20interactive%20geometry%20software | Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric constructions, primarily in plane geometry. In most IGS, one starts construction by putting a few points and using them to define new objects such as lines, circles o... |
https://en.wikipedia.org/wiki/Pre-intuitionism | In the philosophy of mathematics, the pre-intuitionists were a small but influential group who informally shared similar philosophies on the nature of mathematics. The term itself was used by L. E. J. Brouwer, who in his 1951 lectures at Cambridge described the differences between intuitionism and its predecessors:
Of... |
https://en.wikipedia.org/wiki/Elongated%20triangular%20cupola | In geometry, the elongated triangular cupola is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a triangular cupola () by attaching a hexagonal prism to its base.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length ... |
https://en.wikipedia.org/wiki/Gyroelongated%20triangular%20cupola | In geometry, the gyroelongated triangular cupola is one of the Johnson solids (J22). It can be constructed by attaching a hexagonal antiprism to the base of a triangular cupola (J3). This is called "gyroelongation", which means that an antiprism is joined to the base of a solid, or between the bases of more than one ... |
https://en.wikipedia.org/wiki/Triangular%20orthobicupola | In geometry, the triangular orthobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by attaching two triangular cupolas () along their bases. It has an equal number of squares and triangles at each vertex; however, it is not vertex-transitive. It is also called an anticuboctahedron, t... |
https://en.wikipedia.org/wiki/Pentagonal%20orthocupolarotunda | In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by joining a pentagonal cupola () and a pentagonal rotunda () along their decagonal bases, matching the pentagonal faces. A 36-degree rotation of one of the halves before the joining yields a pe... |
https://en.wikipedia.org/wiki/Pentagonal%20gyrocupolarotunda | In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids (). Like the pentagonal orthocupolarotunda (), it can be constructed by joining a pentagonal cupola () and a pentagonal rotunda () along their decagonal bases. The difference is that in this solid, the two halves are rotated 36 degrees with res... |
https://en.wikipedia.org/wiki/Elongated%20triangular%20orthobicupola | In geometry, the elongated triangular orthobicupola or cantellated triangular prism is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a triangular orthobicupola () by inserting a hexagonal prism between its two halves. The resulting solid is superficially similar to the rhombic... |
https://en.wikipedia.org/wiki/Elongated%20triangular%20gyrobicupola | In geometry, the elongated triangular gyrobicupola is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a "triangular gyrobicupola," or cuboctahedron, by inserting a hexagonal prism between its two halves, which are congruent triangular cupolae (). Rotating one of the cupolae thro... |
https://en.wikipedia.org/wiki/Gyroelongated%20triangular%20bicupola | In geometry, the gyroelongated triangular bicupola is one of the Johnson solids (). As the name suggests, it can be constructed by gyroelongating a triangular bicupola (either triangular orthobicupola, , or the cuboctahedron) by inserting a hexagonal antiprism between its congruent halves.
The gyroelongated triangula... |
https://en.wikipedia.org/wiki/O%27Nan%20group | In the area of abstract algebra known as group theory, the O'Nan group O'N or O'Nan–Sims group is a sporadic simple group of order
2934573111931
= 460815505920
≈ 5.
History
O'Nan is one of the 26 sporadic groups and was found by in a study of groups with a Sylow 2-subgroup of "Alperin type", meaning isomorphic t... |
https://en.wikipedia.org/wiki/Rudvalis%20group | In the area of modern algebra known as group theory, the Rudvalis group Ru is a sporadic simple group of order
214335371329
= 145926144000
≈ 1.
History
Ru is one of the 26 sporadic groups and was found by and constructed by . Its Schur multiplier has order 2, and its outer automorphism group is trivial.
In 1982... |
https://en.wikipedia.org/wiki/Harada%E2%80%93Norton%20group | In the area of modern algebra known as group theory, the Harada–Norton group HN is a sporadic simple group of order
214365671119
= 273030912000000
≈ 3.
History and properties
HN is one of the 26 sporadic groups and was found by and ).
Its Schur multiplier is trivial and its outer automorphism group has order 2.... |
https://en.wikipedia.org/wiki/Mohr%E2%80%93Mascheroni%20theorem | In mathematics, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone.
It must be understood that "any geometric construction" refers to figures that contain no straight lines, as it is clearly impossible to draw a str... |
https://en.wikipedia.org/wiki/Initial%20topology | In general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on a set with respect to a family of functions on is the coarsest topology on that makes those functions continuous.
The subspace topology and product topology c... |
https://en.wikipedia.org/wiki/Formal%20proof | In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference. It differs from a natural language argument i... |
https://en.wikipedia.org/wiki/Subgroup%20growth | In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group.
Let be a finitely generated group. Then, for each integer define to be the number of subgroups of index in . Similarly, if is a topological group, denotes the number of open subgrou... |
https://en.wikipedia.org/wiki/Conditional%20convergence | In mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely.
Definition
More precisely, a series of real numbers is said to converge conditionally if
exists (as a finite real number, i.e. not or ), but
A classic example is the alternating harmo... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20gyrocupolarotunda | In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda () by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola () or the pentagonal rotunda () through 36 degrees... |
https://en.wikipedia.org/wiki/Elongated%20pentagonal%20orthocupolarotunda | In geometry, the elongated pentagonal orthocupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a pentagonal orthocupolarotunda () by inserting a decagonal prism between its halves. Rotating either the cupola or the rotunda through 36 degrees before inserting the pris... |
https://en.wikipedia.org/wiki/Gyroelongated%20pentagonal%20cupolarotunda | In geometry, the gyroelongated pentagonal cupolarotunda is one of the Johnson solids (). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda ( or ) by inserting a decagonal antiprism between its two halves.
The gyroelongated pentagonal cupolarotunda is one of five Johnson solids wh... |
https://en.wikipedia.org/wiki/Augmented%20truncated%20tetrahedron | In geometry, the augmented truncated tetrahedron is one of the Johnson solids (). It is created by attaching a triangular cupola () to one hexagonal face of a truncated tetrahedron.
External links
Johnson solids |
https://en.wikipedia.org/wiki/California%20Academy%20of%20Mathematics%20and%20Science | The California Academy of Mathematics and Science (CAMS) is a public magnet high school in Carson, California, United States focusing on science and mathematics. Its California API scores are fourth-highest in the state.
Located on the campus of California State University, Dominguez Hills, CAMS shares many facilities... |
https://en.wikipedia.org/wiki/Comodule | In mathematics, a comodule or corepresentation is a concept dual to a module. The definition of a comodule over a coalgebra is formed by dualizing the definition of a module over an associative algebra.
Formal definition
Let K be a field, and C be a coalgebra over K. A (right) comodule over C is a K-vector space M ... |
https://en.wikipedia.org/wiki/Homotopy%20sphere | In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere. It thus has the same homotopy groups and the same homology groups as the n-sphere, and so every homotopy sphere is necessarily a homology sphere.
The topological generalized Poincaré conjectu... |
https://en.wikipedia.org/wiki/Voigt%20profile | The Voigt profile (named after Woldemar Voigt) is a probability distribution given by a convolution of a Cauchy-Lorentz distribution and a Gaussian distribution. It is often used in analyzing data from spectroscopy or diffraction.
Definition
Without loss of generality, we can consider only centered profiles, which pe... |
https://en.wikipedia.org/wiki/Stopping%20time | In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time) is a specific type of “random time”: a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behav... |
https://en.wikipedia.org/wiki/Autocovariance | In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question.
Auto-covariance of stochastic processes
Definition
With... |
https://en.wikipedia.org/wiki/Pr%C3%BCfer%20rank | In mathematics, especially in the area of algebra known as group theory, the Prüfer rank of a pro-p group measures the size of a group in terms of the ranks of its elementary abelian sections. The rank is well behaved and helps to define analytic pro-p-groups. The term is named after Heinz Prüfer.
Definition
The Prü... |
https://en.wikipedia.org/wiki/Gluing%20axiom | In mathematics, the gluing axiom is introduced to define what a sheaf on a topological space must satisfy, given that it is a presheaf, which is by definition a contravariant functor
to a category which initially one takes to be the category of sets. Here is the partial order of open sets of ordered by inclusion ... |
https://en.wikipedia.org/wiki/Folk%20theorem | Folk theorem may refer to:
Folk theorem (game theory), a general feasibility theorem
Ethnomathematics, the study of the relationship between mathematics and culture
Mathematical folklore, theorems that are widely known to mathematicians but cannot be traced back to an individual
Mathematics disambiguation pages |
https://en.wikipedia.org/wiki/Practical%20number | In number theory, a practical number or panarithmic number is a positive integer such that all smaller positive integers can be represented as sums of distinct divisors of . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as... |
https://en.wikipedia.org/wiki/Stein%20factorization | In algebraic geometry, the Stein factorization, introduced by for the case of complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Roughly speaking, Stein factorization contracts the connected components of the fibers of a ma... |
https://en.wikipedia.org/wiki/Spherical%203-manifold | In mathematics, a spherical 3-manifold M is a 3-manifold of the form
where is a finite subgroup of SO(4) acting freely by rotations on the 3-sphere . All such manifolds are prime, orientable, and closed. Spherical 3-manifolds are sometimes called elliptic 3-manifolds or Clifford-Klein manifolds.
Properties
A spheric... |
https://en.wikipedia.org/wiki/Biquaternion | In abstract algebra, the biquaternions are the numbers , where , and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions corresponding to complex numbers and the variations thereof:
Biquaternions... |
https://en.wikipedia.org/wiki/Grete%20Hermann | Grete Hermann (2 March 1901 – 15 April 1984) was a German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education. She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored critique of a "... |
https://en.wikipedia.org/wiki/Primary%20decomposition | In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals). The theorem was firs... |
https://en.wikipedia.org/wiki/Bicyclic%20semigroup | In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is usually referred to as simply a semigroup. It is perhaps most easily understood as the syntactic monoid describing the Dyck language of balanced pairs of parentheses. Th... |
https://en.wikipedia.org/wiki/Martin-Andersen-Nex%C3%B6-Gymnasium%20Dresden | The Martin-Andersen-Nexö-Gymnasium Dresden (MANOS) is a selective high school (gymnasium) in Dresden, Germany, with a special focus on mathematics and sciences. It was formerly the school for radio mechanics in the GDR. It is named after the Danish writer Martin Andersen Nexø.
The current head of school is Mr. Holm Wi... |
https://en.wikipedia.org/wiki/Denjoy%20integral | The Denjoy integral in mathematics can refer to two closely related integrals connected to the work of Arnaud Denjoy:
the narrow Denjoy integral, or just Denjoy integral, also known as Henstock–Kurzweil integral,
the (more general) wide Denjoy integral, or Khinchin integral. |
https://en.wikipedia.org/wiki/Abstract%20polytope | In mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely geometric properties such as points and lines.
A geometric polytope is said to be a realization of an abstract polytope in some real N-dimensional space, typ... |
https://en.wikipedia.org/wiki/Least%20fixed%20point | In order theory, a branch of mathematics, the least fixed point (lfp or LFP, sometimes also smallest fixed point) of a function from a partially ordered set to itself is the fixed point which is less than each other fixed point, according to the order of the poset. A function need not have a least fixed point, but if i... |
https://en.wikipedia.org/wiki/Richard%20Schwartz%20%28mathematician%29 | Richard Evan Schwartz (born August 11, 1966) is an American mathematician notable for his contributions to geometric group theory and to an area of mathematics known as billiards. Geometric group theory is a relatively new area of mathematics beginning around the late 1980s which explores finitely generated groups, and... |
https://en.wikipedia.org/wiki/Block%20LU%20decomposition | In linear algebra, a Block LU decomposition is a matrix decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular matrix U. This decomposition is used in numerical analysis to reduce the complexity of the block matrix formula.
Block LDU decomposition
Block Cholesky decomposi... |
https://en.wikipedia.org/wiki/CPV | CPV may refer to:
In mathematics, science and technology
Viruses
Canine parvovirus
Cricket paralysis virus
Cryptosporidium parvum virus, a dsRNA virus of the single-celled causative agent of Cryptosporidiosis
Other uses in mathematics, science and technology
Cauchy principal value, a method for assigning values... |
https://en.wikipedia.org/wiki/Paul%20Ernest | Paul Ernest is a contributor to the social constructivist philosophy of mathematics.
Life
Paul Ernest is currently emeritus professor of the philosophy of mathematics education at Exeter University, UK. He is best known for his work on philosophical aspects of mathematics education and his contributions to developing ... |
https://en.wikipedia.org/wiki/Discrete-time%20Fourier%20transform | In mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values.
The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on d... |
https://en.wikipedia.org/wiki/Algebra%20of%20random%20variables | The algebra of random variables in statistics, provides rules for the symbolic manipulation of random variables, while avoiding delving too deeply into the mathematically sophisticated ideas of probability theory. Its symbolism allows the treatment of sums, products, ratios and general functions of random variables, as... |
https://en.wikipedia.org/wiki/Misuse%20of%20statistics | Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the p... |
https://en.wikipedia.org/wiki/Swadesh%20list | The Swadesh list () is a classic compilation of tentatively universal concepts for the purposes of lexicostatistics. Translations of the Swadesh list into a set of languages allow researchers to quantify the interrelatedness of those languages. The Swadesh list is named after linguist Morris Swadesh. It is used in lexi... |
https://en.wikipedia.org/wiki/Sturm%27s%20theorem | In mathematics, the Sturm sequence of a univariate polynomial is a sequence of polynomials associated with and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of located in an interval in terms of the number of changes of signs of the val... |
https://en.wikipedia.org/wiki/Tame%20group | In mathematical group theory, a tame group is a certain kind of group defined in model theory.
Formally, we define a bad field as a structure of the form (K, T), where K is an algebraically closed field and T is an infinite, proper, distinguished subgroup of K, such that (K, T) is of finite Morley rank in its full lan... |
https://en.wikipedia.org/wiki/Sheaf | Sheaf may refer to:
Sheaf (agriculture), a bundle of harvested cereal stems
Sheaf (mathematics), a mathematical tool
Sheaf toss, a Scottish sport
River Sheaf, a tributary of River Don in England
The Sheaf, a student-run newspaper serving the University of Saskatchewan
Aluma, a settlement in Israel whose name tra... |
https://en.wikipedia.org/wiki/Hull%E2%80%93White%20model | In financial mathematics, the Hull–White model is a model of future interest rates. In its most generic formulation, it belongs to the class of no-arbitrage models that are able to fit today's term structure of interest rates. It is relatively straightforward to translate the mathematical description of the evolution o... |
https://en.wikipedia.org/wiki/Principal%20part | In mathematics, the principal part has several independent meanings, but usually refers to the negative-power portion of the Laurent series of a function.
Laurent series definition
The principal part at of a function
is the portion of the Laurent series consisting of terms with negative degree. That is,
is the pr... |
https://en.wikipedia.org/wiki/Urn%20%28disambiguation%29 | An urn is a vase-like container.
Urn may refer to:
Urn problem of probability theory
Urn (album), an album by Ne Obliviscaris
The acronym URN may refer to:
Uniform Resource Name, an Internet identifier
Unique Reference Number, an identifier of UK schools
University Radio Nottingham, England
See also |
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