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https://en.wikipedia.org/wiki/Ring%20of%20symmetric%20functions | In algebra and in particular in algebraic combinatorics, the ring of symmetric functions is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity. This ring serves as universal structure in which relations between symmetric polynomials can be expressed in a way independent of... |
https://en.wikipedia.org/wiki/Projective%20module | In mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, by keeping some of the main properties of free modules. Various equivalent characterizations of these modules appear below.
Every free module is a projective mo... |
https://en.wikipedia.org/wiki/Scheme%20%28mathematics%29 | In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, F... |
https://en.wikipedia.org/wiki/Conformal%20field%20theory | A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified.
Conformal field theory has important ap... |
https://en.wikipedia.org/wiki/Conformal%20group | In mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that preserve the conformal geometry of the space.
Several specific conformal groups are particularly important:
The conformal... |
https://en.wikipedia.org/wiki/Quotient%20module | In algebra, given a module and a submodule, one can construct their quotient module. This construction, described below, is very similar to that of a quotient vector space. It differs from analogous quotient constructions of rings and groups by the fact that in these cases, the subspace that is used for defining the q... |
https://en.wikipedia.org/wiki/Wishart%20distribution | In statistics, the Wishart distribution is a generalization to multiple dimensions of the gamma distribution. It is named in honor of John Wishart, who first formulated the distribution in 1928. Other names include Wishart ensemble (in random matrix theory, probability distributions over matrices are usually called "en... |
https://en.wikipedia.org/wiki/Finite%20intersection%20property | In general topology, a branch of mathematics, a non-empty family A of subsets of a set is said to have the finite intersection property (FIP) if the intersection over any finite subcollection of is non-empty. It has the strong finite intersection property (SFIP) if the intersection over any finite subcollection of i... |
https://en.wikipedia.org/wiki/Heptagon | In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.
The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning an... |
https://en.wikipedia.org/wiki/Ford%20circle | In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the -axis at rational points. For each rational number , expressed in lowest terms, there is a Ford circle whose center is at the point and whose radius is . It is tangent to the -axis at its bottom point, ... |
https://en.wikipedia.org/wiki/Missing%20square%20puzzle | The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different c... |
https://en.wikipedia.org/wiki/Banach%E2%80%93Mazur%20game | In general topology, set theory and game theory, a Banach–Mazur game is a topological game played by two players, trying to pin down elements in a set (space). The concept of a Banach–Mazur game is closely related to the concept of Baire spaces. This game was the first infinite positional game of perfect information ... |
https://en.wikipedia.org/wiki/Claude%20Chevalley | Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a founding member of the Bourbaki group.
Life
His father, Abel Chevalley, was a Frenc... |
https://en.wikipedia.org/wiki/Pontryagin%20duality | In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), the finite abelian groups (with the discrete topology), and the additive grou... |
https://en.wikipedia.org/wiki/Typed%20lambda%20calculus | A typed lambda calculus is a typed formalism that uses the lambda-symbol () to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered (see kinds below). From a certain point ... |
https://en.wikipedia.org/wiki/Mathematical%20puzzle | Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to ... |
https://en.wikipedia.org/wiki/Frame%20bundle | In mathematics, a frame bundle is a principal fiber bundle F(E) associated to any vector bundle E. The fiber of F(E) over a point x is the set of all ordered bases, or frames, for Ex. The general linear group acts naturally on F(E) via a change of basis, giving the frame bundle the structure of a principal GL(k, R)-bun... |
https://en.wikipedia.org/wiki/Applied%20probability | Applied probability is the application of probability theory to statistical problems and other scientific and engineering domains.
Scope
Much research involving probability is done under the auspices of applied probability. However, while such research is motivated (to some degree) by applied problems, it is usually t... |
https://en.wikipedia.org/wiki/Indeterminate%20form | In calculus and other branches of mathematical analysis, when the limit of the sum, difference, product, quotient or power of two functions is taken, it may often be possible to simply add, subtract, multiply, divide or exponentiate the corresponding limits of these two functions respectively. However, there are occasi... |
https://en.wikipedia.org/wiki/Knot%20%28mathematics%29 | In mathematics, a knot is an embedding of the circle into three-dimensional Euclidean space, (also known as ). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other.
A crucial difference between the standard m... |
https://en.wikipedia.org/wiki/Plus%E2%80%93minus%20sign | The plus–minus sign, , is a mathematical symbol with multiple meanings:
In mathematics, it generally indicates a choice of exactly two possible values, one of which is obtained through addition and the other through subtraction.
In experimental sciences, the sign commonly indicates the confidence interval or uncertaint... |
https://en.wikipedia.org/wiki/Antipodal%20point | In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the intersections of the sphere with a diameter, a straight line passing through its center.
Given any point on a sphere, its antipodal point is the unique point at greatest distance, whe... |
https://en.wikipedia.org/wiki/Section%20%28fiber%20bundle%29 | In the mathematical field of topology, a section (or cross section) of a fiber bundle is a continuous right inverse of the projection function . In other words, if is a fiber bundle over a base space, :
then a section of that fiber bundle is a continuous map,
such that
for all .
A section is an abstract characte... |
https://en.wikipedia.org/wiki/Probabilist | probabilist may refer to:
A follower of probabilism (in theology or philosophy)
A mathematician who studies and applies probability theory
List of mathematical probabilists |
https://en.wikipedia.org/wiki/Lebesgue%E2%80%93Stieltjes%20integration | In measure-theoretic analysis and related branches of mathematics, Lebesgue–Stieltjes integration generalizes both Riemann–Stieltjes and Lebesgue integration, preserving the many advantages of the former in a more general measure-theoretic framework. The Lebesgue–Stieltjes integral is the ordinary Lebesgue integral wi... |
https://en.wikipedia.org/wiki/Sphere%20packing | In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dim... |
https://en.wikipedia.org/wiki/Moment%20%28mathematics%29 | In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. ... |
https://en.wikipedia.org/wiki/27%20%28number%29 | 27 (twenty-seven; Roman numeral XXVII) is the natural number following 26 and preceding 28.
In mathematics
Twenty-seven is equal to the cube of three: ; also 23 (see tetration). It is divisible by the number of prime numbers below it (9).
In decimal, 27 is the first composite number not divisible by any of its digit... |
https://en.wikipedia.org/wiki/Sequence%20%28disambiguation%29 | A sequence, in mathematics, is an ordered list of elements.
Sequence may also refer to:
Arts and media
Film
Sequence (filmmaking), a series of shots or scenes, edited together in succession
Sequence (journal), a film journal
Séquences, a Quebec film magazine
Sequence (2013 film), a 2013 short fantasy horror film... |
https://en.wikipedia.org/wiki/Frequency%20domain | In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows h... |
https://en.wikipedia.org/wiki/SVP | SVP may refer to:
Science and mathematics
Shortest vector problem, the problem of finding the smallest non-zero vector in a lattice space
Society of Vertebrate Paleontology, a society of paleontologists
Saturated vapour pressure, the pressure exerted by a vapour in thermodynamic equilibrium with its condensed phase... |
https://en.wikipedia.org/wiki/Savant%20syndrome | Savant syndrome () is a phenomenon, sometimes following a brain injury, where someone demonstrates exceptional aptitude in one domain, such as art or mathematics, despite significant social or intellectual impairment.
Those with the condition generally have a neurodevelopmental disorder such as autism spectrum disor... |
https://en.wikipedia.org/wiki/L%C3%A9vy%20flight | A Lévy flight is a random walk in which the step-lengths have a stable distribution, a probability distribution that is heavy-tailed. When defined as a walk in a space of dimension greater than one, the steps made are in isotropic random directions. Later researchers have extended the use of the term "Lévy flight" to a... |
https://en.wikipedia.org/wiki/Foliation | In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space Rn into the cosets x + Rp of the standardly embedded subspac... |
https://en.wikipedia.org/wiki/Quantitative%20psychological%20research | Quantitative psychological research is psychological research that employs quantitative research methods.
Quantitative research falls under the category of empirical research.
See also
Statistics
Quantitative psychology
Quantitative research
References
Applied statistics
Experimental psychology
Quantitative resea... |
https://en.wikipedia.org/wiki/Frobenius | Frobenius is a surname. Notable people with the surname include:
Ferdinand Georg Frobenius (1849–1917), mathematician
Frobenius algebra
Frobenius endomorphism
Frobenius inner product
Frobenius norm
Frobenius method
Frobenius group
Frobenius theorem (differential topology)
Georg Ludwig Frobenius (1566–1645), G... |
https://en.wikipedia.org/wiki/Semiring | In abstract algebra, a semiring is an algebraic structure. It is a generalization of a ring, dropping the requirement that each element must have an additive inverse. At the same time, it is a generalization of bounded distributive lattices.
The smallest semiring that is not a ring is the two-element Boolean algebra, ... |
https://en.wikipedia.org/wiki/Anyonic%20Lie%20algebra | In mathematics, an anyonic Lie algebra is a U(1) graded vector space over equipped with a bilinear operator and linear maps (some authors use ) and such that , satisfying following axioms:
for pure graded elements X, Y, and Z.
References
Vector spaces
Lie algebras |
https://en.wikipedia.org/wiki/Real%20tree | In mathematics, real trees (also called -trees) are a class of metric spaces generalising simplicial trees. They arise naturally in many mathematical contexts, in particular geometric group theory and probability theory. They are also the simplest examples of Gromov hyperbolic spaces.
Definition and examples
Formal d... |
https://en.wikipedia.org/wiki/Open%20and%20closed%20maps | In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets.
That is, a function is open if for any open set in the image is open in
Likewise, a closed map is a function that maps closed sets to closed sets.
A map may be open, closed, ... |
https://en.wikipedia.org/wiki/Weierstrass%20preparation%20theorem | In mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P. It states that such a function is, up to multiplication by a function not zero at P, a polynomial in one fixed variable z, which is monic, and whose coefficients of lower d... |
https://en.wikipedia.org/wiki/Tensor%20product%20of%20fields | In mathematics, the tensor product of two fields is their tensor product as algebras over a common subfield. If no subfield is explicitly specified, the two fields must have the same characteristic and the common subfield is their prime subfield.
The tensor product of two fields is sometimes a field, and often a dire... |
https://en.wikipedia.org/wiki/Radical%20of%20a%20ring | In ring theory, a branch of mathematics, a radical of a ring is an ideal of "not-good" elements of the ring.
The first example of a radical was the nilradical introduced by , based on a suggestion of . In the next few years several other radicals were discovered, of which the most important example is the Jacobson rad... |
https://en.wikipedia.org/wiki/Magic%20cube | In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal, the so-called magic constant of the cub... |
https://en.wikipedia.org/wiki/Perfect%20magic%20cube | In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant.
Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist, and cubes of order... |
https://en.wikipedia.org/wiki/Semiperfect%20magic%20cube | In mathematics, a semiperfect magic cube is a magic cube that is not a perfect magic cube, i.e., a magic cube for which the cross section diagonals do not necessarily sum up to the cube's magic constant.
References
.
Magic squares |
https://en.wikipedia.org/wiki/Tensor%20product%20of%20algebras | In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra. This gives the tensor product of algebras. When the ring is a field, the most common application of such products is to describe the product of algebra representations.
Definition
Let R be a commutative ring and let A an... |
https://en.wikipedia.org/wiki/Multimagic%20cube | In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their k th powers for 1 ≤ k ≤ P. cubes are called bimagic, cubes are called trimagic, and cubes tetramagic. A cube is said to be semi-perfect if the k th power cubes are perfect for 1 ≤ k < ... |
https://en.wikipedia.org/wiki/Opposite%20category | In category theory, a branch of mathematics, the opposite category or dual category Cop of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite category is the original ca... |
https://en.wikipedia.org/wiki/Multimagic%20square | In mathematics, a P-multimagic square (also known as a satanic square) is a magic square that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. squares are called bimagic, squares are called trimagic, squares tetramagic, and squares pentamagic.
Constants for normal squares
If t... |
https://en.wikipedia.org/wiki/Magic%20hypercube | In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magic cubes, that is, an n × n × n × ... × n array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the same. The common sum is called the magic constan... |
https://en.wikipedia.org/wiki/Grothendieck%27s%20Galois%20theory | In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry. It provides, in the classical setting of field theory, an alternative perspective to that... |
https://en.wikipedia.org/wiki/Schur%20decomposition | In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily equivalent to an upper triangular matrix whose diagonal elements are the eigenvalues of the origina... |
https://en.wikipedia.org/wiki/Schur%20complement | In linear algebra and the theory of matrices, the Schur complement of a block matrix is defined as follows.
Suppose p, q are nonnegative integers, and suppose A, B, C, D are respectively p × p, p × q, q × p, and q × q matrices of complex numbers. Let
so that M is a (p + q) × (p + q) matrix.
If D is invertible, then ... |
https://en.wikipedia.org/wiki/Pathological%20%28mathematics%29 | In mathematics, when a mathematical phenomenon runs counter to some intuition, then the phenomenon is sometimes called pathological. On the other hand, if a phenomenon does not run counter to intuition,
it is sometimes called well-behaved. These terms are sometimes useful in mathematical research and teaching, but the... |
https://en.wikipedia.org/wiki/Jordan%20decomposition | In mathematics, Jordan decomposition may refer to
Hahn decomposition theorem, and the Jordan decomposition of a measure
Jordan normal form of a matrix
Jordan–Chevalley decomposition of a matrix
Deligne–Lusztig theory, and its Jordan decomposition of a character of a finite group of Lie type
The Jordan–Hölder theo... |
https://en.wikipedia.org/wiki/Polynomial%20ring | In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
Often, the term "polynomia... |
https://en.wikipedia.org/wiki/Equinumerosity | In mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (or bijection) between them, that is, if there exists a function from A to B such that for every element y of B, there is exactly one element x of A with f(x) = y. Equinumerous sets are said to have the same cardina... |
https://en.wikipedia.org/wiki/Limit%20ordinal | In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less than λ, and whenever β is an ordinal less than λ, then there exists an ordinal γ such that β < γ < λ. Every ordinal number is either zero, or a suc... |
https://en.wikipedia.org/wiki/Cardinal%20assignment | In set theory, the concept of cardinality is significantly developable without recourse to actually defining cardinal numbers as objects in the theory itself (this is in fact a viewpoint taken by Frege; Frege cardinals are basically equivalence classes on the entire universe of sets, by equinumerosity). The concepts ar... |
https://en.wikipedia.org/wiki/Lie%20group%20decomposition | In mathematics, Lie group decompositions are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of subgroups. They are essential technical tools in the representation theory of Lie groups and Lie algebras; they can also be used to study the algebraic topology of suc... |
https://en.wikipedia.org/wiki/Language%20of%20mathematics | The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc) with concision, precision and unambiguity.
Features
The main features of the ... |
https://en.wikipedia.org/wiki/Mikio%20Sato | was a Japanese mathematician known for founding the fields of algebraic analysis, hyperfunctions, and holonomic quantum fields. He was a professor at the Research Institute for Mathematical Sciences in Kyoto.
Biography
Born in Tokyo on 18 April 1928, Sato studied at the University of Tokyo, receiving his BSc in 1952 a... |
https://en.wikipedia.org/wiki/Grassmannian | In mathematics, the Grassmannian is a differentiable manifold that parameterizes the set of all -dimensional linear subspaces of an -dimensional vector space over a field .
For example, the Grassmannian is the space of lines through the origin in , so it is the same as the projective space of one dimension lower ... |
https://en.wikipedia.org/wiki/Law%20of%20trichotomy | In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero.
More generally, a binary relation R on a set X is trichotomous if for all x and y in X, exactly one of xRy, yRx and x=y holds. Writing R as <, this is stated in formal logic as:
Properties
A relation is tricho... |
https://en.wikipedia.org/wiki/Gibbs%20phenomenon | In mathematics, the Gibbs phenomenon is the oscillatory behavior of the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity. The th partial Fourier series of the function (formed by summing the lowest constituent sinusoids of the Fourier series of the function) produ... |
https://en.wikipedia.org/wiki/Limit%20cardinal | In mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This means that one cannot "reach" λ from another cardinal by repeated successor operations. These cardinals are sometimes called simply "limit cardinals" when the c... |
https://en.wikipedia.org/wiki/Regular%20cardinal | In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that is a regular cardinal if and only if every unbounded subset has cardinality . Infinite well-ordered cardinals that are not regular are called singular cardinals. Finite cardinal numbers are ... |
https://en.wikipedia.org/wiki/Inverse%20trigonometric%20functions | In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, s... |
https://en.wikipedia.org/wiki/Triangular%20matrix | In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called if all the entries above the main diagonal are zero. Similarly, a square matrix is called if all the entries below the main diagonal are zero.
Because matrix equations with triangular matrices are easier to solve, they... |
https://en.wikipedia.org/wiki/MathWorld | MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign.
History
... |
https://en.wikipedia.org/wiki/Trigonometric%20substitution | In mathematics, trigonometric substitution is the replacement of trigonometric functions for other expressions. In calculus, trigonometric substitution is a technique for evaluating integrals. Moreover, one may use the trigonometric identities to simplify certain integrals containing radical expressions. Like other met... |
https://en.wikipedia.org/wiki/Successor%20cardinal | In set theory, one can define a successor operation on cardinal numbers in a similar way to the successor operation on the ordinal numbers. The cardinal successor coincides with the ordinal successor for finite cardinals, but in the infinite case they diverge because every infinite ordinal and its successor have the sa... |
https://en.wikipedia.org/wiki/Successor%20ordinal | In set theory, the successor of an ordinal number α is the smallest ordinal number greater than α. An ordinal number that is a successor is called a successor ordinal. The ordinals 1, 2, and 3 are the first three successor ordinals and the ordinals ω+1, ω+2 and ω+3 are the first three infinite successor ordinals.
Pro... |
https://en.wikipedia.org/wiki/Mereology | In logic, philosophy and related fields, mereology ( (root: , mere-, 'part') and the suffix -logy, 'study, discussion, science') is the study of parts and the wholes they form. Whereas set theory is founded on the membership relation between a set and its elements, mereology emphasizes the meronomic relation between e... |
https://en.wikipedia.org/wiki/Frieze%20group | In mathematics, a frieze or frieze pattern is a two-dimensional design that repeats in one direction. Such patterns occur frequently in architecture and decorative art. Frieze patterns can be classified into seven types according to their symmetries. The set of symmetries of a frieze pattern is called a frieze group.
... |
https://en.wikipedia.org/wiki/Identity | Identity may refer to:
Identity document
Identity (philosophy)
Identity (social science)
Identity (mathematics)
Arts and entertainment
Film and television
Identity (1987 film), an Iranian film
Identity (2003 film), an American slasher film
Identity (game show), an American game show
Identity (TV series)... |
https://en.wikipedia.org/wiki/Truncated%20dodecahedron | In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.
Geometric relations
This polyhedron can be formed from a regular dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the ... |
https://en.wikipedia.org/wiki/Pixel%20geometry | The components of the pixels (primary colors red, green and blue) in an image sensor or display can be ordered in different patterns, called pixel geometry.
The geometric arrangement of the primary colors within a pixel varies depending on usage (see figure 1). In monitors, such as LCDs or CRTs, that typically display... |
https://en.wikipedia.org/wiki/Ten15 | Ten15 is an algebraically specified abstract machine. It was developed by Foster, Currie et al. at the Royal Signals and Radar Establishment at Malvern, Worcestershire, during the 1980s. It arose from earlier work on the Flex machine, which was a capability computer implemented via microcode. Ten15 was intended to offe... |
https://en.wikipedia.org/wiki/Nontraditional%20student | A nontraditional student is a term originating in North America, that refers to a category of students at colleges and universities.
The National Center for Education Statistics (NCES) notes that there are varying definitions of nontraditional student. Nontraditional students are contrasted with traditional students w... |
https://en.wikipedia.org/wiki/Branching%20process | In probability theory, a branching process is a type of mathematical object known as a stochastic process, which consists of collections of random variables. The random variables of a stochastic process are indexed by the natural numbers. The original purpose of branching processes was to serve as a mathematical model ... |
https://en.wikipedia.org/wiki/Hankel%20matrix | In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.:
More generally, a Hankel matrix is any matrix of the form
In terms of the components, if the element of is denoted with , and ass... |
https://en.wikipedia.org/wiki/Covering | Covering may refer to:
Window covering, material used to cover a window
Cover (topology), a collection of subsets of whose union is all of
Covering space, a certain kind of continuous maps
Covering (martial arts), an act of protecting against an opponent's strikes
The Covering, a studio album by American Christ... |
https://en.wikipedia.org/wiki/88%20%28number%29 | 88 (eighty-eight) is the natural number following 87 and preceding 89.
In mathematics
88 is:
a refactorable number.
a primitive semiperfect number.
an untouchable number.
a hexadecagonal number.
an Erdős–Woods number, since it is possible to find sequences of 88 consecutive integers such that each inner member ... |
https://en.wikipedia.org/wiki/76%20%28number%29 | 76 (seventy-six) is the natural number following 75 and preceding 77.
In mathematics
76 is:
a composite number; a square-prime, of the form (p2, q) where q is a higher prime. It is the ninth of this general form and the seventh of the form (22.q).
a Lucas number.
a telephone or involution number, the number of di... |
https://en.wikipedia.org/wiki/69%20%28number%29 | 69 (sixty-nine) is the natural number following 68 and preceding 70.
In mathematics
69 is:
a lucky number.
the twentieth semiprime (3.23) and the seventh of the form (3.q) where q is a higher prime.
the aliquot sum of sixty-nine is 27 within the aliquot sequence (69,27,13,1,0) and is the third composite number ... |
https://en.wikipedia.org/wiki/72%20%28number%29 | 72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or 6 dozen (i.e., 60 in duodecimal).
In mathematics
Seventy-two is a pronic number, as it is the product of 8 and 9. It is the smallest Achilles number, as it's a powerful number that is not itself a power.
72 is an abundant numb... |
https://en.wikipedia.org/wiki/Lowest%20common%20denominator | In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.
Description
The lowest common denominator of a set of fractions is the lowest number that is ... |
https://en.wikipedia.org/wiki/William%20Lowell%20Putnam%20Mathematical%20Competition | The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash p... |
https://en.wikipedia.org/wiki/Mayer%E2%80%93Vietoris%20sequence | In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to two Austrian mathematicians, Walther Mayer and Leopold Vietoris. The metho... |
https://en.wikipedia.org/wiki/Gauss%20map | In differential geometry, the Gauss map of a surface is a function that maps each point in the surface to a unit vector that is orthogonal to the surface at that point. Namely, given a surface X in Euclidean space R3, the Gauss map is a map N: X → S2 (where S2 is the unit sphere) such that for each p in X, the functi... |
https://en.wikipedia.org/wiki/Equivalence%20of%20categories | In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstr... |
https://en.wikipedia.org/wiki/List%20of%20cities%20and%20towns%20in%20Bangladesh | This article presents a list of cities and towns in Bangladesh. According to the Bangladesh Bureau of Statistics and the Ministry of Local Government, Rural Development and Co-operatives of Bangladesh, there are 532 urban centres in Bangladesh.
The bureau defines an urban centre with a population of 100,000 or more as... |
https://en.wikipedia.org/wiki/35%20%28number%29 | 35 (thirty-five) is the natural number following 34 and preceding 36.
In mathematics
35 is the sum of the first five triangular numbers, making it a tetrahedral number.
35 is the 10th discrete semiprime () and the first with 5 as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a hig... |
https://en.wikipedia.org/wiki/Stone%20duality | In mathematics, there is an ample supply of categorical dualities between certain categories of topological spaces and categories of partially ordered sets. Today, these dualities are usually collected under the label Stone duality, since they form a natural generalization of Stone's representation theorem for Boolean ... |
https://en.wikipedia.org/wiki/Decimal%20system | Decimal system may refer to:
Decimal (base ten) number system, used in mathematics for writing numbers and performing arithmetic
Dewey Decimal System, a subject classification system used in libraries
Decimal currency system, where each unit of currency can be divided into 100 (or 10 or 1000) sub-units
See also
M... |
https://en.wikipedia.org/wiki/D.%20H.%20Lehmer | Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991), almost always cited as D.H. Lehmer, was an American mathematician significant to the development of computational number theory. Lehmer refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes. His peripatetic career a... |
https://en.wikipedia.org/wiki/One-sided%20limit | In calculus, a one-sided limit refers to either one of the two limits of a function of a real variable as approaches a specified point either from the left or from the right.
The limit as decreases in value approaching ( approaches "from the right" or "from above") can be denoted:
The limit as increases in val... |
https://en.wikipedia.org/wiki/Inflection%20point | In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave ... |
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