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https://en.wikipedia.org/wiki/Postfix | Postfix may refer to:
Postfix (linguistics), an affix which is placed after the stem of a word
Postfix notation, a way of writing algebraic and other expressions
Postfix (software), a mail transfer agent |
https://en.wikipedia.org/wiki/Acyclic | Acyclic may refer to:
In chemistry, a compound which is an open-chain compound, e.g. alkanes and acyclic aliphatic compounds
In mathematics:
A graph without a cycle, especially
A directed acyclic graph
An acyclic complex is a chain complex all of whose homology groups are zero
In economics, an economic indicator ... |
https://en.wikipedia.org/wiki/P-adic%20analysis | In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers.
The theory of complex-valued numerical functions on the p-adic numbers is part of the theory of locally compact groups. The usual meaning taken for p-adic analysis is the theory of p-a... |
https://en.wikipedia.org/wiki/Sadleirian%20Professor%20of%20Pure%20Mathematics | The Sadleirian Professorship of Pure Mathematics, originally spelled in the statutes and for the first two professors as Sadlerian, is a professorship in pure mathematics within the DPMMS at the University of Cambridge. It was founded on a bequest from Lady Mary Sadleir for lectureships "for the full and clear explicat... |
https://en.wikipedia.org/wiki/Fatou%27s%20lemma | In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after Pierre Fatou.
Fatou's lemma can be used to prove the Fatou–Lebesgue theorem and Lebesgue's dominated c... |
https://en.wikipedia.org/wiki/Glossary%20of%20field%20theory | Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.)
Definition of a field
A field is a commutative ring in which and every nonzero element has a multiplicative inverse. In a... |
https://en.wikipedia.org/wiki/Seminorm | In mathematics, particularly in functional analysis, a seminorm is a vector space norm that need not be positive definite. Seminorms are intimately connected with convex sets: every seminorm is the Minkowski functional of some absorbing disk and, conversely, the Minkowski functional of any such set is a seminorm.
A t... |
https://en.wikipedia.org/wiki/Sarvadaman%20Chowla | Sarvadaman D. S. Chowla (22 October 1907 – 10 December 1995) was an Indian American mathematician, specializing in number theory.
Early life
He was born in London, since his father, Gopal Chowla, a professor of mathematics in Lahore, was then studying in Cambridge. His family returned to India, where he received his m... |
https://en.wikipedia.org/wiki/Self-selection%20bias | In statistics, self-selection bias arises in any situation in which individuals select themselves into a group, causing a biased sample with nonprobability sampling. It is commonly used to describe situations where the characteristics of the people which cause them to select themselves in the group create abnormal or ... |
https://en.wikipedia.org/wiki/Richard%20Borcherds | Richard Ewen Borcherds (; born 29 November 1959) is a British mathematician currently working in quantum field theory. He is known for his work in lattices, group theory, and infinite-dimensional algebras, for which he was awarded the Fields Medal in 1998.
Early life
Borcherds was born in Cape Town, South Africa, but... |
https://en.wikipedia.org/wiki/Partial | Partial may refer to:
Mathematics
Partial derivative, derivative with respect to one of several variables of a function, with the other variables held constant
∂, a symbol that can denote a partial derivative, sometimes pronounced "partial dee"
Partial differential equation, a differential equation that contains unkn... |
https://en.wikipedia.org/wiki/Stochastic | Stochastic (; ) refers to the property of being well-described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability... |
https://en.wikipedia.org/wiki/Topologist%27s%20sine%20curve | In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example.
It can be defined as the graph of the function sin(1/x) on the half-open interval (0, 1], together with the origin, und... |
https://en.wikipedia.org/wiki/Combinatorial%20game%20theory | Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a position that the players take turns changing in defined ways or moves to achieve a defined winning cond... |
https://en.wikipedia.org/wiki/Transitive%20closure | In mathematics, the transitive closure of a homogeneous binary relation on a set is the smallest relation on that contains and is transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets is the unique minimal transitive superset of .
For examp... |
https://en.wikipedia.org/wiki/One-to-one | One-to-one or one to one may refer to:
Mathematics and communication
One-to-one function, also called an injective function
One-to-one correspondence, also called a bijective function
One-to-one (communication), the act of an individual communicating with another
One-to-one (data model), a relationship in a data mode... |
https://en.wikipedia.org/wiki/Cube%20root | In mathematics, a cube root of a number is a number such that . All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of , denoted , is , because , while the other c... |
https://en.wikipedia.org/wiki/Representation%20of%20a%20Lie%20group | In mathematics and theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of invertible operators on the vector space. Representations play an important role in the study of continuous ... |
https://en.wikipedia.org/wiki/Unitary%20representation | In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in the case that G is a locally compact (Hausdorff) topological group and the representations are strongly conti... |
https://en.wikipedia.org/wiki/Simple%20Lie%20group | In mathematics, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can be used to read off the list of simple Lie algebras and Riemannian symmetric spaces.
Together with the commutative Lie group of the real numbers, , and ... |
https://en.wikipedia.org/wiki/Symplectic%20vector%20space | In mathematics, a symplectic vector space is a vector space V over a field F (for example the real numbers R) equipped with a symplectic bilinear form.
A symplectic bilinear form is a mapping that is
Bilinear Linear in each argument separately;
Alternating holds for all ; and
Non-degenerate for all implies that... |
https://en.wikipedia.org/wiki/G2%20%28mathematics%29 | {{DISPLAYTITLE:G2 (mathematics)}}
In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has two fund... |
https://en.wikipedia.org/wiki/F4%20%28mathematics%29 | {{DISPLAYTITLE:F4 (mathematics)}}
In mathematics, F4 is the name of a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The compact form is simply connected and its outer automorphism group is the trivial group. Its fundamental representation is... |
https://en.wikipedia.org/wiki/Suprematism | Suprematism () is an early twentieth-century art movement focused on the fundamentals of geometry (circles, squares, rectangles), painted in a limited range of colors. The term suprematism refers to an abstract art based upon "the supremacy of pure artistic feeling" rather than on visual depiction of objects.
Founded ... |
https://en.wikipedia.org/wiki/Character%20%28mathematics%29 | In mathematics, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers). There are at least two distinct, but overlapping meanings. Other uses of the word "character" are almost always qualified.
Multiplicative character
A multiplicative character (or linear cha... |
https://en.wikipedia.org/wiki/%2A-algebra | In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings and , where is commutative and has the structure of an associative algebra over . Involutive algebras generalize the idea of a number system equipped with conj... |
https://en.wikipedia.org/wiki/Antilinear%20map | In mathematics, a function between two complex vector spaces is said to be antilinear or conjugate-linear if
hold for all vectors and every complex number where denotes the complex conjugate of
Antilinear maps stand in contrast to linear maps, which are additive maps that are homogeneous rather than conjugate ... |
https://en.wikipedia.org/wiki/Involution%20%28mathematics%29 | In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse,
for all in the domain of . Equivalently, applying twice produces the original value.
General properties
Any involution is a bijection.
The identity map is a trivial example of an involution. Exam... |
https://en.wikipedia.org/wiki/24-cell | In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,4,3}. It is also called C24, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, octacube, hyper-diamond or polyoctahedron, being constructed of octahedral... |
https://en.wikipedia.org/wiki/Orbifold | In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space.
Definitions of orbifold have been given several times: by Ichirô Satake in ... |
https://en.wikipedia.org/wiki/Indefinite%20orthogonal%20group | In mathematics, the indefinite orthogonal group, is the Lie group of all linear transformations of an n-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear form of signature , where . It is also called the pseudo-orthogonal group or generalized orthogonal group. The dimension of the ... |
https://en.wikipedia.org/wiki/Eddington%E2%80%93Finkelstein%20coordinates | In general relativity, Eddington–Finkelstein coordinates are a pair of coordinate systems for a Schwarzschild geometry (e.g. a spherically symmetric black hole) which are adapted to radial null geodesics. Null geodesics are the worldlines of photons; radial ones are those that are moving directly towards or away from ... |
https://en.wikipedia.org/wiki/E6%20%28mathematics%29 | {{DISPLAYTITLE:E6 (mathematics)}}
In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras , all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6. The designation E6 comes from the Cartan–Killing class... |
https://en.wikipedia.org/wiki/E6 | E6, E06, E.VI or E-6 can mean:
Science, mathematics and engineering
The E6 series (number series) of preferred numbers for electronic components
E6 (mathematics), a Lie group in mathematics
E6 polytope in geometry
E06, Thyroiditis ICD-10 code
E-6 process, a common photographic process for developing transparenc... |
https://en.wikipedia.org/wiki/Closure%20%28mathematics%29 | In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: is not a natural number, although both 1 and 2 are... |
https://en.wikipedia.org/wiki/Aleph%20number | In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Hebrew letter aleph ().
The ca... |
https://en.wikipedia.org/wiki/Arithmetization%20of%20analysis | The arithmetization of analysis was a research program in the foundations of mathematics carried out in the second half of the 19th century.
History
Kronecker originally introduced the term arithmetization of analysis, by which he meant its constructivization in the context of the natural numbers (see quotation at bot... |
https://en.wikipedia.org/wiki/Von%20Neumann%20algebra | In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra.
Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of ... |
https://en.wikipedia.org/wiki/Commute | Commute, commutation or commutative may refer to:
Commuting, the process of travelling between a place of residence and a place of work
Mathematics
Commutative property, a property of a mathematical operation whose result is insensitive to the order of its arguments
Equivariant map, a function whose composition wit... |
https://en.wikipedia.org/wiki/Symplectic%20geometry | Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain... |
https://en.wikipedia.org/wiki/Poisson%20bracket | In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system. The Poisson bracket also distinguishes a certain class of coordinate transfo... |
https://en.wikipedia.org/wiki/Chern%20class | In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since become fundamental concepts in many branches of mathematics and physics, such as string theory, Chern–Simons theory, kno... |
https://en.wikipedia.org/wiki/Anticommutative%20property | In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped arguments. The notion inverse refers to a group structure on the operation's co... |
https://en.wikipedia.org/wiki/Jacobi%20identity | In mathematics, the Jacobi identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product, affects the result of the operation. By contrast, for operations with the associative property, any order of evaluation gives the same result (parenthes... |
https://en.wikipedia.org/wiki/Chern%E2%80%93Simons%20form | In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.
Definition
Given a manifold and a Lie algebra valued ... |
https://en.wikipedia.org/wiki/Commutative%20property | In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like or , the property can also be used in... |
https://en.wikipedia.org/wiki/Lie%20derivative | In differential geometry, the Lie derivative ( ), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate invariant and therefore the Lie derivative is de... |
https://en.wikipedia.org/wiki/Peter%E2%80%93Weyl%20theorem | In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian. It was initially proved by Hermann Weyl, with his student Fritz Peter, in the setting of a compact topological group G . The theorem is a collect... |
https://en.wikipedia.org/wiki/Smooth | Smooth may refer to:
Mathematics
Smooth function, a function that is infinitely differentiable; used in calculus and topology
Smooth manifold, a differentiable manifold for which all the transition maps are smooth functions
Smooth algebraic variety, an algebraic variety with no singular points
Smooth number, a num... |
https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange%20equation | In the calculus of variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematicia... |
https://en.wikipedia.org/wiki/Locally%20constant%20function | In mathematics, a locally constant function is a function from a topological space into a set with the property that around every point of its domain, there exists some neighborhood of that point on which it restricts to a constant function.
Definition
Let be a function from a topological space into a set
If t... |
https://en.wikipedia.org/wiki/Reflection%20%28mathematics%29 | In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis ... |
https://en.wikipedia.org/wiki/Inversive%20geometry | In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied. Inversion seems to h... |
https://en.wikipedia.org/wiki/Conformal%20geometry | In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.
In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal t... |
https://en.wikipedia.org/wiki/Noncommutative%20geometry | Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense). A noncommutative algebra is an associative algebra in whic... |
https://en.wikipedia.org/wiki/Field%20theory | Field theory may refer to:
Science
Field (mathematics), the theory of the algebraic concept of field
Field theory (physics), a physical theory which employs fields in the physical sense, consisting of three types:
Classical field theory, the theory and dynamics of classical fields
Quantum field theory, the theory ... |
https://en.wikipedia.org/wiki/BPS | BPS, Bps or bps may refer to:
Science and mathematics
Plural of bp, base pair, a measure of length of DNA
Plural of bp, basis point, one one-hundredth of a percentage point - ‱
Battered person syndrome, a physical and psychological condition found in victims of abuse
Best practice statement, a qualification of a metho... |
https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Ko%E2%80%93Rado%20theorem | In mathematics, the Erdős–Ko–Rado theorem limits the number of sets in a family of sets for which every two sets have at least one element in common. Paul Erdős, Chao Ko, and Richard Rado proved the theorem in 1938, but did not publish it until 1961. It is part of the field of combinatorics, and one of the central resu... |
https://en.wikipedia.org/wiki/Institut%20national%20de%20la%20statistique%20et%20des%20%C3%A9tudes%20%C3%A9conomiques | The National Institute of Statistics and Economic Studies (), abbreviated INSEE or Insee ( , ), is the national statistics bureau of France. It collects and publishes information about the French economy and people and carries out the periodic national census. Headquartered in Montrouge, a commune in the southern Paris... |
https://en.wikipedia.org/wiki/Weyl%20group | In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to the roots, and as such is a finite refl... |
https://en.wikipedia.org/wiki/Schild%27s%20Ladder | Schild's Ladder is a 2002 science fiction novel by Australian author Greg Egan. The book derives its name from Schild's ladder, a construction in differential geometry, devised by the mathematician and physicist Alfred Schild.
Plot summary
Twenty-thousand years in the future, Cass, a humanoid physicist from Earth, tr... |
https://en.wikipedia.org/wiki/Construction%20of%20the%20real%20numbers | In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain any smaller complete ordered field. Such a definition does not prove that such a complete ordered field exists, and the existence proof consists of constructing a ... |
https://en.wikipedia.org/wiki/Universe%20%28mathematics%29 | In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains all the entities one wishes to consider in a given situation.
In set theory, universes are often classes that contain (as elements) all sets for which one hopes to ... |
https://en.wikipedia.org/wiki/Necklace%20problem | The necklace problem is a problem in recreational mathematics concerning the reconstruction of necklaces (cyclic arrangements of binary values) from partial information.
Formulation
The necklace problem involves the reconstruction of a necklace of beads, each of which is either black or white, from partial informati... |
https://en.wikipedia.org/wiki/Coxeter%20group | In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry groups of regular polyhedra are an example. Howe... |
https://en.wikipedia.org/wiki/Word%20problem%20%28mathematics%20education%29 | In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred ... |
https://en.wikipedia.org/wiki/Transcendental%20function | In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.
In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically using a finite amount of terms.
Examples of transcendental fu... |
https://en.wikipedia.org/wiki/Aryabhata | Aryabhata ( ISO: ) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old) and the Arya-siddhanta.
For his explicit mention ... |
https://en.wikipedia.org/wiki/Brahmagupta | Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the Brāhmasphuṭasiddhānta (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical treatise, and the Khaṇḍakhādyaka ("edible bite", dated 665), a more practical text.
In ... |
https://en.wikipedia.org/wiki/Gelfand%E2%80%93Naimark%E2%80%93Segal%20construction | In functional analysis, a discipline within mathematics, given a C*-algebra A, the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic *-representations of A and certain linear functionals on A (called states). The correspondence is shown by an explicit construction of the *-representation ... |
https://en.wikipedia.org/wiki/Composition%20series | In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed in... |
https://en.wikipedia.org/wiki/Lie%20superalgebra | In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. In most of these theories, the even elements of the superalgebra correspond to bosons and odd elements ... |
https://en.wikipedia.org/wiki/Homotopy%20group | In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological spa... |
https://en.wikipedia.org/wiki/Jensen%27s%20inequality | In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in... |
https://en.wikipedia.org/wiki/Chord%20%28geometry%29 | A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (La... |
https://en.wikipedia.org/wiki/Brownian%20tree | In probability theory, the Brownian tree, or Aldous tree, or Continuum Random Tree (CRT) is a random real tree that can be defined from a Brownian excursion. The Brownian tree was defined and studied by David Aldous in three articles published in 1991 and 1993. This tree has since then been generalized.
This random tr... |
https://en.wikipedia.org/wiki/Identity%20%28mathematics%29 | In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables within a certain range of validity. In other words, A = B is an identity if A and B define... |
https://en.wikipedia.org/wiki/Affine%20group | In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself. In the case of a Euclidean space (where the associated field of scalars is the real numbers), the affine group consists of those functions from the space to its... |
https://en.wikipedia.org/wiki/Affine%20space | In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. Affine spac... |
https://en.wikipedia.org/wiki/Affine%20combination | In mathematics, an affine combination of is a linear combination
such that
Here, can be elements (vectors) of a vector space over a field , and the coefficients are elements of .
The elements can also be points of a Euclidean space, and, more generally, of an affine space over a field . In this case the are ... |
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Carl%20Friedrich%20Gauss | Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymous adjective Gaussian is pronounced .
Mathematics
Algebra and linear algebr... |
https://en.wikipedia.org/wiki/Double%20play | In baseball and softball, a double play (denoted as DP in baseball statistics) is the act of making two outs during the same continuous play. Double plays can occur any time there is at least one baserunner and fewer than two outs.
In Major League Baseball (MLB), the double play is defined in the Official Rules in the... |
https://en.wikipedia.org/wiki/Triple%20play | In baseball, a triple play (denoted as TP in baseball statistics) is the act of making three outs during the same play. There have only been 735 triple plays in Major League Baseball (MLB) since 1876, an average of just over five per season.
They depend on a combination of two factors, which are themselves uncommon:
... |
https://en.wikipedia.org/wiki/Error%20%28baseball%29 | In baseball and softball statistics, an error is an act, in the judgment of the official scorer, of a fielder misplaying a ball in a manner that allows a batter or baserunner to advance one or more bases or allows a plate appearance to continue after the batter should have been put out. The term error is sometimes use... |
https://en.wikipedia.org/wiki/Dy | DY, D. Y., Dy, or dy may refer to:
In science and technology, and mathematics
Astronomy
DY Persei, a variable star in the Perseus constellation
DY Persei variable, a subclass of R Coronae Borealis variables
DY Eridani, a triple star system less than 16.5 light years away from Earth
Other sciences
, in calculus,... |
https://en.wikipedia.org/wiki/James%20H.%20Wilkinson | James Hardy Wilkinson FRS (27 September 1919 – 5 October 1986) was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering.
Education
Born in Strood, England, he won a Foundation Scholarship to Sir Joseph ... |
https://en.wikipedia.org/wiki/Functional%20derivative | In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional (a functional in this sense is a function that acts on functions) to a change in a function on which the functional depends.
In the calculus of variations, functionals... |
https://en.wikipedia.org/wiki/Functional%20integration | Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of ... |
https://en.wikipedia.org/wiki/Anti-de%20Sitter%20space | In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observ... |
https://en.wikipedia.org/wiki/Adjoint%20representation | In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n-by-n invertible matrices, then the adjoint representation ... |
https://en.wikipedia.org/wiki/Self-adjoint | In mathematics, and more specifically in abstract algebra, an element x of a *-algebra is self-adjoint if . A self-adjoint element is also Hermitian, though the reverse doesn't necessarily hold.
A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation. For example, ... |
https://en.wikipedia.org/wiki/Lies%2C%20damned%20lies%2C%20and%20statistics | "Lies, damned lies, and statistics" is a phrase describing the persuasive power of statistics to bolster weak arguments, "one of the best, and best-known" critiques of applied statistics. It is also sometimes colloquially used to doubt statistics used to prove an opponent's point.
The phrase was popularized in the Uni... |
https://en.wikipedia.org/wiki/Rhomboid | Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. The terms rhomboid and parallelogram are often erroneously conflated with each other (i.e, when most people refer to a "parallelogram" they almost always mean a rhomb... |
https://en.wikipedia.org/wiki/Wronskian | In the mathematics of a square matrix, the Wronskian (or Wrońskian) is a determinant introduced by the Polish mathematician . It is used in the study of differential equations, where it can sometimes show linear independence of a set of solutions.
Definition
The Wronskian of two differentiable functions and is .
... |
https://en.wikipedia.org/wiki/Crispin%20Wright | Crispin James Garth Wright (; born 21 December 1942) is a British philosopher, who has written on neo-Fregean (neo-logicist) philosophy of mathematics, Wittgenstein's later philosophy, and on issues related to truth, realism, cognitivism, skepticism, knowledge, and objectivity. He is Professor of Philosophical Researc... |
https://en.wikipedia.org/wiki/Gaussian%20process | In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The dist... |
https://en.wikipedia.org/wiki/Shing-Tung%20Yau | Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician and the William Caspar Graustein Professor of Mathematics at Harvard University. In April 2022, Yau retired from Harvard to become a professor of mathematics at Tsinghua University.
Yau was born in Shantou, China, moved to Hong Kong at a young... |
https://en.wikipedia.org/wiki/Gudermannian%20function | In mathematics, the Gudermannian function relates a hyperbolic angle measure to a circular angle measure called the gudermannian of and denoted . The Gudermannian function reveals a close relationship between the circular functions and hyperbolic functions. It was introduced in the 1760s by Johann Heinrich Lambert, ... |
https://en.wikipedia.org/wiki/Totally%20disconnected%20space | In topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets. In every topological space, the singletons (and, when it is considered connected, the empty set) are connected; in a totally disconnected space, these are the only connecte... |
https://en.wikipedia.org/wiki/Quintic%20function | In mathematics, a quintic function is a function of the form
where , , , , and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. In other words, a quintic function is defined by a polynomial of degree five.
Because they have an odd degree, normal quint... |
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