source
stringlengths
31
168
text
stringlengths
51
3k
https://en.wikipedia.org/wiki/List%20of%20geometry%20topics
This is a list of geometry topics. Types, methodologies, and terminologies of geometry. Absolute geometry Affine geometry Algebraic geometry Analytic geometry Archimedes' use of infinitesimals Birational geometry Complex geometry Combinatorial geometry Computational geometry Conformal geometry Constructive...
https://en.wikipedia.org/wiki/Orthonormal%20frame
In Riemannian geometry and relativity theory, an orthonormal frame is a tool for studying the structure of a differentiable manifold equipped with a metric. If M is a manifold equipped with a metric g, then an orthonormal frame at a point P of M is an ordered basis of the tangent space at P consisting of vectors which...
https://en.wikipedia.org/wiki/Coherence%20%28philosophical%20gambling%20strategy%29
In a thought experiment proposed by the Italian probabilist Bruno de Finetti in order to justify Bayesian probability, an array of wagers is coherent precisely if it does not expose the wagerer to certain loss regardless of the outcomes of events on which they are wagering, even if their opponent makes the most judicio...
https://en.wikipedia.org/wiki/List%20of%20algebraic%20geometry%20topics
This is a list of algebraic geometry topics, by Wikipedia page. Classical topics in projective geometry Affine space Projective space Projective line, cross-ratio Projective plane Line at infinity Complex projective plane Complex projective space Plane at infinity, hyperplane at infinity Projective frame Projective tr...
https://en.wikipedia.org/wiki/Almost%20surely
In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. The concept is analogous to the concept of "almost everywhere" in measure t...
https://en.wikipedia.org/wiki/List%20of%20abstract%20algebra%20topics
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rule...
https://en.wikipedia.org/wiki/Cantor%20space
In mathematics, a Cantor space, named for Georg Cantor, is a topological abstraction of the classical Cantor set: a topological space is a Cantor space if it is homeomorphic to the Cantor set. In set theory, the topological space 2ω is called "the" Cantor space. Examples The Cantor set itself is a Cantor space. But...
https://en.wikipedia.org/wiki/1917%20in%20science
The year 1917 in science and technology involved some significant events, listed below. Biology D'Arcy Wentworth Thompson's On Growth and Form is published. Mathematics Paul Ehrenfest gives a conditional principle for a three-dimensional space. Medicine Shinobu Ishihara publishes his color perception test. Juliu...
https://en.wikipedia.org/wiki/Germ%20%28mathematics%29
In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind that captures their shared local properties. In particular, the objects in question are mostly functions (or maps) and subsets. In specific implementations of this idea, the fun...
https://en.wikipedia.org/wiki/Spin%E2%80%93statistics%20theorem
In quantum mechanics, the spin–statistics theorem relates the intrinsic spin of a particle (angular momentum not due to the orbital motion) to the particle statistics it obeys. In units of the reduced Planck constant ħ, all particles that move in 3 dimensions have either integer spin or half-integer spin. Background ...
https://en.wikipedia.org/wiki/List%20of%20general%20topology%20topics
This is a list of general topology topics. Basic concepts Topological space Topological property Open set, closed set Clopen set Closure (topology) Boundary (topology) Dense (topology) G-delta set, F-sigma set closeness (mathematics) neighbourhood (mathematics) Continuity (topology) Homeomorphism Local homeomorphism ...
https://en.wikipedia.org/wiki/Chen%20Jingrun
Chen Jingrun (; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime. Life and career Chen was the third son in a large family from Fuzhou, Fujian, China. His father was a postal worker. ...
https://en.wikipedia.org/wiki/CW%20complex
A CW complex (also called cellular complex or cell complex) is a kind of a topological space that is particularly important in algebraic topology. It was introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial comp...
https://en.wikipedia.org/wiki/Vilnius%20County
Vilnius County () is the largest of the 10 counties of Lithuania, located in the east of the country around the city Vilnius and is also known as Capital Region () by the statistics department and Eurostat. On 1 July 2010, the county administration was abolished, and since that date, Vilnius County remains as the terri...
https://en.wikipedia.org/wiki/Outline%20of%20linear%20algebra
<noinclude>This is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices. Linear equations Linear equation System of linear equations Determinant Minor Cauchy–Binet formula Cramer's rule Gaus...
https://en.wikipedia.org/wiki/Outline%20of%20category%20theory
The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific,...
https://en.wikipedia.org/wiki/Affine%20representation
In mathematics, an affine representation of a topological Lie group G on an affine space A is a continuous (smooth) group homomorphism from G to the automorphism group of A, the affine group Aff(A). Similarly, an affine representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff(A...
https://en.wikipedia.org/wiki/Percentile
In statistics, a k-th percentile, also known as percentile score or centile, is a score a given percentage k of scores in its frequency distribution falls ("exclusive" definition) or a score a given percentage falls ("inclusive" definition). Percentiles are expressed in the same unit of measurement as the input scor...
https://en.wikipedia.org/wiki/Quiver%20%28mathematics%29
In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between two vertices are allowed. Quivers are commonly used in representation theory: a representation  of a quiver assigns a vector space  to each vertex  of the quiv...
https://en.wikipedia.org/wiki/Monad%20%28category%20theory%29
In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is a monoid in the category of endofunctors of some fixed category. An endofunctor is a functor mapping a category to itself, and a monad is an endofunctor together with two natural transformati...
https://en.wikipedia.org/wiki/Outline%20of%20discrete%20mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this ...
https://en.wikipedia.org/wiki/Camille%20Jordan
Marie Ennemond Camille Jordan (; 5 January 1838 – 22 January 1922) was a French mathematician, known both for his foundational work in group theory and for his influential Cours d'analyse. Biography Jordan was born in Lyon and educated at the École polytechnique. He was an engineer by profession; later in life he taug...
https://en.wikipedia.org/wiki/Annulus%20%28mathematics%29
In mathematics, an annulus (: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer. The word "annulus" is borrowed from the Latin word anulus or annulus meaning 'little ring'. The adjectival form is annular (as in annular eclipse). The open annulu...
https://en.wikipedia.org/wiki/Submersion%20%28mathematics%29
In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective. This is a basic concept in differential topology. The notion of a submersion is dual to the notion of an immersion. Definition Let M and N be differentiable manifolds and be a differenti...
https://en.wikipedia.org/wiki/Yasha
Yasha may refer to: People with the name Gu Yasha (born 1990), Chinese footballer Nidhi Yasha (born 1983), Indian costume designer Yasha Asley (born 2003), British mathematics child prodigy Yasha Khalili (born 1988), Iranian footballer Yasha Levine (born 1981), Russian-American investigative journalist and author...
https://en.wikipedia.org/wiki/Decision%20mathematics
Decision mathematics may refer to: Discrete mathematics Decision theory, identifying the values, uncertainties and other issues relevant in a decision
https://en.wikipedia.org/wiki/Gr%C3%B6bner%20basis
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field . A Gröbner basis allows many important properties of the ideal and the associated alg...
https://en.wikipedia.org/wiki/Cauchy%E2%80%93Binet%20formula
In mathematics, specifically linear algebra, the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity for the determinant of the product of two rectangular matrices of transpose shapes (so that the product is well-defined and square). It generalizes the statement that...
https://en.wikipedia.org/wiki/Dickson%27s%20lemma
In mathematics, Dickson's lemma states that every set of -tuples of natural numbers has finitely many minimal elements. This simple fact from combinatorics has become attributed to the American algebraist L. E. Dickson, who used it to prove a result in number theory about perfect numbers. However, the lemma was certain...
https://en.wikipedia.org/wiki/Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. ...
https://en.wikipedia.org/wiki/Induced%20representation
In group theory, the induced representation is a representation of a group, , which is constructed using a known representation of a subgroup . Given a representation of , the induced representation is, in a sense, the "most general" representation of that extends the given one. Since it is often easier to find repres...
https://en.wikipedia.org/wiki/Posterior%20probability
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposit...
https://en.wikipedia.org/wiki/Proof%20by%20infinite%20descent
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading t...
https://en.wikipedia.org/wiki/Cayley%20graph
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. It is a central...
https://en.wikipedia.org/wiki/Closed%20form
Closed form may refer to: Mathematics Closed-form expression, a finitary expression Closed differential form, a differential form whose exterior derivative is the zero form , meaning . Poetry In poetry analysis, a type of poetry that exhibits regular structure, such as meter or a rhyming pattern Trobar clus, an...
https://en.wikipedia.org/wiki/Peano%20curve
In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit interval onto the unit square, however it is not injective. Peano was motivated by an earlier result of Georg Cantor that these two set...
https://en.wikipedia.org/wiki/Random%20graph
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a ...
https://en.wikipedia.org/wiki/Girard%20Desargues
Girard Desargues (; 21 February 1591September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Biography Born in Lyon, Desargues came from a family devoted...
https://en.wikipedia.org/wiki/Desargues%27s%20theorem
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in perspective centrally. Denote the three vertices of one triangle by and , and those of the other by and . Axial perspectivity means that lines and meet in a poi...
https://en.wikipedia.org/wiki/Method%20of%20complements
In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism) for addition throughout the whole range. For a given number of places half of the possible representations of numbers encode t...
https://en.wikipedia.org/wiki/Lucas%20primality%20test
In computational number theory, the Lucas test is a primality test for a natural number n; it requires that the prime factors of n − 1 be already known. It is the basis of the Pratt certificate that gives a concise verification that n is prime. Concepts Let n be a positive integer. If there exists an integer a, 1 < ...
https://en.wikipedia.org/wiki/Serre%20duality
In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The basic version applies to vector bundles on a smooth projective variety, but Alexander Grothendieck found wide generalizations, for example to singular var...
https://en.wikipedia.org/wiki/Oscar%20Zariski
Oscar Zariski (April 24, 1899 – July 4, 1986) was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century. Education Zariski was born Oscher (also transliterated as Ascher or Osher) Zaritsky to a Jewish family (his parents were Bezalel Zaritsky and Hanna Tennenbaum...
https://en.wikipedia.org/wiki/List%20of%20mathematical%20examples
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of...
https://en.wikipedia.org/wiki/Cumulant
In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa. The first cumulant is the mea...
https://en.wikipedia.org/wiki/Unicoherent%20space
In mathematics, a unicoherent space is a topological space that is connected and in which the following property holds: For any closed, connected with , the intersection is connected. For example, any closed interval on the real line is unicoherent, but a circle is not. If a unicoherent space is more strongly he...
https://en.wikipedia.org/wiki/Regular%20representation
In mathematics, and in particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself by translation. One distinguishes the left regular representation λ given by left translation and the right regular representation ρ gi...
https://en.wikipedia.org/wiki/Free%20product
In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “universal” group having these properties, in the sense that any two homomorphisms f...
https://en.wikipedia.org/wiki/Constructive%20proof
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a part...
https://en.wikipedia.org/wiki/Function%20of%20several%20complex%20variables
The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space , that is, -tuples of complex numbers. The name of the field dealing with the properties of these functions is called several complex variables (and analytic space), which the...
https://en.wikipedia.org/wiki/Gimel%20function
In axiomatic set theory, the gimel function is the following function mapping cardinal numbers to cardinal numbers: where cf denotes the cofinality function; the gimel function is used for studying the continuum function and the cardinal exponentiation function. The symbol is a serif form of the Hebrew letter gimel. ...
https://en.wikipedia.org/wiki/Amalgamation
Amalgamation is the process of combining or uniting multiple entities into one form. Amalgamation, amalgam, and other derivatives may refer to: Mathematics and science Amalgam (chemistry), the combination of mercury with another metal Pan amalgamation, another extraction method with additional compound Patio process...
https://en.wikipedia.org/wiki/Weil%20restriction
In mathematics, restriction of scalars (also known as "Weil restriction") is a functor which, for any finite extension of fields L/k and any algebraic variety X over L, produces another variety ResL/kX, defined over k. It is useful for reducing questions about varieties over large fields to questions about more complic...
https://en.wikipedia.org/wiki/Generalized%20hypergeometric%20function
In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation...
https://en.wikipedia.org/wiki/Rational%20function
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of...
https://en.wikipedia.org/wiki/Negentropy
In information theory and statistics, negentropy is used as a measure of distance to normality. The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-science book What is Life? Later, French physicist Léon Brillouin shortened the phrase to néguentropie (negentropy). In 1974,...
https://en.wikipedia.org/wiki/Line%20bundle
In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example, a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising these. More formally, in algebraic topology and differential topology, a li...
https://en.wikipedia.org/wiki/Descent%20%28mathematics%29
In mathematics, the idea of descent extends the intuitive idea of 'gluing' in topology. Since the topologists' glue is the use of equivalence relations on topological spaces, the theory starts with some ideas on identification. Descent of vector bundles The case of the construction of vector bundles from data on a di...
https://en.wikipedia.org/wiki/Second%20Hardy%E2%80%93Littlewood%20conjecture
In number theory, the second Hardy–Littlewood conjecture concerns the number of primes in intervals. Along with the first Hardy–Littlewood conjecture, the second Hardy–Littlewood conjecture was proposed by G. H. Hardy and John Edensor Littlewood in 1923. Statement The conjecture states that for integers , where deno...
https://en.wikipedia.org/wiki/Moduli%20space
In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can ...
https://en.wikipedia.org/wiki/Order%20theory
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic t...
https://en.wikipedia.org/wiki/Idempotent%20%28ring%20theory%29
In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element such that . That is, the element is idempotent under the ring's multiplication. Inductively then, one can also conclude that for any positive integer . For example, an idempotent element of a matrix ring is pre...
https://en.wikipedia.org/wiki/SCFG
SCFG may refer to Stochastic context-free grammar, generative probability model that takes the shape of a context-free grammar Synchronous context-free grammar, in machine translation
https://en.wikipedia.org/wiki/22%20%28number%29
22 (twenty-two) is the natural number following 21 and preceding 23. In mathematics 22 is a palindromic number. It is the second Smith number, the second Erdős–Woods number, and the fourth large Schröder number. It is also a Perrin number, from a sum of 10 and 12. 22 is the sixth distinct semiprime, and the fout...
https://en.wikipedia.org/wiki/24%20%28number%29
24 (twenty-four) is the natural number following 23 and preceding 25. In mathematics 24 is an even composite number, with 2 and 3 as its distinct prime factors. It is the first number of the form 2q, where q is an odd prime. It is the smallest number with at least eight positive divisors: 1, 2, 3, 4, 6, 8, 12, and 24;...
https://en.wikipedia.org/wiki/23%20%28number%29
23 (twenty-three) is the natural number following 22 and preceding 24. In mathematics Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. It is, however, a cousin prime with 19, and a sexy prime with 17 and 29; while also being the largest member of the first prime sextuplet (7, 1...
https://en.wikipedia.org/wiki/25%20%28number%29
25 (twenty-five) is the natural number following 24 and preceding 26. In mathematics It is a square number, being 52 = 5 × 5, and hence the third non-unitary square prime of the form p2. It is one of two two-digit numbers whose square and higher powers of the number also ends in the same last two digits, e.g., 252 =...
https://en.wikipedia.org/wiki/26%20%28number%29
26 (twenty-six) is the natural number following 25 and preceding 27. In mathematics 26 is the seventh discrete semiprime () and the fifth with 2 as the lowest non-unitary factor thus of the form (2.q), where q is a higher prime. with an aliquot sum of 16, within an aliquot sequence of five composite numbers (26,16...
https://en.wikipedia.org/wiki/29%20%28number%29
29 (twenty-nine) is the natural number following 28 and preceding 30. Mathematics 29 is the tenth prime number, and the fifth primorial prime. 29 forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. 29 is the sum of three consecutive squares, ...
https://en.wikipedia.org/wiki/28%20%28number%29
28 (twenty-eight) is the natural number following 27 and preceding 29. In mathematics It is a composite number; a square-prime, of the form (p2,q) where q is a higher prime. It is the third of this form and of the specific form (22.q), with proper divisors being 1, 2, 4, 7, and 14. Twenty-eight is the second perfect...
https://en.wikipedia.org/wiki/Walks%20plus%20hits%20per%20inning%20pitched
In baseball statistics, walks plus hits per inning pitched (WHIP) is a sabermetric measurement of the number of baserunners a pitcher has allowed per inning pitched. WHIP is calculated by adding the number of walks and hits allowed and dividing this sum by the number of innings pitched. WHIP reflects a pitcher's prope...
https://en.wikipedia.org/wiki/Separable%20polynomial
In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots is equal to the degree of the polynomial. This concept is closely related to square-free polynomial. If K is a perfect field then the two concepts coincide. ...
https://en.wikipedia.org/wiki/Karol%20Borsuk
Karol Borsuk (8 May 1905 – 24 January 1982) was a Polish mathematician. His main interest was topology, while he obtained significant results also in functional analysis. Borsuk introduced the theory of absolute retracts (ARs) and absolute neighborhood retracts (ANRs), and the cohomotopy groups, later called Borsuk–S...
https://en.wikipedia.org/wiki/Samuel%20Eilenberg
Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra. Early life and education He was born in Warsaw, Kingdom of Poland to a Jewish family. He spent much of his career as a professor at Columbia Univ...
https://en.wikipedia.org/wiki/Henri%20Cartan
Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer , physicist and mathematician , and the son-in-law of physicist Pierr...
https://en.wikipedia.org/wiki/J.%20A.%20Todd
John Arthur Todd (23 August 1908 – 22 December 1994) was an English mathematician who specialised in geometry. Biography He was born in Liverpool, and went up to Trinity College, Cambridge in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester. He became a lecturer at C...
https://en.wikipedia.org/wiki/Kazimierz%20Zarankiewicz
Kazimierz Zarankiewicz (2 May 1902 – 5 September 1959) was a Polish mathematician and Professor at the Warsaw University of Technology who was interested primarily in topology and graph theory. Biography Zarankiewicz was born in Częstochowa to father Stanisław and mother Józefa (née Borowska). He studied at the Unive...
https://en.wikipedia.org/wiki/Stanis%C5%82aw%20Saks
Stanisław Saks (30 December 1897 – 23 November 1942) was a Polish mathematician and university tutor, a member of the Lwów School of Mathematics, known primarily for his membership in the Scottish Café circle, an extensive monograph on the theory of integrals, his works on measure theory and the Vitali–Hahn–Saks theore...
https://en.wikipedia.org/wiki/Scottish%20Caf%C3%A9
The Scottish Café () was a café in Lwów, Poland (now Lviv, Ukraine) where, in the 1930s and 1940s, mathematicians from the Lwów School of Mathematics collaboratively discussed research problems, particularly in functional analysis and topology. Stanisław Ulam recounts that the tables of the café had marble tops, so t...
https://en.wikipedia.org/wiki/W%C5%82adys%C5%82aw%20Orlicz
Władysław Roman Orlicz (May 24, 1903 – August 9, 1990) was a Polish mathematician of Lwów School of Mathematics. His main interests were functional analysis and topology: Orlicz spaces are named after him. Education and career Orlicz was the third of Franciszek and Maria Orlicz's five children. His youngest brother d...
https://en.wikipedia.org/wiki/Fantasy%20hockey
Fantasy hockey is a form of fantasy sport where players build a team that competes with other players who do the same, based on the statistics generated by professional hockey players or teams. The majority of fantasy hockey pools are based on the teams and players of the ice hockey National Hockey League (NHL). A typ...
https://en.wikipedia.org/wiki/Johnny%20Ball
Johnny Ball (born Graham Thalben Ball; 23 May 1938) is an English television personality and a populariser of mathematics. He is also the father of BBC Radio 2 DJ Zoe Ball. Early life Ball was born in Bristol and attended Kingswood Primary School on the eastern edge of the city. Later in his childhood the family moved...
https://en.wikipedia.org/wiki/Parallelogram%20law
In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. We use these notations for the...
https://en.wikipedia.org/wiki/SPSD
SPSD can refer to: Southfield Public School District Saskatoon Public School Division Symmetric Positive Semi-Definite matrix, in linear algebra
https://en.wikipedia.org/wiki/38%20%28number%29
38 (thirty-eight) is the natural number following 37 and preceding 39. In mathematics specifically, the 11th discrete Semiprime, it being the 7th of the form (2.q). the first member of the third cluster of two discrete semiprimes 38, 39 the next such cluster is 57, 58. with an aliquot sum of 22 in an aliquot seque...
https://en.wikipedia.org/wiki/Homogeneous%20space
In mathematics, a homogeneous space is, very informally, a space that looks the same everywhere, as you move through it, with movement given by the action of a group. Homogeneous spaces occur in the theories of Lie groups, algebraic groups and topological groups. More precisely, a homogeneous space for a group G is a n...
https://en.wikipedia.org/wiki/Separable%20extension
In field theory, a branch of algebra, an algebraic field extension is called a separable extension if for every , the minimal polynomial of over is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). There is also a more g...
https://en.wikipedia.org/wiki/Fredholm%20integral%20equation
In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. A useful method to solve such equations, the Adomian decomposition method, is due to George Ado...
https://en.wikipedia.org/wiki/Combinatorial%20topology
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes. After the proof of the simpli...
https://en.wikipedia.org/wiki/Principal%20homogeneous%20space
In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial. Equivalently, a principal homogeneous space for a group G is a non-empty set X on which G acts freely and transitively (meaning that, for any x, y in X, ther...
https://en.wikipedia.org/wiki/Colombeau%20algebra
In mathematics, a Colombeau algebra is an algebra of a certain kind containing the space of Schwartz distributions. While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this. Such a multiplication of distributions has long...
https://en.wikipedia.org/wiki/Characteristic%20class
In mathematics, a characteristic class is a way of associating to each principal bundle of X a cohomology class of X. The cohomology class measures the extent the bundle is "twisted" and whether it possesses sections. Characteristic classes are global invariants that measure the deviation of a local product structure f...
https://en.wikipedia.org/wiki/Serre%E2%80%93Swan%20theorem
In the mathematical fields of topology and K-theory, the Serre–Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective modules and gives rise to a common intuition throughout mathematics: "projective modules over commutative rings are like vector b...
https://en.wikipedia.org/wiki/Universal%20enveloping%20algebra
In mathematics, the universal enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal enveloping algebras are used in the representation theory of Lie groups and Lie algebras. For example, Verma modules can b...
https://en.wikipedia.org/wiki/Tensor%20algebra
In mathematics, the tensor algebra of a vector space V, denoted T(V) or T(V), is the algebra of tensors on V (of any rank) with multiplication being the tensor product. It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the "most general" algeb...
https://en.wikipedia.org/wiki/Invariant%20theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under ...
https://en.wikipedia.org/wiki/Canonical%20correlation
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices. If we have two vectors X = (X1, ..., Xn) and Y = (Y1, ..., Ym) of random variables, and there are correlations among the variables, then canonical-correlation ...
https://en.wikipedia.org/wiki/Benjamin%20Peirce
Benjamin Peirce (; April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philosophy of mathematics. Early life He was born in Salem, Massachusetts, the son of...
https://en.wikipedia.org/wiki/Gelfand%20representation
In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things: a way of representing commutative Banach algebras as algebras of continuous functions; the fact that for commutative C*-algebras, this representation is an isometric isomorphism. In the former case...
https://en.wikipedia.org/wiki/Functional%20equation
In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning is often used, where a functional equation is an equation that relates seve...