text
stringlengths
100
500k
subset
stringclasses
4 values
abc conjecture The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985.[1][2] It is stated in terms of three positive integers $a,b$ and $c$ (hence the name) that are relatively prime and satisfy $a+b=...
Wikipedia
ABS methods ABS methods, where the acronym contains the initials of Jozsef Abaffy, Charles G. Broyden and Emilio Spedicato, have been developed since 1981 to generate a large class of algorithms for the following applications: • solution of general linear algebraic systems, determined or underdetermined, • full o...
Wikipedia
AC0 AC0 is a complexity class used in circuit complexity. It is the smallest class in the AC hierarchy, and consists of all families of circuits of depth O(1) and polynomial size, with unlimited-fanin AND gates and OR gates (we allow NOT gates only at the inputs).[1] It thus contains NC0, which has only bounded-fanin ...
Wikipedia
ACC0 ACC0, sometimes called ACC, is a class of computational models and problems defined in circuit complexity, a field of theoretical computer science. The class is defined by augmenting the class AC0 of constant-depth "alternating circuits" with the ability to count; the acronym ACC stands for "AC with counters".[1]...
Wikipedia
ACORN (random number generator) The ACORN or ″Additive Congruential Random Number″ generators are a robust family of pseudorandom number generators (PRNGs) for sequences of uniformly distributed pseudo-random numbers, introduced in 1989 and still valid in 2019, thirty years later. Introduced by R.S.Wikramaratna,[1] A...
Wikipedia
AC (complexity) In circuit complexity, AC is a complexity class hierarchy. Each class, ACi, consists of the languages recognized by Boolean circuits with depth $O(\log ^{i}n)$ and a polynomial number of unlimited fan-in AND and OR gates. The name "AC" was chosen by analogy to NC, with the "A" in the name standing for...
Wikipedia
AD+ In set theory, AD+ is an extension, proposed by W. Hugh Woodin, to the axiom of determinacy. The axiom, which is to be understood in the context of ZF plus DC$\mathbb {R} $ (the axiom of dependent choice for real numbers), states two things: 1. Every set of reals is ∞-Borel. 2. For any ordinal λ less than Θ, ...
Wikipedia
Advanced Encryption Standard The Advanced Encryption Standard (AES), also known by its original name Rijndael (Dutch pronunciation: [ˈrɛindaːl]),[5] is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.[6] Advanced Encryption St...
Wikipedia
AES-GCM-SIV AES-GCM-SIV is a mode of operation for the Advanced Encryption Standard which provides similar performance to Galois/Counter Mode as well as misuse resistance in the event of the reuse of a cryptographic nonce. The construction is defined in RFC 8452.[1] About AES-GCM-SIV is designed to preserve both pri...
Wikipedia
AF+BG theorem In algebraic geometry the AF+BG theorem (also known as Max Noether's fundamental theorem) is a result of Max Noether that asserts that, if the equation of an algebraic curve in the complex projective plane belongs locally (at each intersection point) to the ideal generated by the equations of two other a...
Wikipedia
Approximately finite-dimensional C*-algebra In mathematics, an approximately finite-dimensional (AF) C*-algebra is a C*-algebra that is the inductive limit of a sequence of finite-dimensional C*-algebras. Approximate finite-dimensionality was first defined and described combinatorially by Ola Bratteli. Later, George A...
Wikipedia
AKNS system In mathematics, the AKNS system is an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, Alan C. Newell, and Harvey Segur from their publication in Studies in Applied Mathematics: Ablowitz, Kaup, and Newell et al. (1974). Definition The AKN...
Wikipedia
ALL (complexity) In computability and complexity theory, ALL is the class of all decision problems. Relations to other classes ALL contains all of the complex classes of decision problems, including RE and co-RE. External links • Complexity Zoo: Class ALL Important complexity classes Considered feasible • DLOG...
Wikipedia
AM-GM Inequality In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every...
Wikipedia
Pythagorean means In mathematics, the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and later generations of Greek mathematicians[1] because of their importance in geometry and music. Defin...
Wikipedia
American Mathematics Competitions The American Mathematics Competitions (AMC) are the first of a series of competitions in secondary school mathematics that determine the United States of America's team for the International Mathematical Olympiad (IMO). The selection process takes place over the course of roughly five...
Wikipedia
Analysis of variance Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total va...
Wikipedia
Adleman–Pomerance–Rumely primality test In computational number theory, the Adleman–Pomerance–Rumely primality test is an algorithm for determining whether a number is prime. Unlike other, more efficient algorithms for this purpose, it avoids the use of random numbers, so it is a deterministic primality test. It is na...
Wikipedia
ASUI The Average Service Unavailability Index (ASUI)[1] is a reliability index commonly used by electric power utilities. It is calculated as ${\mbox{ASUI}}={\frac {\sum {U_{i}N_{i}}}{\sum {N_{i}}\times 8760}}=1-{\mbox{ASAI}}$ where $N_{i}$ is the number of customers and $U_{i}$ is the annual outage time (in hours) ...
Wikipedia
ATS theorem In mathematics, the ATS theorem is the theorem on the approximation of a trigonometric sum by a shorter one. The application of the ATS theorem in certain problems of mathematical and theoretical physics can be very helpful. History of the problem In some fields of mathematics and mathematical physics, s...
Wikipedia
AW*-algebra In mathematics, an AW*-algebra is an algebraic generalization of a W*-algebra. They were introduced by Irving Kaplansky in 1951.[1] As operator algebras, von Neumann algebras, among all C*-algebras, are typically handled using one of two means: they are the dual space of some Banach space, and they are det...
Wikipedia
AWM-SIAM Sonia Kovalevsky Lecture The AWM-SIAM Sonia Kovalevsky Lecture is an award and lecture series that "highlights significant contributions of women to applied or computational mathematics."[1] The Association for Women in Mathematics (AWM) and the Society for Industrial and Applied Mathematics (SIAM) planned th...
Wikipedia
A Beautiful Mind (film) A Beautiful Mind is a 2001 American biographical drama film directed by Ron Howard. Written by Akiva Goldsman, its screenplay was inspired by Sylvia Nasar's 1998 biography of the mathematician John Nash, a Nobel Laureate in Economics. A Beautiful Mind stars Russell Crowe as Nash, along with Ed ...
Wikipedia
A Biography of Maria Gaetana Agnesi A Biography of Maria Gaetana Agnesi, an Eighteenth-Century Woman Mathematician: With Translations of Some of Her Work from Italian into English is a biography of Italian mathematician and philosopher Maria Gaetana Agnesi (1718–1799). It was written and translated by Antonella Cupill...
Wikipedia
A Guide to the Classification Theorem for Compact Surfaces A Guide to the Classification Theorem for Compact Surfaces is a textbook in topology, on the classification of two-dimensional surfaces. It was written by Jean Gallier and Dianna Xu, and published in 2013 by Springer-Verlag as volume 9 of their Geometry and Co...
Wikipedia
A History of Folding in Mathematics A History of Folding in Mathematics: Mathematizing the Margins is a book in the history of mathematics on the mathematics of paper folding. It was written by Michael Friedman and published in 2018 by Birkhäuser as volume 59 of their Historical Studies series. Topics The book consi...
Wikipedia
A History of Mathematical Notations A History of Mathematical Notations is a book on the history of mathematics and of mathematical notation. It was written by Swiss-American historian of mathematics Florian Cajori (1859–1930), and originally published as a two-volume set by the Open Court Publishing Company in 1928 a...
Wikipedia
A History of Pi A History of Pi (also titled A History of π) is a 1970 non-fiction book by Petr Beckmann that presents a layman's introduction to the concept of the mathematical constant pi (π).[1] A History of Pi Book cover of A History of Pi (3rd ed.) AuthorPetr Beckmann CountryUnited States LanguageEnglish Subject...
Wikipedia
A History of Greek Mathematics A History of Greek Mathematics is a book by English historian of mathematics Thomas Heath about history of Greek mathematics. It was published in Oxford in 1921, in two volumes titled Volume I, From Thales to Euclid and Volume II, From Aristarchus to Diophantus. It got positive reviews a...
Wikipedia
A Passage to Infinity A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact [1][2][3] is a 2009 book by George Gheverghese Joseph chronicling the social and mathematical origins of the Kerala school of astronomy and mathematics. The book discusses the highlights of the achievements of Kerala sc...
Wikipedia
A Primer of Real Functions A Primer of Real Functions is a revised edition of a classic Carus Monograph on the theory of functions of a real variable. It is authored by R. P. Boas, Jr and updated by his son Harold P. Boas.[1] A Primer of Real Functions AuthorR. P. Boas, Jr, Harold P. Boas CountryUnited States Languag...
Wikipedia
A Topological Picturebook A Topological Picturebook is a book on mathematical visualization in low-dimensional topology by George K. Francis. It was originally published by Springer in 1987, and reprinted in paperback in 2007. The Basic Library List Committee of the Mathematical Association of America has recommended ...
Wikipedia
A Treatise on the Circle and the Sphere A Treatise on the Circle and the Sphere is a mathematics book on circles, spheres, and inversive geometry. It was written by Julian Coolidge, and published by the Clarendon Press in 1916.[1][2][3][4] The Chelsea Publishing Company published a corrected reprint in 1971,[5][6] and...
Wikipedia
A-group In mathematics, in the area of abstract algebra known as group theory, an A-group is a type of group that is similar to abelian groups. The groups were first studied in the 1940s by Philip Hall, and are still studied today. A great deal is known about their structure. Definition An A-group is a finite group ...
Wikipedia
Ak singularity In mathematics, and in particular singularity theory, an Ak singularity, where k ≥ 0 is an integer, describes a level of degeneracy of a function. The notation was introduced by V. I. Arnold. Let $f:\mathbb {R} ^{n}\to \mathbb {R} $ be a smooth function. We denote by $\Omega (\mathbb {R} ^{n},\mathbb {...
Wikipedia
Proof that 22/7 exceeds π Proofs of the mathematical result that the rational number 22/7 is greater than π (pi) date back to antiquity. One of these proofs, more recently developed but requiring only elementary techniques from calculus, has attracted attention in modern mathematics due to its mathematical elegance an...
Wikipedia
Adriaan Cornelis Zaanen Adriaan Cornelis "Aad" Zaanen (14 June 1913 in Rotterdam – 1 April 2003 in Wassenaar) was a Dutch mathematician working in analysis. He is known for his books on Riesz spaces (together with Wim Luxemburg). Aad Zaanen Zaanen in 1967 Born Adriaan Cornelis Zaanen 14 June 1913 Rotterdam, Netherla...
Wikipedia
Aaron Galuten Aaron Galuten (March 2, 1917–September 23, 1994)[1] was an American mathematician, known mainly as the founder and principal operator of the Chelsea Publishing Company.[2] References 1. "Aaron Galuten (1917-1994)". 2. Halmos, Paul R. (1985). I Want to be a Mathematician: An Automathography. Springe...
Wikipedia
Aaron Robertson (mathematician) Aaron Robertson (born November 8, 1971) is an American mathematician who specializes in Ramsey theory. He is a professor at Colgate University.[1] Aaron Robertson Born Aaron Robertson (1971-11-08) November 8, 1971 Torrance, California, U.S. Alma mater • University of Michigan (BS) ...
Wikipedia
Mental abacus The abacus system of mental calculation is a system where users mentally visualize an abacus to carry out arithmetical calculations.[1] No physical abacus is used; only the answers are written down. Calculations can be made at great speed in this way. For example, in the Flash Anzan event at the All Japa...
Wikipedia
Saeid Abbasbandy Saeid Abbasbandy is an Iranian mathematician[2] and university professor at Imam Khomeini International University. Abbasbandy was born on March 17, 1967, in Tehran. He finished his high school course in Shariati High school and attended in the university entrance exam, then could enter University of ...
Wikipedia
Abdias Treu Abdias Treu (sometimes spelled Trew) (29 July 1597 – 12 April 1669) was a German mathematician and academic. He was the professor of mathematics and physical science at the University of Altdorf from 1636-1669. He is best known for his contributions to the field of astronomy.[1] He also contributed writing...
Wikipedia
Abdul–Aziz Yakubu (mathematician) Abdul–Aziz Yakubu (???? – August 2022)[1] was a mathematical biologist.[2] Yakubu was a professor at Howard University for over 20 years and served as chair of the mathematics department from 2004 to 2014.[3] Abdul–Aziz Yakubu Born???? Accra, Ghana DiedAugust 13 or 14, 2022 Academic ...
Wikipedia
Abdus Salam School of Mathematical Sciences The Abdus Salam School of Mathematical Sciences (AS-SMS), (درس گاہ عبدالسلام برائے علوم ریاضی) is an autonomous institute affiliated with the Government College University Lahore, Pakistan.[1] The school is named after the theoretical physicist and Nobel Laureate Abdus Salam...
Wikipedia
Abdusalam Abubakar Abdusalam Abubakar (born 1989/1990)[1] is a Somali-born Irish scientist from Dublin. He was the winner of the 43rd Young Scientist and Technology Exhibition in 2007 at the age of seventeen. He went on to be named EU Young Scientist of the Year in September 2007. Abdusalam Abubakar Born1989 or 1990 ...
Wikipedia
Abel's binomial theorem Abel's binomial theorem, named after Niels Henrik Abel, is a mathematical identity involving sums of binomial coefficients. It states the following: $\sum _{k=0}^{m}{\binom {m}{k}}(w+m-k)^{m-k-1}(z+k)^{k}=w^{-1}(z+w+m)^{m}.$ Example The case m = 2 ${\begin{aligned}&{}\quad {\binom {2}{0}}(w...
Wikipedia
Abel's test In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series. The test is named after mathematician Niels Henrik Abel. There are two slightly different versions of Abel's test – one is used with series of real numbers, and the other is used w...
Wikipedia
Abel's identity In mathematics, Abel's identity (also called Abel's formula[1] or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation. The ...
Wikipedia
Functional equation In mathematics, a functional equation [1][2] 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...
Wikipedia
Abel's inequality In mathematics, Abel's inequality, named after Niels Henrik Abel, supplies a simple bound on the absolute value of the inner product of two vectors in an important special case. Mathematical description Let {a1, a2,...} be a sequence of real numbers that is either nonincreasing or nondecreasing, an...
Wikipedia
Abel's irreducibility theorem In mathematics, Abel's irreducibility theorem, a field theory result described in 1829 by Niels Henrik Abel,[1] asserts that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x). Equivalently...
Wikipedia
Abel's summation formula In mathematics, Abel's summation formula, introduced by Niels Henrik Abel, is intensively used in analytic number theory and the study of special functions to compute series. Other concepts sometimes known by this name are summation by parts and Abel–Plana formula. Formula Wikibooks has a b...
Wikipedia
Abel–Jacobi map In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety. In Riemannian geometry, it is a more general construction mapping a manifold to its Jacobi torus. The name derives from the theorem of Abel and Jacobi that two effective...
Wikipedia
Abel elliptic functions In mathematics Abel elliptic functions are a special kind of elliptic functions, that were established by the Norwegian mathematician Niels Henrik Abel. He published his paper "Recherches sur les Fonctions elliptiques" in Crelle's Journal in 1827.[1] It was the first work on elliptic functions ...
Wikipedia
Abel equation The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form $f(h(x))=h(x+1)$ This article is about certain functional equations. For ordinary differential equations which are cubic in the unknown function, see Abel equation of the first kind. or $\alpha (f(x))=\alpha...
Wikipedia
Abel equation of the first kind In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function. In other words, it is an equation of the form $y'=f_{3}(x)y^{3}+f_{2}(x)y^{2}+f_{1}(x)y+f_{0}(x)\,$ This article is about cert...
Wikipedia
Abel's theorem In mathematics, Abel's theorem for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik Abel. This article is about Abel's theorem on power series. For Abel's theorem on algebraic curves, see Abel–Jacobi map. For Abel's th...
Wikipedia
Abel polynomials The Abel polynomials in mathematics form a polynomial sequence, the nth term of which is of the form $p_{n}(x)=x(x-an)^{n-1}.$ The sequence is named after Niels Henrik Abel (1802-1829), the Norwegian mathematician. This polynomial sequence is of binomial type: conversely, every polynomial sequence ...
Wikipedia
Abel Prize The Abel Prize (/ˈɑːbəl/ AH-bəl; Norwegian: Abelprisen [ˈɑ̀ːbl̩ˌpriːsn̩]) is awarded annually by the King of Norway to one or more outstanding mathematicians.[1] It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes.[2][3][4][5][6][7][8] It c...
Wikipedia
Abel transform In mathematics, the Abel transform,[1] named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f(r) is given by $F(y)=2\int _{y}^{\infty }{\frac {f(r)r}{\sqrt {r^{2}-y^{2}}}}\,dr.$ Assumi...
Wikipedia
Abelian integral In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form $\int _{z_{0}}^{z}R(x,w)\,dx,$ where $R(x,w)$ is an arbitrary rational function of the two variables $x$ and $w$, which are related by the equation $F(x,w)...
Wikipedia
Abelian Lie group In geometry, an abelian Lie group is a Lie group that is an abelian group. A connected abelian real Lie group is isomorphic to $\mathbb {R} ^{k}\times (S^{1})^{h}$.[1] In particular, a connected abelian (real) compact Lie group is a torus; i.e., a Lie group isomorphic to $(S^{1})^{h}$. A connected c...
Wikipedia
Abelian category In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototypical example of an abelian category is the category of abelian groups, Ab. The theory originated in an effort to ...
Wikipedia
Abelian extension In abstract algebra, an abelian extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension. Going in the other direction, a Galois extension is called solvable if its Galois group is solvable, i.e., if the group...
Wikipedia
Mathematical joke A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians. The humor may come from a pun, or from a double meaning of a mathematical term, or from a lay person's misunderstanding of a mathematical concept. Mathematician and author John Allen Paulo...
Wikipedia
Abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the ...
Wikipedia
Abelian surface In mathematics, an abelian surface is a 2-dimensional abelian variety. One-dimensional complex tori are just elliptic curves and are all algebraic, but Riemann discovered that most complex tori of dimension 2 are not algebraic via the Riemann bilinear relations. Essentially, these are conditions on th...
Wikipedia
Abelian von Neumann algebra In functional analysis, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra L∞(X, μ) for μ a σ-finite measure on X realized as an algebra of operator...
Wikipedia
Abel–Ruffini theorem In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients. Here, general means that the coefficients of the equation are viewed and manipula...
Wikipedia