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English Wikipedia references for Ams.org 1-50 of 2481
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| Algebraically closed field mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F, has a root in F. Algebraically_closed_field | |
| Algebraic number mathematics, an algebraic number is a complex number that is a root of a non-zero polynomial in one variable with rational (or equivalently, integer) coefficients. Numbers such as pi that are not algebraic are said to be transcendental, and are infinitely more numerous within the complex number field. Algebraic_number | |
| André Weil André Weil should not be confused with Hermann Weyl (1885–1955) or Andrew Wiles (1953–).André Weil (May 6, 1906 – August 6, 1998) () was an influential mathematician of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. André_Weil | |
| Atle Selberg Atle Selberg (14 June 1917 Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory. Atle_Selberg | |
| Andrew Wiles Sir Andrew John Wiles KBE FRS (born 11 April 1953) is a British mathematician and a professor at Princeton University, specialising in number theory. He is most famous for proving Fermat's Last Theorem. Andrew_Wiles | |
| Alexander Grothendieck Alexander Grothendieck (born March 28, 1928 in Berlin, Germany) is considered one of the greatest mathematicians of the 20th century.He is most famous for his revolutionary advances in algebraic geometry, but he has also made major contributions to algebraic topology, number theory, category theory, Galois theory, descent theory, commutative homological algebra and functional analysis. Alexander_Grothendieck | |
| Annals of Mathematics The Annals of Mathematics (ISSN 0003-486X), abbreviated as Ann. of Math. and often just called Annals, is a bimonthly mathematics research journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as citation intensity.The journal began as The Analyst in 1874, founded and edited by Joel E. Annals_of_Mathematics | |
| Abelian group 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 their order (the axiom of commutativity). Abelian groups generalize the arithmetic of addition of integers. Abelian_group | |
| Arithmetic-geometric mean mathematics, the arithmetic-geometric mean (AGM) of two positive real numbers x and y is defined as followsFirst compute the arithmetic mean of x and y and call it a1. Next compute the geometric mean of x and y and call it g1; this is the square root of the product xy: Arithmetic-geometric_mean | |
| Amicable number Amicable numbers are two different numbers so related that the sum of the proper divisors of one of the numbers is equal to the other. (A proper divisor of a number is a positive integer divisor other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.) Amicable_number | |
| Bletchley Park Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, England. Since 1967, Bletchley has been part of Milton Keynes. During World War II, Bletchley Park was the site of the United Kingdom's main decryption establishment. Ciphers and codes of several Axis countries were decrypted there, most importantly ciphers generated by the German Enigma and Lorenz machines. Bletchley_Park | |
| Bézier curve In words, the degree Bézier curve is a linear interpolation between two degree Bézier curves. Bézier_curve | |
| Bernoulli number mathematics, the Bernoulli numbers are a sequence of rational numbers with deep connections to number theory. They are closely related to the values of the Riemann zeta function at negative integers.In Europe, they were first studied by Jakob Bernoulli, after whom they were named by Abraham de Moivre. Bernoulli_number | |
| Continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis, advanced by Georg Cantor, about the possible sizes of infinite sets. Continuum_hypothesis | |
| Compact space In mathematics, a topological space is called compact if each of its open covers has a finite subcover. Otherwise it is called non-compact.NoteBourbaki use the term "quasi-compact" for this instead, and reserve the term "compact" for topological spaces that are both Hausdorff and "quasi-compact". Compact_space | |
| Countable set Talk:Countable_set | |
| Cantor set mathematics, the Cantor set, introduced by German mathematician Georg Cantor in 1883 (but discovered in 1875 by Henry John Stephen Smith{3} ight).The Cantor ternary set contains all points in the interval The first six steps of this process are illustrated below. Cantor_set | |
| Commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Commutator | |
| Classification of finite simple groups The classification of the finite simple groups, also called the enormous theorem, is believed to classify all finite simple groups. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic building blocks of the natural numbers. The Jordan-Hölder theorem is a more precise way of stating this fact about finite groups. Classification_of_finite_simple_groups | |
| Convolution In mathematics and, in particular, functional analysis, convolution is a mat Convolution | |
| Convolution Talk:Convolution | |
| Computational complexity theory Computational complexity theory is a branch of the theory of computation in computer science that investigates the problems related to the resources required to run algorithms, and the inherent difficulty in providing algorithms that are efficient for both general and specific computational problems. Computational_complexity_theory | |
| Clay Mathematics Institute Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Cambridge, Massachusetts. The Institute is dedicated to increasing and disseminating mathematical knowledge. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998 through the vision and generosity of Boston businessman Landon T. Clay. Harvard mathematician Arthur Jaffe was the first president of CMI. Clay_Mathematics_Institute | |
| Carmichael number number theory, a Carmichael number is a composite positive integer which satisfies the congruence for all integers which are relatively prime to (see modular arithmetic). They are named for Robert Carmichael. The Carmichael numbers are the Knödel numbers K1. Carmichael_number | |
| Dual space mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors which are studied in tensor algebra. Dual_space | |
| Donald Knuth Donald Ervin Knuth () (born January 10, 1938) is a renowned computer scientist and Professor Emeritus of the Art of Computer Programming at Stanford University.Author of the seminal multi-volume work The Art of Computer Programming ("TAOCP"), Knuth has been called the "father" of the analysis of algorithms, contributing to the development of, and systematizing formal mathematical techniques for, the rigorous analysis of the computational complexity of algorithms, and in the process popularizing asymptotic notation. Donald_Knuth | |
| David Hilbert David Hilbert (January 23, 1862 German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered or developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis. David_Hilbert | |
| Douglas Hofstadter Douglas Richard Hofstadter (born February 15, 1945 in New York, New York) is an American academic whose research focuses on consciousness, thinking and creativity. He is best known for his book Gödel, Escher, Bach, first published in 1979, for which he was awarded the 1980 Pulitzer Prize for general non-fiction. Douglas_Hofstadter | |
| Direct product mathematics, one can often define a direct product of objects Cartesian product of the underlying sets, together with a suitably defined structure on the product set.product in category theory, which formalizes these notions.Examples are the product of sets (see Cartesian product), groups (described below), the product of rings and of other algebraic structures. The product of topological spaces is another instance. Direct_product | |
| Dynamical system The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake. Dynamical_system | |
| Expander graph combinatorics, an expander graph is a sparse graph which has high connectivity properties, quantified using vertex or edge expansion as described below. Expander constructions have spawned research in pure and applied mathematics, with several applications to theoretical computer science, design of robust computer networks, and the theory of error-correcting codes. Expander_graph | |
| Euler's sum of powers conjecture Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem which was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n kth powers of positive integers is itself a kth power, then n is not smaller than k.In symbols, if and are positive integers, then .If the conjecture were true, it would be a generalization of Fermat's last theorem, which could be seen as the special case n , then . Euler's_sum_of_powers_conjecture | |
| Erdős number Erdős number (), honouring the late Hungarian mathematician Paul Erdős, is a way of describing the "collaborative distance" between a person and Erdős, It was created by friends as a humorous tribute to the enormous output of Erdős, one of the most prolific modern writers of mathematical papers, and has become well-known in scientific circles as a tongue-in-cheek measurement of mathematical prominence. Erdős_number | |
| Évariste Galois Évariste Galois (; October 25, 1811 May 31, 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. Évariste_Galois | |
| Elementary function a fact that cannot be seen directly from the definition of elementary function but can be proven using the Risch algorithm. Elementary_function | |
| Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. The Fields Medal is often viewed as the top honor a mathematician can receive. Fields_Medal | |
| Four color theorem In mathematics, the four color theorem, or the four color map theorem, states that given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two adjacent regions have the same color. Four_color_theorem | |
| Feynman diagram Feynman_diagram | |
| Gregory Chaitin Gregory John Chaitin (born 1947) is an Argentine-American mathematician and computer scientist.Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a new incompleteness theorem in reaction to Gödel's incompleteness theorem. He attended the Bronx High School of Science and City College of New York, where he (still in his teens) developed the theories that led to his independent discovery of Kolmogorov complexity. Gregory_Chaitin | |
| Group homomorphism In mathematics, given two groups (G, *) and (H, ·), a group homomorphism from (G, *) to (H, ·) is a function h G → H such that for all u and v in G it holds that where the group operation on the left hand side of the equation is that of G and on the right hand side that of H. Group_homomorphism | |
| Groupoid ''In abstract algebra, a branch of mathematics, especially in category theory and homotopy theory, a groupoid generalises the notion of group and of category in several equivalent ways. A groupoid can be seen as a Group with a partial function replacing the binary operation; Category in which every morphism is an isomorphism. A category of this sort can be viewed as augmented with a unary operation, called inverse by analogy with group theory. Groupoid | |
| Group representation mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication. Group_representation | |
| Group action algebra and geometry, a group action is a way of describing symmetries of objects using groups. The essential elements of the object are described by a set and the symmetries of the object are described by the symmetry group of this set, which consists of bijective transformations of the set. Group_action | |
| George Dantzig George Bernard Dantzig (Nov 8 1914 May 13 2005) was an American mathematician, and the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford. George Dantzig is known as the father of linear programming and as the inventor of the "simplex method," an algorithm for solving linear programming problems. George_Dantzig | |
| Harvey Mudd College Harvey Mudd College is a private college of science, engineering, and mathematics, located in Claremont, California. It is one of the institutions of the contiguous Claremont Colleges.Harvey Mudd shares university resources (libraries, dining halls, etc.) with the other institutions in the Claremont Colleges, including Pitzer College, Scripps College, Claremont McKenna College, and Pomona College. Harvey_Mudd_College | |
| Heisuke Hironaka Heisuke Hironaka (広中 平祐 Hironaka Heisuke; born April 9, 1931) is a Japanese mathematician. After completing his undergraduate studies at Kyoto University, he received his Ph. D. from Harvard while under the direction of Oscar Zariski. He won the Fields Medal in 1970.He is celebrated for proving in 1964 that singularities of algebraic varieties admit resolutions in characteristic zero. Heisuke_Hironaka | |
| Institut des Hautes Études Scientifiques Institut_des_Hautes_Études_Scientifiques | |
| Icosahedron In geometry, an icosahedron (, from eikosi twenty + hedron seat; ; plural onto the -eigenspace of yields thus the twelve vertices of the icosahedron.A second straightforward construction of the icosahedron uses representation theory of the alternating group acting by direct isometries on the icosahedron. Icosahedron | |
| Inverse limit mathematics, the inverse limit (also called the projective limit) is a construction which allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects. Inverse limits can be defined in any category. Inverse_limit | |
| Lightbulb joke A lightbulb joke is a joke that asks how many people of a certain group are needed to change, replace, or screw in a light bulb. Generally, the punch line answer highlights a stereotype of the target group. There are numerous versions of the lightbulb joke satirizing a wide range of cultures, beliefs and occupations.The original formulations of the joke, popular in the late 1960s and the 1970s, were used to insult the intelligence of Poles. Lightbulb_joke |
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