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Audrey Terras
Audrey Anne Terras (born September 10, 1942) is an American mathematician who works primarily in number theory. Her research has focused on quantum chaos and on various types of zeta functions. Early life and education Audrey Terras was born September 10, 1942, in Washington, D.C. She received a BS degree in mathematics from the University of Maryland, College Park (UMD) in 1964, and MA and PhD degrees from Yale University in 1966 and 1970 respectively. She was married to fellow UMD alumnus Riho Terras. She stated in a 2008 interview that she chose to study mathematics because "The U.S. government paid me! And not much! It was the time of Sputnik, so we needed to produce more mathematicians, and when I was deciding between Math and History, they weren’t paying me to do history, they were paying me to do math." Career Terras joined the University of California, San Diego, as an assistant professor in 1972, and became a full professor there in 1983. She retired in 2010, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riho Terras (mathematician)
Riho Terras (June 13, 1939 – November 28, 2005) was an Estonian-American mathematician. He was born in Tartu, Estonia, and moved to Ulm, Germany, before starting school. In 1951, he emigrated to the United States along with his mother. In 1965, he was given the Milton Abramowitz award for his studies at the University of Maryland. He finished his PhD in 1970 at the University of Illinois Urbana-Champaign. He is known for the ''Terras theorem'' about the Collatz conjecture, published in 1976, which proved that the conjecture holds for "almost all" numbers and established bounds for the conjecture. He married fellow mathematician Audrey Terras Audrey Anne Terras (born September 10, 1942) is an American mathematician who works primarily in number theory. Her research has focused on quantum chaos and on various types of zeta functions. Early life and education Audrey Terras was born S .... References Estonian emigrants to the United States 1939 births 2005 deaths Est ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary education and research which awards academic degrees in several Discipline (academia), academic disciplines. ''University'' is derived from the Latin phrase , which roughly ..., college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 11 Dupont in the Dupont Circle, Washington, D.C., Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the ''American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Association For Women In Mathematics
The Association for Women in Mathematics (AWM) is a professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment of women and girls in the mathematical sciences. The AWM was founded in 1971 and incorporated in the state of Massachusetts. AWM has approximately 5200 members, including over 250 institutional members, such as colleges, universities, institutes, and mathematical societies. It offers numerous programs and workshops to mentor women and girls in the mathematical sciences. Much of AWM's work is supported through federal grants. History The Association was founded in 1971 as the Association of Women Mathematicians, but the name was changed almost immediately. As reported in "A Brief History of the Association for Women in Mathematics: The Presidents' Perspectives", by Lenore Blum: Mary W. Gray, Mary Gray, an early organizer and first presi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selberg Trace Formula
In mathematics, the Selberg trace formula, introduced by , is an expression for the character of the unitary representation of a Lie group on the space of square-integrable functions, where is a cofinite discrete group. The character is given by the trace of certain functions on . The simplest case is when is cocompact, when the representation breaks up into discrete summands. Here the trace formula is an extension of the Frobenius formula for the character of an induced representation of finite groups. When is the cocompact subgroup of the real numbers , the Selberg trace formula is essentially the Poisson summation formula. The case when is not compact is harder, because there is a continuous spectrum, described using Eisenstein series. Selberg worked out the non-compact case when is the group ; the extension to higher rank groups is the Arthur–Selberg trace formula. When is the fundamental group of a Riemann surface, the Selberg trace formula describes the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a Set (mathematics), set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then this graph is directed, because owing mon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Graph Theory
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants. Branches of algebraic graph theory Using linear algebra The first branch of algebraic graph theory involves the study of graphs in connection with linear algebra. Especially, it studies the spectrum of the adjacency matrix, or the Laplacian matrix of a graph (this part of algebraic graph theory is also called spectral graph theory). For the Petersen graph, for example, the spectrum of the adjacency matrix is (−2, −2, −2, −2, 1, 1, 1, 1, 1, 3). Several theorems relate properties of the spectrum to other graph properties. As a simple example, a connected graph with diameter ''D'' wil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Function
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the list of mathematical functions contains functions that are commonly accepted as special. Tables of special functions Many special functions appear as solutions of differential equations or integrals of elementary functions. Therefore, tables of integrals usually include descriptions of special functions, and tables of special functions include most important integrals; at least, the integral representation of special functions. Because symmetries of differential equations are essential to both physics and mathematics, the theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics. Symbolic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Group
In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century. One major area of study has been classification: the classification of finite simple groups (those with no nontrivial normal subgroup) was completed in 2004. History During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence, the complete classification of finite simple groups was achieved, meaning that all those simple groups from which all finite groups can be bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Space
In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of isometries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification. Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis. In geometric terms, a complete, simply connected Riemannian manifold is a symmetric space if and only if its curvature tensor is invariant under parallel transport. More generally, a Riemannian manifold (''M'', ''g'') is said to be symmetric if and only if, for each point ''p'' of ''M'', there exists an isometry of ''M'' fixing ''p'' and acting on the tangent space T_pM as minus the identity (every symmetric space is complete, since any geodesic can be extended indefinitely via symmetri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals. Generalizing these transforms to other domains is generally called Fourier analysis, although the term is sometimes used interchangeably with harmonic analysis. Harmonic analysis has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis, spectral analysis, and neuroscience. The term "harmonics" originated from the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are integer multiples of one another, as are the freq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique. * Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. *Additive numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
