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 way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.
Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry.
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation.
In abstract algebra, a magma, binar or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with a single binary operation that must be closed by definition. No other properties are imposed.
In mathematics and computer science, the Krohn–Rhodes theory is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback-free manner.
William B. Arveson was a mathematician specializing in operator algebras who worked as a professor of Mathematics at the University of California, Berkeley.
Joachim "Jim" Lambek was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his Ph.D. degree in 1950 with Hans Zassenhaus as advisor.
Anatoly Ivanovich Maltsev was born in Misheronsky, near Moscow, and died in Novosibirsk, USSR. He was a mathematician noted for his work on the decidability of various algebraic groups. Malcev algebras, as well as Malcev Lie algebras are named after him.
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.
Gerard J. Murphy MRIA was a prolific Irish mathematician. His textbooks are internationally acclaimed, and translated into different languages. He died from cancer in October 2006, at the age of 57.
Tudor Ganea was a Romanian-American mathematician, known for his work in algebraic topology, especially homotopy theory. Ganea left Communist Romania to settle in the United States in the early 1960s. He taught at the University of Washington.
Alexander A. Beilinson is the David and Mary Winton Green University Professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1999 Beilinson was awarded the Ostrowski Prize with Helmut Hofer. In 2017 he was elected to the National Academy of Sciences.
Avraham Naumovich Trahtman (Trakhtman) is a mathematician at Bar-Ilan University (Israel). In 2007, Trahtman solved a problem in combinatorics that had been open for 37 years, the Road Coloring Conjecture posed in 1970.
John Robert Stallings Jr. was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.
In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear inequality constraints and nonlinear objective functions; there are criss-cross algorithms for linear-fractional programming problems, quadratic-programming problems, and linear complementarity problems.
Hans Vilhem Rådström (1919–1970) was a Swedish mathematician who worked on complex analysis, continuous groups, convex sets, set-valued analysis, and game theory. From 1952, he was lektor at Stockholm University, and from 1969, he was Professor of Applied Mathematics at Linköping University.
Anton Kazimirovich Sushkevich was a Russian mathematician and textbook author who expanded group theory to include semigroups and other magmas.
Dona Anschel Papert Strauss is a South African mathematician working in topology and functional analysis. Her doctoral thesis was one of the initial sources of pointless topology. She has also been active in the political left, lost one of her faculty positions over her protests of the Vietnam War, and became a founder of European Women in Mathematics.
Zdeněk Hedrlín was a Czech mathematician, specializing in universal algebra and combinatorial theory, both in pure and applied mathematics.
