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Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, 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".
Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns. It has been defined as "that branch of mathematics that concerns itself ultimately with the codification and transmission of insights within the mathematical community through the use of experimental exploration of conjectures and more informal beliefs and a careful analysis of the data acquired in this pursuit."
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
Richard Peter Stanley is an Emeritus Professor of Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. From 2000 to 2010, he was the Norman Levinson Professor of Applied Mathematics. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is an expert in the field of combinatorics and its applications to other mathematical disciplines.
Doron Zeilberger is an Israeli mathematician, known for his work in combinatorics.
In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. These matrices generalize permutation matrices and arise naturally when using Dodgson condensation to compute a determinant. They are also closely related to the six-vertex model with domain wall boundary conditions from statistical mechanics. They were first defined by William Mills, David Robbins, and Howard Rumsey in the former context.
GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms, with apps for desktops, tablets and web.
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Aleksandr Aleksandrovich Razborov, sometimes known as Sasha Razborov, is a Soviet and Russian mathematician and computational theorist. He is Andrew McLeish Distinguished Service Professor at the University of Chicago.
Herbert Saul Wilf was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania. He wrote numerous books and research papers. Together with Neil Calkin he founded The Electronic Journal of Combinatorics in 1994 and was its editor-in-chief until 2001.
In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension condition in terms of D-modules theory. More precisely, a holonomic function is an element of a holonomic module of smooth functions. Holonomic functions can also be described as differentiably finite functions, also known as D-finite functions. When a power series in the variables is the Taylor expansion of a holonomic function, the sequence of its coefficients, in one or several indices, is also called holonomic. Holonomic sequences are also called P-recursive sequences: they are defined recursively by multivariate recurrences satisfied by the whole sequence and by suitable specializations of it. The situation simplifies in the univariate case: any univariate sequence that satisfies a linear homogeneous recurrence relation with polynomial coefficients, or equivalently a linear homogeneous difference equation with polynomial coefficients, is holonomic.
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The progression of both the nature of mathematics and individual mathematical problems into the future is a widely debated topic - many past predictions about modern mathematics have been misplaced or completely false, so there is reason to believe that many predictions today may follow a similar path. However, the subject still carries an important weight and has been written about by many notable mathematicians. Typically, they are motivated by a desire to set a research agenda to direct efforts to specific problems, or a wish to clarify, update and extrapolate the way that subdisciplines relate to the general discipline of mathematics and its possibilities. Examples of agendas pushing for progress in specific areas in the future, historical and recent, include Felix Klein's Erlangen program, Hilbert's problems, Langlands program, and the Millennium Prize Problems. In the Mathematics Subject Classification section 01Axx History of mathematics and mathematicians, the subsection 01A67 is titled Future prospectives.
Manuel Kauers is a German mathematician and computer scientist. He is working on computer algebra and its applications to discrete mathematics. He is currently professor for algebra at Johannes Kepler University (JKU) in Linz, Austria, and leader of the Institute for Algebra at JKU. Before that, he was affiliated with that university's Research Institute for Symbolic Computation (RISC).
The David P. Robbins Prize for papers reporting novel research in algebra, combinatorics, or discrete mathematics is awarded both by the American Mathematical Society (AMS) and by the Mathematical Association of America (MAA). The AMS award recognizes papers with a significant experimental component on a topic which is broadly accessible which provide a simple statement of the problem and clear exposition of the work. Papers eligible for the MAA award are judged on quality of research, clarity of exposition, and accessibility to undergraduates. Both awards consist of $5000 and are awarded once every three years. They are named in the honor of David P. Robbins and were established in 2005 by the members of his family.
Ira Martin Gessel is an American mathematician, known for his work in combinatorics. He is a long-time faculty member at Brandeis University and resides in Arlington, Massachusetts.
Elchanan Mossel is a professor of mathematics at the Massachusetts Institute of Technology. His primary research fields are probability theory, combinatorics, and statistical inference.
Aaron Robertson is an American mathematician who specializes in Ramsey theory. He is a professor at Colgate University.
References
- ↑ "Homepage of Christoph Koutschan". www.koutschan.de. Retrieved 2016-04-27.
- ↑ "Christoph Koutschan: Curriculum Vitae". www.koutschan.de. Retrieved 2016-04-27.
- ↑ "Christoph Koutschan". www.risc.jku.at. Archived from the original on 2016-03-25. Retrieved 2016-04-27.
- ↑ "Christoph Koutschan: Curriculum Vitae". www.koutschan.de. Retrieved 2016-04-27.
- ↑ "Homepage of Christoph Koutschan". www.koutschan.de. Retrieved 2016-04-27.
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