Robert Henry Risch (born 1939) is an American mathematician who worked on computer algebra and is known for his work on symbolic integration, specifically the Risch algorithm. [1] This result was quoted as a milestone in the development of mathematics:
Calculus students worldwide depend on the algorithm, whenever they appeal to Wolfram Alpha to do their homework. [2]
He is also known for results on algebraic properties of elementary functions. [3] He received his PhD from the University of California, Berkeley in 1968 [4] under the supervision of Maxwell A. Rosenlicht. [5] After his PhD, he worked at the Thomas J. Watson Research Center Mathematics of AI group [6] and, between 1970 and 1972, the Institute for Advanced Study. [7]
In mathematics, an elementary function is a function of a single variable that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, including possibly their inverse functions.
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
In symbolic computation, the Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.
Macsyma is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC.
Raoul Bott was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.
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Sir Vaughan Frederick Randal Jones was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials. He was awarded a Fields Medal in 1990.
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.
Keith Oliver Geddes is a professor emeritus in the David R. Cheriton School of Computer Science within the Faculty of Mathematics at the University of Waterloo in Waterloo, Ontario. He is a former director of the Symbolic Computation Group in the School of Computer Science. He received a BA in Mathematics at the University of Saskatchewan in 1968; he completed both his MSc and PhD in Computer Science at the University of Toronto.
In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative that is, itself, not an elementary function. A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis for the Risch algorithm for determining which elementary functions have elementary antiderivatives.
In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a formula for a differentiable function F(x) such that
Hyman Bass is an American mathematician, known for work in algebra and in mathematics education. From 1959 to 1998 he was Professor in the Mathematics Department at Columbia University. He is currently the Samuel Eilenberg Distinguished University Professor of Mathematics and Professor of Mathematics Education at the University of Michigan.
Harley M. Flanders was an American mathematician, known for several textbooks and contributions to his fields: algebra and algebraic number theory, linear algebra, electrical networks, scientific computing.
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables that have no given value and are manipulated as symbols.
Harold Mortimer Edwards, Jr. was an American mathematician working in number theory, algebra, and the history and philosophy of mathematics.
Maxwell Alexander Rosenlicht was an American mathematician known for works in algebraic geometry, algebraic groups, and differential algebra.
Robert C. Hermann was an American mathematician and mathematical physicist. In the 1960s Hermann worked on elementary particle physics and quantum field theory, and published books which revealed the interconnections between vector bundles on Riemannian manifolds and gauge theory in physics, before these interconnections became "common knowledge" among physicists in the 1970s.
Alan Stuart Edelman is an American mathematician and computer scientist. He is a professor of applied mathematics at the Massachusetts Institute of Technology (MIT) and a Principal Investigator at the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) where he leads a group in applied computing. In 2004, he founded a business called Interactive Supercomputing which was later acquired by Microsoft. Edelman is a fellow of American Mathematical Society (AMS), Society for Industrial and Applied Mathematics (SIAM), Institute of Electrical and Electronics Engineers (IEEE), and Association for Computing Machinery (ACM), for his contributions in numerical linear algebra, computational science, parallel computing, and random matrix theory. He is one of the cocreators of the technical programming language Julia.
William Forrest "Woody" Stinespring was an American mathematician, specializing in operator theory. He is known for the Stinespring factorization theorem.