Computational mathematics
Computational mathematics, called also the mathematics of scientific computation,[1] refers to mathematical research in areas of science where computing plays a central and essential role. It involves the study and use of algorithms, numerical methods, symbolic methods, and stochastic methods.[1][2][3] Computational mathematics is closely related to applied mathematics, scientific computing, computational science, and computational engineering. However, computational science and engineering are primarily concerned with research in science itself, with computation serving as a tool. In practice, the difference between the areas above is often very fuzzy, as shown by a small sample of programs and centers below.
One difference is that computational mathematics typically puts emphasis on substantial mathematical analysis,[4] that is, mathematical proofs, especially in numerical analysis.[1] The other related areas outside of mathematics, listed above, are not much concerned about proofs and instead focus on computational performance and the empirical validity of the computational simulations and of the science itself. However, analysis of the complexity of algorithms is also considered a part of theoretical computer science, which overlaps with discrete mathematics.
Computational mathematics has emerged as a distinct part of applied mathematics by early 1980s. At the time, several panels[1] called for specific research support in computational mathematics, resulting, among others, in the NSF program in Computational Mathematics[2].
Academic programs and centers in computational mathematics can be affiliated with a mathematics department or be separate interdisciplinary entities. Numerical analysis, a subset of computational mathematics, is also studied in many computer science departments.
References
- ^ a b c d Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. Distributed by SIAM.
- ^ a b National Science Foundation, Division of Mathematical Science, Program description PD 06-888 Computational Mathematics, 2006. Retrieved April 2007
- ^ NSF Seeks Proposals on Stochastic Systems, SIAM News, August 19, 2005
- ^ Mathematics of Computation, Journal overview, retrieved April 2007
See also
External links
- Princeton Program in Applied and Computational Mathematics
- Applied and Computational Mathematics, Caltech
- Center for Computational Mathematics, University of Colorado at Denver and Health Sciences Center
- Scientific Computing and Computational Mathematics Program, Stanford University
- Manchester Center for Computational Mathematics
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