Computational mathematics

Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Computation in the research is prominent.^[1] Computational mathematics emerged as a distinct part of applied mathematics by early 1950s. Currently, computational mathematics can refer to or include:

• computational science, also known as scientific computation or computational engineering
• solving mathematical problems by computer simulation as opposed to analytic methods of applied mathematics
• numerical methods used in scientific computation, for example numerical linear algebra and numerical solution of partial differential equations
• stochastic methods,^[2] such as Monte Carlo methods and other representations of uncertainty in scientific computation, for example stochastic finite elements
• the mathematics of scientific computation^[3] (the theoretical side involving mathematical proofs^[4]), in particular numerical analysis, the theory of numerical methods (but theory of computation and complexity of algorithms belong to theoretical computer science)
• symbolic computation and computer algebra systems
• computer-assisted research in various areas of mathematics, such as logic (automated theorem proving), discrete mathematics (search for mathematical structures such as groups), number theory (primality testing and factorization), cryptography, and computational algebraic topology
• computational linguistics, the use of mathematical and computer techniques in natural languages

[edit] Books

• Cucker F., 2003. Foundations of Computational Mathematics: Special Volume (Handbook of Numerical Analysis), North-Holland Publishing, ISBN 978-0444512475

• Harris J. W. and Stocker H., 1998. Handbook of Mathematics and Computational Science, Springer-Verlag, ISBN 978-0387947464

• Yang X. S., 2008. Introduction to Computational Mathematics, World Scientific Publishing, ISBN 978-9812818171

• Nonweiler T. R., 1986. Computational Mathematics: An Introduction to Numerical Approximation, John Wiley and Sons, ISBN 978-0470202609

• Gentle J. E., 2007. Foundations of Computational Science, Springer-Verlag, ISBN 978-0387004501

[edit] General References

1. ^ National Science Foundation, Division of Mathematical Science, Program description PD 06-888 Computational Mathematics, 2006. Retrieved April 2007
2. ^ NSF Seeks Proposals on Stochastic Systems, SIAM News, August 19, 2005
3. ^ Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. Distributed by SIAM
4. ^ Mathematics of Computation, Journal overview, retrieved April 2007

[edit] External links

• Computational Mathematics, University of Waterloo
• Princeton Program in Applied and Computational Mathematics
• Applied and Computational Mathematics, Caltech
• Center for Computational Mathematics, University of Colorado Denver
• Scientific Computing and Computational Mathematics Program, Stanford University

• Foundations of Computational Mathematics: a non-profit organization

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