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. Computational mathematics emerged as a distinct part of applied mathematics by the early 1950s. Currently, computational mathematics can refer to or include: [1 ]
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, such as [2 ] Monte Carlo methods and other representations of uncertainty in scientific computation, for example stochastic finite elements the mathematics of scientific computation
(the theoretical side involving [3 ] mathematical proofs ), in particular [4 ] 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
computational algebraic geometry
computational group theory
computational number theory
algorithmic information theory
algorithmic game theory
References [ edit ]
^ 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 . Retrieved . February 2, 2015
^ Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. Distributed by SIAM.
^ Mathematics of Computation, Journal overview. Retrieved April 2007.
Further reading [ edit ]
Cucker, F. (2003). Foundations of Computational Mathematics: Special Volume. Handbook of Numerical Analysis. North-Holland Publishing. ISBN 978-0-444-51247-5.
Harris, J. W.; Stocker, H. (1998). Handbook of Mathematics and Computational Science. Springer-Verlag. ISBN 978-0-387-94746-4.
Hartmann, A.K. (2009). . World Scientific. Practical Guide to Computer Simulations ISBN 978-981-283-415-7.
Nonweiler, T. R. (1986). Computational Mathematics: An Introduction to Numerical Approximation. John Wiley and Sons. ISBN 978-0-470-20260-9.
Gentle, J. E. (2007). Foundations of Computational Science. Springer-Verlag. ISBN 978-0-387-00450-1.
White, R. E. (2003). Computational Mathematics: Models, Methods, and Analysis with MATLAB. Chapman and Hall. ISBN 978-1584883647.
Yang, X. S. (2008). Introduction to Computational Mathematics. World Scientific. ISBN 978-9812818171.
Strang, G. (2007). Computational Science and Engineering. Wiley. ISBN 978-0961408817.
External links [ edit ]