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Areas of computational mathematics

Computational mathematics emerged as a distinct part of applied mathematics by the early 1950s. Currently, computational mathematics can refer to or include:

• Computational sciences, also known as scientific computation or computational engineering
• Systems sciences, for which directly requires the mathematical models from Systems engineering
• Solving mathematical problems by computer simulation as opposed to traditional engineering methods.
• 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
• The mathematics of scientific computation,³⁴ in particular numerical analysis, the theory of numerical methods
• Computational complexity
• Computer algebra and computer algebra systems
• Computer-assisted research in various areas of mathematics, such as logic (automated theorem proving), discrete mathematics, combinatorics, number theory, and computational algebraic topology
• Cryptography and computer security, which involve, in particular, research on primality testing, factorization, elliptic curves, and mathematics of blockchain
• Computational linguistics, the use of mathematical and computer techniques in natural languages
• Computational algebraic geometry
• Computational group theory
• Computational geometry
• Computational number theory
• Computational topology
• Computational statistics
• Algorithmic information theory
• Algorithmic game theory
• Mathematical economics, the use of mathematics in economics, finance and, to certain extents, of accounting.
• Experimental mathematics

Journals

Journals that publish contributions from computational mathematics include

• ACM Transactions on Mathematical Software
• Mathematics of Computation
• SIAM Journal on Scientific Computing
• SIAM Journal on Numerical Analysis

See also

• Mathematics portal
• Computer-based mathematics education

Further reading

• 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). Practical Guide to Computer Simulations. World Scientific. ISBN 978-981-283-415-7. Archived from the original on February 11, 2009. Retrieved May 3, 2012.
• 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

• Foundations of Computational Mathematics, a non-profit organization
• International Journal of Computer Discovered Mathematics

References

1. National Science Foundation, Division of Mathematical Science, Program description PD 06-888 Computational Mathematics, 2006. Retrieved April 2007. /wiki/National_Science_Foundation ↩

2. "NSF Seeks Proposals on Stochastic Systems". SIAM News. August 19, 2005. Archived from the original on February 5, 2012. Retrieved February 2, 2015. https://web.archive.org/web/20120205070148/http://www.siam.org/news/general.php?id=121 ↩

3. Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. Distributed by SIAM. http://www.siam.org/about/science/publications.php ↩

4. Mathematics of Computation, Journal overview. Retrieved April 2007. /wiki/Mathematics_of_Computation ↩