Computational mathematics

Computational mathematics involves mathematical research in mathematics as well as in areas of science where computing plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations.[1]

A black and white rendition of the Yale Babylonian Collection's Tablet YBC 7289 (c. 1800–1600 BCE), showing a Babylonian approximation to the square root of 2 (1 24 51 10 w: sexagesimal) in the context of Pythagoras' Theorem for an isosceles triangle. The tablet also gives an example where one side of the square is 30, and the resulting diagonal is 42 25 35 or 42.4263888.

Computational applied mathematics consists roughly of using mathematics for allowing and improving computer computation in applied mathematics. Computational mathematics may also refer to the use of computers for mathematics itself. This includes the use of computers for mathematical computations (computer algebra), the study of what can (and cannot) be computerized in mathematics (effective methods), which computations may be done with present technology (complexity theory), and which proofs can be done on computers (proof assistants).

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:

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. Archived from the original on February 5, 2012. Retrieved February 2, 2015.
  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.

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.
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