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 mathematics involves mathematical research in mathematics as well as in areas of science where computation plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations.
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:
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  Monte Carlo methods and other representations of uncertainty in scientific computation The mathematics of scientific computation,
 in particular  numerical analysis, the theory of numerical methods
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 number theory
Algorithmic information theory
Algorithmic game theory
Mathematical economics, the use of mathematics in economics, finance and, to certain extents, of accounting. Experimental mathematics References
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. Archived from the original on February 5, 2012 . 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
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). . Springer-Verlag. Handbook of Mathematics and Computational Science 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.
Foundations of Computational Mathematics, a non-profit organization
International Journal of Computer Discovered Mathematics