View source for Computational mathematics

'''Computational mathematics''' involves mathematical research in areas of science where [[computing]] plays a central and essential role, emphasizing [[Algorithm|algorithms]], [[Numerical analysis|numerical methods]], and [[Symbolic computation|symbolic computations]].

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:

* [[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 analysis]] used in scientific computation, for example [[numerical linear algebra]] and numerical solution of [[Partial differential equation|partial differential equations]]
* Stochastic, [[probability]]-based methods, such as [[Monte Carlo method|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 [[Mathematical proof|mathematical proofs]]), 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 [[Group (mathematics)|groups), number theory ([[primality testing]] and [[factorization]]), [[cryptography]], and [[computational algebraic topology]]
* [[Computational linguistics]], the use of mathematical and computer techniques in [[Natural language|natural languages]]
* [[Computational algebraic geometry]]
* [[Computational group theory]]
* [[Computational geometry]]
* [[Computational number theory]]
* [[Computational topology]]
* [[Computational statistics]]
* [[Algorithmic information theory]]
* [[Algorithmic game theory]]
* Use of mathematics in economics, finance and to certain extents of accounting i.e. use of differential and integral calculus ([[Newton's method]]) and financial maths to solve real life problems.

== External links ==

* [https://en.wikipedia.org/wiki/Computational_mathematics Computational mathematics] @ Wikipedia

[[Category:Computation]]
[[Category:Computer science]]
[[Category:Logic]]
[[Category:Mathematics]]