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computational mathematics
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.〔National Science Foundation, Division of Mathematical Science, (Program description PD 06-888 Computational Mathematics ), 2006. Retrieved April 2007.〕 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, for example stochastic finite elements
* the mathematics of scientific computation〔Future Directions in Computational Mathematics, Algorithms, and Scientific Software, Report of panel chaired by R. Rheinbold, 1985. (Distributed by SIAM ).〕 (the theoretical side involving mathematical proofs〔Mathematics of Computation, (Journal overview ). Retrieved April 2007.〕), 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 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 geometry
* computational number theory
* computational topology
* computational statistics
* algorithmic information theory
* algorithmic game theory
==References==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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