Computational mathematics

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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 computations. Computation in research is prominent.[1] 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,[2] such as Monte Carlo methods and other representations of uncertainty in scientific computation, for example stochastic finite elements
   the mathematics of scientific computation[3] (the theoretical side involving mathematical proofs[4]), 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