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Concept
Computational mathematics
Summary
Computational mathematics is an area of mathematics devoted to the interaction between mathematics and computer computation.
A large part of computational mathematics consists roughly of using mathematics for allowing and improving computer computation in areas of science and engineering where mathematics are useful. This involves in particular algorithm design, computational complexity, numerical methods and computer algebra.
Computational mathematics refers also to the use of computers for mathematics itself. This includes mathematical experimentation for establishing conjectures (particularly in number theory), the use of computers for proving theorems (for example the four color theorem), and the design and use of proof assistants.
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
Computational complexity
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 geometry
Computational number theory
Computational topology
Computational statistics
Algorithmic information theory
Algorithmic game theory
Mathematical economics, the use of mathematics in economics, finance and, to certain extents, of accounting.
Official source
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