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. 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 (the theoretical side involving 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 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
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.
