Computational mathematics

Areas of computational mathematics

• 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, 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.