Mathematics and computing 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. **Mathematics and computing** 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[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

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- Statistical methods and algorithms
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- Real and complex analysis
- Numerical methods and computation
- Differential equations
- Optimization methods and applications
- Probability and stochastic processes
- Linear algebra
- Topology and functional analysis
- Applied mathematical techniques
- Computational methods for differential equations
- Finite element theory and its applications
- Modern algebra
- Non-linear optimization

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