Supplementary mathematics/Computational mathematics

Computational mathematics includes mathematical research in branches of science where calculation plays an important and key role. Calculation means algorithms, numerical methods and symbolic methods. Calculation is leading in research. Computational mathematics emerged in the 1950s as a different branch of applied mathematics.

Today, it is necessary to use a computer to perform calculations to solve various scientific problems. Computational mathematics includes or relates to:

• Computing science, or scientific computing or computing engineering or engineering and computing science
• Solving mathematical problems with computer simulation, unlike applied mathematical analytical methods
• Numerical methods used in scientific calculations such as numerical linear algebra, numerical solution of partial differential equations
• Stochastic methods such as Monte Carlo methods and other representations of uncertainty in scientific computing, for example random finite elements
• Mathematics of scientific calculations, which from a mathematical point of view includes mathematical proofs, such as numerical analysis and the theory of numerical methods, and from the point of view of theoretical computer science, including the theory of calculations and computational complexity
• Symbolic calculations and computer algebra devices
• Research with the help of computer in various branches of mathematics such as logic (subsidized proof of proof), discrete mathematics, etc.
• 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 theory of information
• Algorithmic theory of games