User:Adriana.rodriguez2002/Computational mathematics

Computational mathematics involves mathematical research in mathematics as well as in areas of science where computing plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations.

Computational applied mathematics consists roughly of using mathematics for allowing and improving computer computation in applied mathematics. Computational mathematics may also refer to the use of computers for mathematics itself. This includes the use of computers for mathematical computations (computer algebra), the study of what can (and cannot) be computerized in mathematics (effective methods), which computations may be done with present technology (complexity theory), and which proofs can be done on computers (proof assistants). Computational mathematics contains at least 18 different principal areas.

Contents

• 1Areas of computational mathematics
• 2References
• 3Further reading
• 4External links

Areas of computational mathematics[edit]

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, also known as a complexity of an algorithm is the amount of resources required to run it.
• 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, studies zeros of multivariate polynomials. The fundamental objects of study in algebraic geometry are algebraic varieties.
• Computational group theory or analysis of groups by means of computers.
• Computational geometry, also known as geometric modelling and computer-aided geometric design (CAGD).
• Computational number theory, this has cryptography applications, including RSA, mathematics of algebraic structures and post-quantum cryptography.
• Computational topology, or the study of the topological nature of computation.
• Computational statistics is used to refer to computationally intensive statistical methods including resampling methods
• Algorithmic information theory, it can be used to study a wide variety of mathematical objects, including integers.
• Algorithmic game theory helps you understanding and design of algorithms in strategic environments.
• Mathematical economics, the use of mathematics in economics, finance and, to certain extents, of accounting.