# Computational mathematics Computational mathematics may refer to 2 different aspects of the relation between computing and mathematics. **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 be computerized in mathematics (effective methods) * which computations may be done with present technology (complexity theory) * which proofs can be done on computers (proof assistants) Both aspects of computational mathematics involves *mathematical research* in mathematics as well as in areas of science where computing plays a central and essential role, that is, almost all sciences, and emphasize algorithms, numerical methods, and symbolic computations. ## Areas of computational mathematics Computational mathematics emerged as a distinct part of *applied mathematics* by the early 1950s. Currently, computational mathematics can refer to or include: * *computational science*, scientific computation, 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 (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* * *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. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/900-index/980-hierarchy/classification/computational-mathematics.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.