Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. Such applications include numerical analysis, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, biomathematics and bioinformatics, information theory, game theory, probability and statistics, financial mathematics, actuarial science, cryptography and hence combinatorics and even finite geometry to some extent, graph theory as applied to network analysis, and a great deal of what is called computer science. The question of what is applied mathematics does not answer to logical classification so much as to the sociology of professionals who use math. The mathematical methods are usually applied to the specific problem field by means of a mathematical model of the system.

Engineering math describes physical processes, and so is often indistinguishable from theoretical physics. Important subdivisions include:

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  • The Institute for Mathematics and ist Applications (IMA) was founded by and receives major support from the National Science Foundation Division of Mathematical Sciences to carry out a crucial interdisciplinary mission. It also receives support and direction from its Participating Institutions and Participating Corporations.