Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. Such applications include numerical analysis, mathematical physics, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, mathematical biology and bioinformatics, information theory, game theory, probability and statistics, mathematical economics, 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 mathematics. The mathematical methods are usually applied to the specific problem field by means of a mathematical model of the system.

Engineering mathematics describes physical processes, and so is often indistinguishable from theoretical physics. Important subdivisions include: fluid dynamics, acoustic theory, Maxwell's equations that govern electromagnetism, mechanics, numerical relativity, etc.

Fundamental applied mathematics is taught at second-level in some countries, such as Ireland, where it is a minority option at Leaving Certificate.

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