From Encyclopedia Jr, free information reference for Kids
Applied Mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.
[edit] Divisions of Applied Mathematics
Traditionally, applied mathematics consisted of three major areas: Approximation theory (including computational methods), differential equations (especially partial differential equations), and applied probability. One could even do so-called "theoretical applied mathematics" in these areas, by performing research on the fundamentals of the subjects.
Today the term Applied Mathematics is used in a much broader sense. (Some mathematicians distinguish between applied mathematics, as described above, and applicable mathematics, which would be any mathematics that is applied in modeling a non-mathematical problem.) Mathematicians generally consider it incorrect to conflate applied mathematics--areas of mathematics--with applications of mathematics, the actual act of applying mathematics to a real-world problem. Scientists and social scientists who apply mathematics in their work typically do not make this distinction.
Applicable areas of mathematics include most notably:
- differential equations (ODEs and PDEs)
- numerical analysis/scientific computing
- approximation theory and representation theory
- matrix theory
- mathematical physics
- mathematical methods of engineering
- nonlinear optimization
- operations research, including linear programming
- continuous modelling
- control theory
- mathematical biology
- bioinformatics
- information theory
- game theory
- probability
- mathematical economics
- financial mathematics
- actuarial science
- cryptography
- graph theory (as applied to network analysis)
- statistics
- parts of theoretical computer science
- computational topology and computational geometry
Many statisticians would contend that statistics is a separate discipline from mathematics, but in practice they are often taught in the same departments. Engineering mathematics and mathematical physics describe physical processes, and so are often indistinguishable from theoretical physics. Traditionally the subject mechanics was often taught in departments of applied mathematics in American universities rather than in physics departments.
[edit] Segregation within Universities
Some universities in the UK host departments of Applied Mathematics and Theoretical Physics, but it is now much less common to have separate departments of pure and applied mathematics. Schools with separate applied mathematics departments range from Brown University, which has a well-known and large Division of Applied Mathematics that offers degrees through the doctorate, to Santa Clara University, which offers only the M.S. in applied mathematics. Many research universities divide their mathematics department into pure and applied sections (e.g., MIT).
Fundamental applied mathematics is taught at second-level in some countries, such as Ireland, where it is a minority option at Leaving Certificate.
[edit] See also
[edit] External links
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Major topics in Applied mathematics |
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Discrete mathematics: Combinatorics • Graph theory • Game theory • Discrete geometry • Theoretical computer science • Computability theory • Complexity theory • Information theory •
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Probability • Probability distribution • Probability theory • Statistics • Stochastic process • Operations research • Stochastic processes •
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Numerical analysis • Mathematical biology • Optimization • Dynamical systems • Chaos theory • Financial mathematics • Cryptography •
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