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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.
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)
- parts of theoretical computer science
Statistics is, strictly speaking, a separate field from mathematics, but is often included in such a list.
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 instead of Physics.
Segregation within Universities
Some universities 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.
See also
External links
- The Society for Industrial and Applied Mathematics is a professional society dedicated to promoting the interaction between mathematics and other scientific and technical communities.
Anvendt matematik | Angewandte Mathematik | Matemática aplicada | Aplika matematiko | ریاضیات کاربردی | Mathématiques appliquées | מתמטיקה שימושית | 応用数学 | Matemática aplicada | Matematică aplicată | Прикладная математика | Matematik terapan | คณิตศาสตร์ประยุกต์ | Toán học ứng dụng | 应用数学
"Applied mathematics"