Applied mathematics
From Free net encyclopedia
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. 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 "theoretical applied mathematics" in these areas, by performing research on the fundamentals of the subjects. Today the term is often used in a much broader sense, though some distinguish between applied mathematics (the above-mentioned sub-fields of mathematics) and applicable mathematics, 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, numerical analysis, mathematical physics and mathematics methods of engineering, linear programming and other optimization and operations research methods, continuous modelling, control theory, mathematical biology and bioinformatics, information theory, game theory, probability, mathematical economics and financial mathematics, actuarial science, cryptography and hence number theory, graph theory (as applied to network analysis), and areas 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. In fact, there are departments of Applied Mathematics and Theoretical Physics. Traditionally, mechanics was often taught in departments of applied mathematics in American universities. However, 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.da:Anvendt matematik
de:Angewandte Mathematik es:Matemática aplicada eo:Aplika matematiko fa:ریاضیات کاربردی fr:Mathématiques appliquées he:מתמטיקה שימושית pt:Matemática aplicada ro:Matematică aplicată ru:Прикладная математика su:Matematik terapan th:คณิตศาสตร์ประยุกต์ vi:Toán học ứng dụng zh:应用数学