Applied mathematics
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 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 mathematicswith 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 scienceStatistics 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.
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.
*
Pure mathematics* The
Society for Industrial and Applied Mathematics is a professional society dedicated to promoting the interaction between mathematics and other scientific and technical communities.
