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Applied mathematics

2007 Schools Wikipedia Selection. Related subjects: 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.

Divisions of Applied Mathematics

   Traditionally, applied mathematics consisted of three major areas:
   Approximation theory (including representation theory and 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.

   Many statisticians contend that statistics is a separate discipline
   from mathematics, but in practice both subjects are often taught in the
   math department. Engineering mathematics and mathematical physics
   describe physical processes, and so are almost indistinguishable from
   theoretical physics. Traditionally, classical mechanics was often
   taught in applied math departments at American universities rather than
   in physics departments.

   Today the term applied mathematics is often used in a much broader
   sense. Mathematicians generally consider it incorrect to conflate
   applied mathematics (a subset of mathematics) with applications of
   mathematics (the actual act of applying mathematics to real-world
   problems). But scientists and social scientists who utilize mathematics
   in their work do not usually make this distinction.

   An example may serve to sharpen the somewhat fuzzy lines separating
   traditional applied mathematics from pure mathematics and
   distinguishing both of these from applicable mathematics, or the use of
   mathematics as a tool. A "smooth" function, such as cosx, can be
   represented by a Taylor series containing a countably infinite number
   of terms. Pure mathematics is concerned with the problem of proving
   that the Taylor series exists, and with the closely associated problems
   of determining its coefficients and its circle of convergence, or the
   domain in which it is valid. Applied mathematics addresses the more
   practical problems of how the series may best be calculated; how many
   terms must be included to achieve a desired level of precision; and how
   best to tabulate the resulting values, or perhaps encapsulate the
   Taylor series within a computer algorithm. Finally, a surveyor who
   consults the tabulated or computerized values of cosx while making
   trigonometric calculations is not really doing mathematics – he is
   simply using results the mathematicians have derived to complete a
   surveying project.

   Some branches of mathematics – differential equations (ODEs and PDEs),
   matrix theory, continuous modelling, probability, and statistics – are
   widely applicable to many fields of science and technology. Others –
   such as numerical analysis, scientific computing, information theory,
   cryptography, graph theory as applied to network analysis, and
   theoretical computer science – have fueled the rapid proliferation of
   digital computers. Problems associated with computer technology have,
   in their turn, provided the motivation for mathematical advances in all
   these fields. And the increasing power and speed of the computers
   themselves have opened new possibilities in computational topology and
   computational geometry.

   Both physics and engineering have their own specialized mathematical
   dialects, including control theory. Advances in the life sciences have
   stimulated the development of mathematical biology and have recently
   generated an entirely new field, bioinformatics. Economics, finance,
   and insurance have spawned several related disciplines that might be
   characterized as commercial mathematics. Certain special economic
   problems gave the initial impetus to game theory. Additional problems
   from business and commerce have driven mathematical research into
   optimization techniques, including the widely employed methods of
   operations research and linear programming. As time passes all these
   optimization methods are finding new applications in a widening circle
   of disciplines.

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.

   Retrieved from " http://en.wikipedia.org/wiki/Applied_mathematics"
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