Applied mathematics

Applied mathematics is a field of mathematics which uses mathematics to solve problems of other branches of science. The contrary notion is pure mathematics. There are many fields:

Approximation theory:^[1] Sometimes it is not possible to get an exact solution to a problem, because this might take too long, or it may not be possible at all. Approximation theory looks at ways to get a solution which is close to the exact one, and which can be obtained faster.
Numerical analysis and simulation: This field investigates various algorithms to get approximations for mathematical problems.^[2]^[3]^[4]^[5] The study of numerical linear algebra^[6]^[7]^[8] and validated numerics^[9]^[10] are also included in this field.
Probability and Statistics:^[11]^[12]^[13] How likely is it that something will happen? - If a coin is flipped 100 times, and lands heads up 53 times, is this coin good for games of chance, or should another one be taken?
Optimization is about finding better solutions to problems.^[14]
In ecology certain things are known about populations of animals or plants. This is usually called Population model. Biologists use them to tell how a population changes over time.

Applied Mathematics Media

Efficient solutions to the vehicle routing problem require tools from combinatorial optimization and integer programming.
A numerical solution to the heat equation on a pump casing model using the finite element method.
Fluid mechanics is often considered a branch of applied mathematics and mechanical engineering.
Mathematical finance is concerned with the modelling of financial markets.
The Brown University Division of Applied Mathematics is the oldest applied math program in the U.S.
Applied mathematics has substantial overlap with statistics.

References

↑ Trefethen, L. N. (2019). Approximation theory and approximation practice. SIAM.
↑ Stoer, J., & Bulirsch, R. (2013). Introduction to numerical analysis. Springer Science & Business Media.
↑ Conte, S. D., & De Boor, C. (2017). Elementary numerical analysis: an algorithmic approach. Society for Industrial and Applied Mathematics.
↑ Greenspan, D. (2018). Numerical Analysis. CRC Press.
↑ Linz, P. (2019). Theoretical numerical analysis. Courier Dover Publications.
↑ Demmel, J. W. (1997). Applied numerical linear algebra. SIAM.
↑ Ciarlet, P. G., Miara, B., & Thomas, J. M. (1989). Introduction to numerical linear algebra and optimization. Cambridge University Press.
↑ Trefethen, Lloyd; Bau III, David (1997). Numerical Linear Algebra (1st ed.). Philadelphia: SIAM.
↑ Tucker, Warwick (2011). Validated Numerics: A Short Introduction to Rigorous Computations. Princeton University Press.
↑ Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.
↑ DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. Pearson Education.
↑ Johnson, R. A., Miller, I., & Freund, J. E. (2000). Probability and statistics for engineers (Vol. 2000, p. 642p). London: Pearson Education.
↑ Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (1993). Probability and statistics for engineers and scientists (Vol. 5). New York: Macmillan.
↑ Intriligator, M. D. (2002). Mathematical optimization and economic theory. Society for Industrial and Applied Mathematics.

Related pages

Society for Industrial and Applied Mathematics (SIAM)
International Association for Mathematics and Computers in Simulation (IMACS)
International Congress on Industrial and Applied Mathematics
Japan Society for Industrial and Applied Mathematics (JSIAM, Japanese counterpart of SIAM)
Japan Society for Simulation Technology (JSST, Japanese counterpart of IMACS)

Other websites

Wikiversity has more on: School:Mathematics

The English Wikibooks has more information on:

Applicable Mathematics

Media related to Applied mathematics at Wikimedia Commons
The Society for Industrial and Applied Mathematics (SIAM) is a professional society for promoting the interaction between mathematics and other scientific and technical communities. With organizing and sponsoring many conferences, SIAM is a major publisher of research journals and textbooks in applied mathematics.
The Applicable Mathematics Research Group at Notre Dame University
Centre for Applicable Mathematics at Liverpool Hope University
Applicable Mathematics research group at Glasgow Caledonian University

Template:Industrial and applied mathematics

[1] Trefethen, L. N. (2019). Approximation theory and approximation practice. SIAM.

[2] Stoer, J., & Bulirsch, R. (2013). Introduction to numerical analysis. Springer Science & Business Media.

[3] Conte, S. D., & De Boor, C. (2017). Elementary numerical analysis: an algorithmic approach. Society for Industrial and Applied Mathematics.

[4] Greenspan, D. (2018). Numerical Analysis. CRC Press.

[5] Linz, P. (2019). Theoretical numerical analysis. Courier Dover Publications.

[6] Demmel, J. W. (1997). Applied numerical linear algebra. SIAM.

[7] Ciarlet, P. G., Miara, B., & Thomas, J. M. (1989). Introduction to numerical linear algebra and optimization. Cambridge University Press.

[8] Trefethen, Lloyd; Bau III, David (1997). Numerical Linear Algebra (1st ed.). Philadelphia: SIAM.

[9] Tucker, Warwick (2011). Validated Numerics: A Short Introduction to Rigorous Computations. Princeton University Press.

[acta-10] Rump, S. M. (2010). Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19, 287-449.

[11] DeGroot, M. H., & Schervish, M. J. (2012). Probability and statistics. Pearson Education.

[12] Johnson, R. A., Miller, I., & Freund, J. E. (2000). Probability and statistics for engineers (Vol. 2000, p. 642p). London: Pearson Education.

[13] Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (1993). Probability and statistics for engineers and scientists (Vol. 5). New York: Macmillan.

[14] Intriligator, M. D. (2002). Mathematical optimization and economic theory. Society for Industrial and Applied Mathematics.

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