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.

References

  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.
  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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