# 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.