**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.

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