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: 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. The study of numerical linear algebra and validated numerics are also included in this field.
• Probability and Statistics: 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.
• 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.