**Applied mathematics** is a vast generalization of mathematical studies, opposite pure mathematics.

Applied mathematics is often referred to as "mathematics with purpose" and other synonymous expressions. Essentially, the aspects of mathematics that is studied are those with practical or applied value, such as those listed below. Such subjects are relevant to daily life and the sciences, such that the math and the equations are utilized as a tool.

Perhaps a better explanation would be to define **pure mathematics** - "mathematics for the pleasure of the numbers". Essentially meaning the study of math in its purest sense, without application except for the pursuit and benefit of further mathematics.

- Numerical analysis
- Combinatorics
- Probability
- Statistics
- Decision theory
- Game theory
- Mathematical modeling
- Theory of computation
- Computational Biology