Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.

Divisions of applied mathematics
Historically, mathematics was most important in the natural sciences and engineering. However, in recent years, fields outside of the hard sciences have spawned the creation of new areas of mathematics, such as game theory, which grew out of economic considerations, or neural networks, which arose out of the study of the brain in neuroscience.
The advent of the computer has created new applications, both in studying and using the new computer technology itself (computer science, which uses combinatorics, formal logic, and lattice theory), as well as using computers to study problems arising in other areas of science (computational science), and of course studying the mathematics of computation (numerical analysis). Statistics is probably the most widespread application of mathematics in the social sciences, but other areas of math are proving increasingly useful in these disciplines, especially in economics and management science.