Depending on the discipline, researchers use applied mathematics in various ways. For example, some disciplines rely heavily on pure mathematics. Numerical analysis—a form of applied mathematics—is a field that uses pure mathematics to decipher partial differential equations and variational methods (for more information about numerical analysis, see below; for partial differential equations, see “Mathematical Analysis”). There are also areas of applied mathematics that overlap other fields of study. For example, there are mathematicians who use applied mathematics to study the structure of matter—especially the behavior of subatomic particles—a field that also overlaps the same types of studies done by subatomic physicists.

Applied mathematics is used in high-tech image processing, such as with this MRI (Magnetic Resonance Imaginge) machine used in hospitals to create scans of the inside of patients’ bodies.