Traditionally, applied mathematicians solve problems that arise from physical processes and engineering.
In a broad sense, the applied mathematician designs and analyzes models of systems and tests and evaluates performance in research and development or in industrial production. The applied mathematician serves on teams with engineers, physicists, programmers, and other specialists. The common goal is to find ways to improve quality, reduce cost, and increase productivity.
The tasks of the applied mathematician are as diverse as the constituencies served. In the aeronautical field a mathematician may help to develop models for atmospheric flight. Biomedical engineers may rely on mathematicians when designing and interpreting theoretical models of chemical and biological processes. A mechanical engineer may require a study of heat transfer by conduction, convection, and radiation resulting from a gas turbine.
Many problems involve scientific or engineering data and the use of computer techniques to answer questions arising in research, plant operations, product distribution systems, inventory controls, and business system analyses.
What should one study in college?
For a career in classical applied mathematics, a student should obtain a thorough background in calculus, linear algebra, ordinary and partial differential equations, probability, statistics, numerical analysis, and vector calculus. These courses should include appropriate courses in computer sciences. Other supporting work could include physics or chemistry.
Careers in Applied Mathematics and Computational Mathematics, by the Society for Industrial and Applied Mathematics (SIAM)