What is Applied Mathematics?

Applied mathematics uses mathematics to solve problems that come from the sciences, engineering, computer science, business, and industry. While the motivation is often to solve particular problems, the theory developed can be of wide-ranging interest.

Much classical applied mathematics involves developing mathematical models of a problem and solving them, often in the context of solving differential equations or optimizing some process. This dates back to the development of calculus, and continues to be important today. Here at JMU, our entire applied mathematics group uses differential equations in some way to solve problems in a wide range of disciplines.

Another important strand of applied mathematics is computational mathematics, the study of algorithms and techniques to approximate the solutions to problems that can’t be solved exactly. Many JMU faculty use computational techniques to aid them in their research.

Jobs in Applied Mathematics

At one level, an applied mathematician is a problem solver in any area that requires mathematics. The website WeUseMath.org includes a long list of potential jobs for mathematicians. The Society for Industrial and Applied Mathematics (SIAM) includes a site on Careers in Applied Mathematics.

What Do We Offer?

One of the main reasons for the calculus sequence is to represent situations where quantities vary continuously by differential equations, and solve them. As a result, the calculus sequence (MATH 235-7) followed by a course on differential equations (MATH 238 or MATH 336) is core to any applied mathematician. An introductory course on programming and computation for mathematics (MATH 248) also provides invaluable skills going forward.

At the intermediate level, there are a variety of courses with an applied bent. Methods of Applied Calculus (MATH 337) introduces a variety of techniques building on the calculus sequence for solving differential equations and modeling physical processes.  Optimization (MATH 340) introduces a variety of techniques for finding the best possible solution, with applications in the sciences, economics and the social sciences. Nonlinear Dynamics and Chaos (MATH/PHYS 341) moves beyond classical (linear) modeling and looks at some of the strange (and chaotic) behavior of many problems. Mathematical Models in Biology (MATH 342) introduces and solves problems in biology using mathematics.

At the advanced level, there are two main sequences we offer. MATH 440-1 introduce partial differential equations, their applications and solution, and the qualitative theory of ordinary differential equations. MATH 448-9 introduce a variety of topics in numerical analysis, including numerical linear algebra and the numerical solution of systems of equations and differential equations.

Various faculty also teach special topic courses in areas including acoustics, solid mechanics, visualization and computer graphics, and computational applications in geometry and discrete mathematics.

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