Applied Mathematics, Concentration

Applied mathematics explores the pure mathematical principles that undergird subjects of interest to other disciplines. The concentration includes a series of mathematics courses, an elective in applied mathematics or computer science, and an elective in another field.

The Scope and Requirements of the Applied Mathematics Concentration

Philosophy: Much of the history and philosophy of applied mathematics can be summarized by a quote from the preface to The Functions of Mathematical Physics by Harry Hochstadt: "The topics covered ... were first studied by the outstanding mathematicians of the 18th and 19th centuries. Among the many who devoted themselves to these studies are Gauss, Euler Fourier, Legendre and Bessel. These men did not recognize the modern and somewhat artificial distinction between pure and applied mathematics. Much of their work was stimulated by physical problems that led to the studies of differential equations. Frequently they developed generalizations to obtain results having no immediate or obvious applications. As a consequence, mathematics was often ahead of its time, having tools ready before physicists and engineers felt the need for them." The concentration reflects this historic interplay by presenting topics of obvious interest to applied scientists as well as being of purely mathematical interest.

The concept of transformations plays a central role in applied mathematics. Partial differential equations are transformed into ordinary differential equations. Ordinary differential equations are transformed in algebraic equations. Algebraic systems are transformed into simple algebraic systems. Thus, one can understand why linear algebra plays a fundamental role in the concentration.