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.

Content: The concentration consists of five courses. The core of the applied mathematics concentration is made up of the three courses: Calculus III (Math 2412), Linear Algebra (Math 3310) and Applied Mathematics (Math 4315). Fundamental to modern applied mathematics is the study of structures known as vector spaces and the linear operations on those spaces. The student is introduced to these concepts in linear algebra. These ideas are expanded in Calculus III, where the linearity and multidimensionality introduced in linear algebra are combined with the infinite processes of calculus. These concepts continue to be drawn together in Applied Mathematics, where the analogy is completed between discrete problems, continuous one-dimensional problems and continuous multi-dimensional problems.

The fourth course is an applied mathematics elective such as Differential Equations (Math 3324), Probability (Math 3326), Statistics (Math 3327), Numerical Analysis (Math 3338) or a Computer Science course approved by the director.

The fifth course is an elective from a field other than mathematics. This allows the student to tailor the concentration to his or her own interests and reinforces the concentration's interdisciplinary nature.

Possible choices include:

• CHE 3331 Physical Chemistry I 
• ECO 3327 Statistical Theory and Methods 
• ECO 3328 Business and Economic Forecasting
• PHI 4333 Philosophy of Science 
• PHY 3341 Optics 
• PHY 3363 Computational Physics
• PHY 4327 Electromagnetic Theory
• PHY 4423 Theoretical Mechanics
• PHY 4424 Quantum Mechanics
• PSY 3337 Statistical Methods
• Other electives as approved by the department.