Mathematics Concentration

I. Applied Math 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 eighteenth and nineteenth 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 concetration 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. And 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 Concetration is made up of the three courses: Calculus III (Math 2412), Linear Algebra (Math 3310), and Applied Math I (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 I, 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 Applied Mathematics II (Math 4316) or Differential Equations (Math 3324), a Computer Science course approved by the director, or one of the following: Math 3326 Probability, Math 3327 Statistics, Math 3338 Numerical Analysis, Math 3351 Model Building.

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 Chem. I
Eco 3327 Statistical Methods
Eco 3328 Econometrics
Eco 3329 Quantitative Eco.
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
Approved Elective

II. Pure Math Concentration

The concentration provides a coherent set of courses for students interested in mathematics, short of a major, in areas distinct from those of Applied Mathematics.

The concentration consists of five classes (fifteen credits): four upper level mathematics courses and one course from another field of study that enlarges and reflects on the field. The three required classes are: Math 3321 (Linear Point Set Theory), Math 4332 (Abstract Algebra I), and Math 4341 (Analysis I).

The fourth class may be selected from the following list:
Math 3320 Foundations of Geometry
Math 4342 Analysis II
Math 3333 Abstract Algebra II
Math 4334 Topology
Math 4V43/4V44 Research Hours
Courses as approved by the department.

The External Elective can be chosen from the following courses:
Phil 4334 Philosophy of Science
Phil 3339 Symbolic Logic
Phil 4335 Philosophy of Language
Phil 5345 Philosophy of Technology
Phil 5357 Analytical Tradition
MCS 3311 Theory of Computation
Other electives as approved by the department.