## Mathematics Concentration

### I. 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 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 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 Concetration 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 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 Differential Equations (Math 3324),
Probability (Math 3326), Statistics (Math 3327), Numerical Analysis(Math 3338), or
a Computer Science course approved by 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.

### II. Pure Mathematics 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 mathematics classes (fifteen credits): Math 3310
(Linear Algebra), Math 3321 (Linear Point Set Theory); two of Math 4332 (Abstract
Algebra I), Math 4334 (Topology), or Math 4341 (Analysis I); and a fifth class, selected
from the following list:

MAT 3320 Foundations of Geometry

MAT 3322 History and Philosophy of Mathematics

MAT 3331 Number Theory

MAT 4332 or 4333 Abstract Algebra I or II

MAT 4334 Topology

MAT 4341 or 4342 Analysis I or II

MAT 4V43/4V44 Research Hours

Courses as approved by the department.