5000

Prerequisite: Permission of the instructor. This course will concentrate on the bridge between a variety of mathematical ideas and their applications to problems in the natural and social sciences through the techniques of mathematical modeling. The course will emphasize out-of-class project work and the written presentation of modeling results and conclusions.

Prerequisite: Permission of the instructor. A review of the origins and development of the great ideas of classical and modern mathematics.

Prerequisite: Permission of the instructor. An introduction to the basic structures of algebra including groups, rings, and fields along with their substructures as well as the ideas of homomorphism and isomorphism.

Prerequisite: Permission of the instructor. An introduction to the basic problems, terminology, and methods of elementary number theory. Topics include: diophantine problems, congruences, perfect numbers, Euler’s theorem and function, primitive roots, and quadratic reciprocity.

Prerequisites: Permission of the instructor. Basic properties of the real numbers, limits, continuity of functions, formal definitions of derivative and integral.

Prerequisite: Permission of the instructor. An introduction to functions of a complex variable. Topics include the Cauchy-Riemann equations, line integrals, the Cauchy integral formulas, Laurent series, harmonic functions and conformal mapping.

Prerequisite: Permission of the instructor. Ordinary differential equations with applications are the primary focus. Some consideration is given to existence and uniqueness theorems.

Prerequisite: Permission of the instructor. An axiomatic development of Euclidean geometry and an introduction to non-Euclidean geometry.

Prerequisite: Permission of the instructor. A calculus-based first course in probability theory. Topics include combinatorial analysis, probability axioms, conditional probability, independence, discrete and continuous random variables, jointly distributed random variables, expectation, and limit laws such as the weak and strong laws of large numbers and the central limit theorem.

Prerequisite: Permission of the instructor. A calculus-based introduction to the theory and applications of statistical methods. Topics include estimation and prediction, inference and hypothesis testing, linear and multiple regression, analysis of variance, and nonparametric statistical methods.

Prerequisite: Permission of the instructor. A general algorithmic approach to numerical analysis with emphasis on concrete numerical methods.

Prerequisite: Permission of the instructor. An introductory survey of graphs and digraphs with applications. Applications include transportation problems, the traveling salesman problem, modeling, and recreational mathematics.

Prerequisite: Approval of the instructor. Investigation of a topic of special interest under the supervision of a faculty member.

Prerequisite: Approval of the instructor. Selected topics not available in other departmental courses.