4000

Prerequisite: C or better in both MATH 2263 and MATH 2150. 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: C or better in MATH 3030. This course is a review of the origins and development of the great ideas of classical and modern mathematics. The emphasis will be on mathematics as a living organism, constantly being invented, improved, and expanded. Important theorems and important mathematicians will be studied, as well as the historical and cultural contexts in which they arose.

Prerequisite: C or better in MATH 3030. 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: C or better in MATH 3030. An introduction to the basic problems, terminology, and methods of elementary number theory. Topics include: division algorithm, Euclidean algorithm, Diophantine equations, fundamental theorem of arithmetic, prime numbers and their distribution, perfect numbers, congruences, Fermat's Little Theorem, Wilson's Theorem, Euler's Phi Function, Euler's Theorem, primitive roots, and quadratic reciprocity.

Prerequisite: C or better in MATH 2150. A rigorous study of vector spaces and linear transformations over arbitrary fields. Topics include linear maps and dual spaces, inner products and orthogonality, eigenvalues and eigenvectors, triangulation and canonical forms.

Prerequisite: C or better in both MATH 2263 and MATH 3030. Basic properties of the real numbers, limits, continuity of functions, formal definitions of derivative and integral.

Prerequisite: C or better in both MATH 2263 and MATH 3030. 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: C or better in MATH 2263. Ordinary differential equations with applications are the primary focus. Some consideration is given to existence and uniqueness theorems.

Prerequisite: C or better in MATH 3030. An axiomatic development of Euclidean geometry and an introduction to non-Euclidean geometry.

Prerequisite: C or better in MATH 2263 and (C or better in MATH 2150 or C or better in MATH 3030). 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: C or better in MATH 4600. 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: C or better in MATH 2150, MATH 1262, and CSCI 1302 or equivalents. A general algorithmic approach to numerical analysis with emphasis on concrete numerical methods. (This course is equivalent to CSCI 4650.)

Prerequisite: C or better in both MATH 2263 and MATH 2150. A basic introduction to operations research. Linear, integer and dynamic programming will be considered. The theory of queues is presented and the idea of stochastic simulation is introduced.

Prerequisite: C or better in MATH 3030 and permission of the instructor. This course consists of directed readings in mathematics under the supervision of a faculty member. Material may be drawn from classical and modern texts as well as the literature. This course is repeatable for credit.

Prerequisite: Permission of the instructor. Investigation of a topic of special interest under the supervision of a faculty member. This course is repeatable for credit.

Prerequisite: Permission of the instructor. Selected topics not available in other departmental courses. This course is repeatable for credit.

Prerequisite: Selection for participation in a University-approved Internship program. An individually designed course involving off-campus study, research, and/or work in a governmental agency or business organization. This course is repeatable for credit.

Prerequisite: Permission of faculty advisor and instructor of MATH 4950. Research, writing, and presentation of a scholarly project developed in conjunction with the instructor of MATH 4950. This course is a component of the Senior Capstone Experience for Mathematics majors. Corequisite: MATH 4950.

Prerequisites: Completion of all Area F mathematics requirements with a grade of B or better and permission of the instructor. This course affords interested junior and senior students an opportunity to participate in a basic research experience with a member of the Department faculty. This course is repeatable for credit.