400

MTH 401 Real Analysis I

A rigorous treatment of properties of the real numbers and functions of a single real variable. Topics include completeness, limits, continuity, differentiation, integration, and sequences. Additional topics may include series, an introduction to Euclidean or metric spaces.

3

Prerequisites

MTH 311

MTH 402 Real Analysis II

Topics may include sequences and series of functions, uniform convergence, Fourier series, the Riemann-Stieltjes integral, and functions in several variables.

3

Prerequisites

MTH 401

MTH 404 Complex Variables

Complex numbers and functions of a complex variable; limits, differentiability; Cauchy's theorem; power series, Laurent series, residue theorem with applications, maximum modulus theorem, Liouville's theorem; conformal mapping and applications.

3

Prerequisites

MTH 301, MTH 311

MTH 431 Modern Geometry

A foundations course in elementary geometry discussing the following: incidence geometries; finite, metric, and synthetic geometries; Euclidean, hyperbolic, and elliptical geometries; and some axiomatic theory.

3

Prerequisites

MTH 301, MTH 341

MTH 435 Topology

An introduction to fundamental concepts in point-set topology. Topics are taken from the following: open and closed sets, continuity, connectedness, compactness, separability, metric spaces.

3

Prerequisites

MTH 311

MTH 441 Modern Algebra I

The study of algebraic structures that are like the integers, polynomials, and the rational numbers. The integers and their properties. Groups: examples, properties, and counting theorems. Rings: examples and properties. Fields: roots of polynomials and field extensions.

3

Prerequisites

MTH 311, MTH 341

MTH 442 Modern Algebra II

Unique factorization in special rings. Field theory and the use of groups to understand field extensions: finite fields, Galois theory. Classical construction problems, solution of n-th degree polynomials.

3

Prerequisites

MTH 441

MTH 461 Probability and Statistics I

Probability, discrete and continuous random variables, expectation, important probability distributions, introduction to sampling, estimation, and hypothesis testing.

3

Prerequisites

MTH 202, MTH 311

MTH 462 Probability and Statistics II

Topics from simple linear and multiple regression, analysis of variance and design of experiments, methods for categorical data, distribution-free methods.

3

Prerequisites

MTH 461

MTH 490 Directed Study

Credit arranged.

Variable

MTH 491 Seminar in Mathematics

Carries a title reflecting the subject or subjects studied and/or the nature of the class structure. May be repeated for credit.

Variable

MTH 493 Research in Mathematics

Faculty-directed student research. Before enrolling, a student must consult with a faculty member to define project. May be repeated for credit.

MTH 497 Internship

Practical field experience in selected industries or agencies. Department permission and supervision is required. Credit arranged.
Variable

MTH 499 Senior Thesis

Research, study, or original work under the direction of a faculty mentor, leading to a scholarly thesis document with a public presentation of results. Requires approval of thesis director, department chair, dean, and the director of the honors program, when appropriate.

3

Prerequisites

Senior standing; 3.0 G.P.A. in the thesis area or good standing in the honors program.