400
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
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
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
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
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
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
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
Probability, discrete and continuous random variables, expectation, important probability distributions, introduction to sampling, estimation, and hypothesis testing.
3
Prerequisites
MTH 202,
MTH 311
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
Carries a title reflecting the subject or subjects studied and/or the nature of the class structure. May be repeated for credit.
Variable
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.