2017-18 Academic Catalog

This course is an introduction to error-correcting codes. The course will cover topics including linear codes, Hamming codes and cyclic codes. Additional topics may include low-density parity-check codes and perfect codes. Prerequisite: Mathematics 232

Differential Forms provide a modern approach to a classical topic: Vector Calculus. They find applications in such diverse fields as geometry, algebra, engineering, electricity and magnetism, and general relativity. This course will rigorously develop differential forms then apply them to classical topics including divergence, gradient, and curl. A primary focus of the course will be the proof of the generalized Stokes' Theorem which is a general n-dimensional form of the familiar Fundamental Theorem of Calculus. Modern treatments of other topics from advanced calculus will be considered as time permits. Prerequisite: Mathematics 236 or instructor permission

Methods of mathematical approximation and applications to scientific computing. Topics include optimization, interpolation, numerical linear algebra, solution of differential equations, and Fourier methods. Both theory and implementation of numerical algorithms will be emphasized. Prerequisite: Mathematics 232

A combinatorial introduction to the study of manifolds in dimensions less than four, including selected topics in knot theory.    Prerequisite: Mathematics 236

Introduction to set-theoretic foundations of mathematics. The axiom system of Zermelo-Fraenkel, cardinal and ordinal numbers, and the Axiom of Choice. As time permits, additional topics may include construction of the real number, transfinite induction, or consistency/independence proofs. Prerequisite: Mathematics 236 or instructor permission