This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

<- Return to Course List

Description

This is an introduction to topology for qualified undergraduates.

Prerequisites

MATH 410

Topics

Metric spaces, topological spaces
Continuous maps and homeomorphisms
Connectedness, compactness (including Heine-Borel, Bolzano-Weierstrass, Ascoli-Arzela theorems),
Cantor sets
Fundamental group (homotopy, covering spaces, the fundamental theorem of algebra, Brouwer fixed point theorem)
Surfaces (e.g., Euler characteristic, the index of a vector field, hairy sphere theorem)
Elements of combinatorial topology (graphs and trees, planarity, coloring problems)