Description

This is an introduction to topology for qualified undergraduates.

Prerequisites

Minimum grade of C- in MATH410.

Level of Rigor

Advanced

Sample Textbooks

Topology, 2nd Edition, by J. Munkres

Topology of Surfaces, by L.C. Kinsey

Applications

If you like this course, you might also consider the following courses

Additional Notes

Students interested in grad school in MATH should strongly consider this course

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)