MAT 444-01 - Senior Seminar: Algebraic Topology

4 credits (Spring)

In analysis, we learn that continuous functions on the real line are, roughly speaking, functions that send inputs that are close together to outputs that are close together. But what does it mean for a function defined on a more complex geometric object to be continuous? How do we make sense of “closeness” and “connectedness” in general? Topology gives us a framework to answer these questions. The first part of this course will establish the basics of point-set topology. Then, once we’ve made precise the ideas of topological space and continuity, we’ll turn to studying properties of spaces. Algebraic topology studies spaces using “algebraic invariants”, which are ways to assign to each space a group or a ring. We can then use tools from abstract algebra to answer topological questions. This will be an inquiry-based course, and students will discover the theory through guided readings, exercises, and in-class discussions.

Prerequisite: MAT 321 with grade S, C, or better. MAT 316 with grade S, C, or better highly recommended.
Instructor: Hazel