MAT 530: Geometry and Topology I (Fall 2022)

About the course

The field of topology was developed about 100 years ago to provide foundations for analysis and geometry. In the course, we will look at the most important definitions and results from basic point set topology and elementary algebraic topology. For textbook, we will use the second edition of Topology by James Munkres; the paperback version costs around $40 on amazon. (Here is a link to an online copy.) Please have a look at the syllabus for additional information. When I taught the course in 2014, I typed up lecture notes; you can find those here.

Time and location

We meet on Tuesday and Thursday, 9:45–11:05 am, in room P-117 of the Physics building. There is an extra (inofficial) recitation hour for interested parties, on Friday, 2–3 pm (in our usual classroom P-117). Other office hours are on Monday, 2:00–4:00pm in room 4-110 of the Mathematics building.

Midterm

The midterm was held in class on Tuesday, October 18. It was based on the lecture notes (1–13) and the homework (1–6). Here are the solutions. The average was 22 (out of 50) and the median 27; the highest score was 49, the lowest one 0.

Make-up lecture

There will be a make-up lecture on Tuesday, December 6, at 9:45 in our regular classroom P–117. The topic is applications of homology groups (such as the Jordan curve theorem).

Homework assignments

Lecture notes

Here are notes for the lectures so far, together with a list of topics.

This note contains an elementary proof for the invariance of domain (and Brouwer's fixed point theorem). It uses Sperner's lemma and general topology, but no algebraic topology; I learned some of the details from Terry Tao's blog.

This note contains an elementary proof of the Jordan curve theorem. It uses some ideas from the proof of the Seifert-van Kampen theorem.