Math 5520 – Introduction to Topology
Spring 2020

Instructor: Ken Bromberg
Office: JWB 303
Office hours: MWF 10:30-11:30

Prerequisites: “C” or better in Math 5510 or consent of the instructor. Math 5310 will also be helpful but not required.

Meeting place and time: MWF 9:40-10:30, LCB 222

Text: Topology, 2nd Ed., by James Munkres
We will start with Chapter 9.
We will also cover parts of Chapter 11.

Worksheet for class on Wednesday, March 18th.

The midterm.

Notes on groups.

Lecture notes

Day 1
Day 3
Day 4
Class exercise, days 5 and 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 13
Day 14
Day 15
Day 16
Day 18
Day 19
Day 21
Day 22
Day 23


Lecture 1.1
Lecture 1.2

Lecture 2.1
Lecture 2.2
Lecture 2.3
Lecture 2.4
Lecture 2.5


Homework 1, Due Wednesday, January 22nd - submit via Canvas by 11PM
Section 52, Problems 2,3,4,5. Due Monday, Febuary 3rd - submit via Canvas by 11PM
Section 53, Problems 3,4,5 and Section 54, Problem 8. Due February 12th - submit via Canvas by 11PM
Homework 4, Due Monday, Febuary 24th - submit via Canvas by 11PM
Homework 5, Due Friday, March 6th - submit via Canvas by 11PM
Homework 8, Due Friday, April 10th - submit via Canvas by 11PM

Midterm - February, 28th

Course description: This course is the second semester of an introduction to topology and geometry. The first part of the course will be an introduction to algebraic topology and in particular the fundamental group. While I will probably not follow it precisely, Munkres book will be our main written source and most homework problems will come from the book. I'm anticipating that this will take ten weeks. For the last part of the course I am planning on disucssing some basic differential geometry of curves and surfaces which should complement the geometry that was covered last fall in 5510. I have some notes that I'll use for this but I will also give references to text books that should be easily available online.

The course will be rigorous and proof based and should be good preparation for anyone planning to study pure math in graduate school.

Grades: I plan on assigning around 10 homework sets (approximately due ever week and a half). You will be required to submit your answers in TeX. Homework assignments will be posted here. I will grade some but not all of the problems. Homework will be 50% of your grade. There will also be a midterm which will be 20% and a final which will be 30%. The final exam is April 24th from 8:00-10:00 AM.

University Policies

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