Math 426: Introduction to Topology

Course Information

Instructor

The instructor for the course is me, Jim Bryan

TA/Grader

The TA/Grader for the course is Danny Ofek.

Description

This is an introduction to topology, the aim of which is to introduce topological spaces, continuous functions, the fundamental group and covering spaces. This course feeds into Math 427/527 (Algebraic Topology).

Lectures

The class meets MWF at 2pm in MATH 225.

Office Hour

There is an office hour 11am on Tuesdays. This may change. My office is Math 226.

Notes

Here are my lecture notes from last year. For the most part I will follow these notes. If they change, I will try to post updates here.

References

The classic reference for the topics of this course Topology, 2nd Edition by Munkres. It covers almost all of what this course will cover and does it rather exhaustively. We are not officially using this book because it is too slow and we will want to streamline the topics quite a bit, but it is a good source to fall back on.

The book Topology and Geometry by Glen Bredon has a more streamlined approach to the same material as Munkres given in chapters 1 and 3. This book in general has a very good choice of topics and is a nice reference to have. It is one of our "recommended texts"

The book Algebraic Topology: An Introduction by W.S. Massey is very good and covers a lot of what we cover.

Another "recommended text" is Algebraic Topology by Alan Hatcher. This book is freely available online. Chapter 1 covers the material on the fundamental group and covering spaces. It is also a classic text on homology and cohomology which will be primary topics if you go on to Math 427/527. There is a good chance it will be the primary book for that course. This is more advanced that Munkres.

Syllabus

A copy of the pdf syllabus can be found here.

Assessment

Homework

Homework will assigned every couple weeks and will be due by submission on Canvas every most Tuesdays by 11:59pm, starting on September 18th. Submission in the form of a PDF produced using LaTeX or an equivalent is required. Scans of handwritten work will not be accepted.

Grade

Grades will be composed of 25% homework score, 25% midterm score and 50% final exam score.

Midterm

Midterm will take place in class on November 8th. It will cover all material up to the Van Kampen theorem. It will be closed book and the format will be as follows. (1) A short answer section where you will be asked to state basic definitions or results, (2) an example/counterexample section, (3) short proof section.

Final Exam

The final exam will take place Saturday, Dec 14th 2024 at 3:30 pm. Location TBD.

Homework

Homework 1

Here is Homework 1. It is due on Monday September 16th at 11:59pm. Solutions are available.

Homework 2

Here is Homework 2. It is due on Tuesday Oct 1st at 11:59pm. Solutions are available.

Homework 3

Here is Homework 3. It is due on Sunday, October 27th at 11:59pm. LaTeX file: HW3.tex

Solutions are available.

Homework 4

Here is Homework 4. It is due on December 8th at 11:59 pm. Solutions are available.