MAT327 • TOPOLOGY

WELCOME

This is a "genericized" version of the course website for my course MAT327 - Introduction to Topology. I made this page so I can easily share my notes and list of problems with anyone who may be interested. All of the course notes were written by myself, because I was unsatisfied with any existing textbook for this subject. I also compiled the Big List of Problems, and wrote many of them myself.

This website is statically generated from Markdown files by a simple Python script I wrote.

MAT327 is a course at the University of Toronto aimed at third year undergraduates who are specialising in mathematics or very strong mathematics majors. The course usually aims to cover the basics of point-set topology, and the beginnings of algebraic topology. It is usually taught from James Munkres' Topology.

When I run the course, I do not use this textbook, and I cover a different set of content.

  • I try to focus on the craft of point-set topology, and of mathematics in general. Point-set topology can be taught in a "memorize this list of definitions" sort of way. However, I try to focus on...
    • Why these things are defined the way they are.
    • Why you should believe the definitions are right.
    • How we come up with the theorems we prove.
  • This subject also lends itself to discussing some mathematical concepts that are a big deal. For example:
    • Countability and uncountability.
    • Partial orders and linear orders.
    • The Axiom of Choice (and Zorn's Lemma, and Well-Ordering).
    • Ultrafilters.
  • I do not cover any algebraic topology.
    • I don't think there is time for it to be done well.
    • I can't assume students know anything about groups when they start the course.
    • I think the value added by focusing more on other things outweighs the value lost by not covering it.

It is also notable that I do not assign graded homework. Read my syllabus for some elaboration on this.

I ranthis course for four consecutive summer terms at the University of Toronto, St. George campus (2016 through 2019). Reviews were very positive.

If you find any typos or mathematical errors in my notes, or if you just want to discuss some aspect of my notes or this course, feel free to send me an email. Contact information is available on the Course Information tab.

- Ivan

COURSE INFO

This information is contained in the syllabus.

  • Ivan Khatchatourian is the course coordinator.

    • ivan [at] math [dot] toronto [dot] edu

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