We will cover a traditional first semester course in Algebraic Topology. That is, the fundamental group, homology, cohomology, and homotopy.
- no lectures added
One semester of each algebra and topology will do. I will cover the more advanced topics as we go along. As far as algebra goes, there isn't much that you need to know in depth beyond some group theory. Nothing beyond the level of M. Artin's Algebra, or Dummit and Foote's Abstract Algebra.
As far as topology goes, we will once again cover anything super complicated. You should be familiar with homeomorphisms, quotient topology, etc. We'll go over the wedge sum and smash product in the first lecture.
I will be posting YouTube videos and placing links on the course subreddit every week on Thursday. This will begin with an introductory video on July 26. The course should run 13 weeks, at which point we will decide if/how to continue.
The course will follow Allen Hatcher's book Algebraic Topology pretty closely. This is available as a .pdf freely on his website, http://www.math.cornell.edu/~hatcher/AT/ATpage.html.
There will also be a problem set every week. Although you can probably find all of the solutions to to the problems in the book on the internet, I am a strong believer in not providing solutions to math problems. You can discuss solutions on the subreddit, and collaboration is strongly encouraged.
On lecture notes: Students are encouraged to volunteer one week to typeset a summary of the lecture and/or the textbook section.