Here are some of the course notes I've taken over the years. But first, a few remarks:
- Some rows can be expanded to see other relevant documents (syllabi, problem sets, etc.)
- If the updated date is green, I am currently working on updating those notes.
- Notes from before the summer of 2012 are scanned, so they'll take a bit longer to download.
Stuff from PROMYS:
- Playing fast and loose with geometric series
- Counting colorings cleverly
- Category theory
- An introduction to differential topology
- Vector bundles
There is an error about parallelizable manifolds on page 5 of these notes; see this math.SE thread. This originates from an error on page 115 in the 1st edition of Lee's Smooth Manifolds; see the errata for the book.
- Point-set topology
- My final project for complex analysis. I was kind of rushed towards the end, there's a lot that I'd like to add sometime.
- A proof that sheaves can be glued (Hartshorne, Exercise 2.1.22). I wanted to get every last detail…
- I wrote up a brief introduction to higher ramification groups as my final project in one of my graduate number theory courses at Brown.
- For the final exam in one of my undergraduate real analysis courses, we were allowed to take exactly one sheet of notes with us. This is what I brought.
- Here is my write-up for a fun little open-ended project on happy numbers, from my undergraduate number theory course.