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## Notes

I’ve uploaded current notes for the classes I’m taking. I make no claim that these notes are complete or correct, but they may be useful to somebody. The notes for Dylan Thurston’s class are particularly fun to take; I’ve been drawing the pictures in Paper and I’m generally very happy with the way they’re turning out.

Edit: It would probably be a good idea for me to briefly describe these classes.

• Homological Algebra (Wodzicki): An introduction to homological algebra aimed towards triangulated categories. Taking these notes is a good exercise in live-TeXing commutative diagrams.
• Curves on Surfaces (Thurston): An introduction to various interesting structures related to curves on surfaces. There are cluster algebra structures involved related to Teichmüller space, the Jones polynomial, and 3- and 4-manifold invariants, but the actual curves on the actual surfaces remain very visualizable. Taking these notes is a good exercise in drawing pictures like this (a curve on a thrice-punctured disc being acted on by an element of the mapping class group, which in this case is the braid group $B_3$):

• Quantum Field Theory (Reshetikhin): An introduction to the mathematics of quantum field theory. The course website has more details. Taking this class is a strong incentive for me to learn differential, Riemannian, and symplectic geometry.

### 11 Responses

1. the pictures in the curves on surfaces notes are very nice, thank you

2. Those look great! I’m taking 253 as well and have also been TeX-ing notes for the course. It’s definitely nice to see another person’s TeX’d notes on the same subject material. Some of Wodzicki’s more elaborate commutative diagrams are too difficult for me to quickly conjure up on the spot (e.g. a symbol-only definition of monomorphism using a commutative diagram with equality of arrows). For now, I’ve just been taking notes on paper and TeX-ing them up afterwards.

I’m also quite fond of your setup for Dylan Thurston’s 274. Your drawings in Paper look amazing.

• Thanks! Paper’s doing most of the work; there’s some voodoo going on involving smoothing out whatever I draw if I draw it fast enough that’s working in my favor.

3. Thank you for taking notes! I hope to start attending Kolya’s and Dylan’s classes once I get back to Berkeley in two weeks — now I will know what I’ve missed. In the past I have live-TeXed many classes, and if I were in town I would probably be TeXing Kolya’s class. But perhaps I will feel OK not doing so this semester, if you continue.

• Only if you promise to explain what’s in these notes to me at some point!

4. Thank you for sharing the notes! I’ve read Reshetikhin’s notes on TQFT to some extent, and quite liked them, so it’s nice to know someone is writing up his QFT lectures :-)

5. hey t0rajir0u! Just noticed you’re at Berkeley now, that’s pretty cool. (the annoying and stupid user named serialk11r on AoPS if you can still remember) Wish I could take 253 with Wodzicki, but I’m overloaded. Maybe I’ll bump into you someday around here.

6. Hey Qiaochu!

I have been writing up notes for my courses at UChicago, and I figured I would put them under a Creative Commons license, but after Googling I found that the owner of the copyright for course notes is a somewhat murky issue, and in particular, I found that Berkeley apparently has a policy (http://campuspol.chance.berkeley.edu/policies/coursenotes.pdf) against the sharing of course notes with students not currently enrolled in the course with you. I’m certainly not encouraging you to take down your notes, both because I find them interesting and also because I disagree with such a policy, but just thought I’d mention it.

Hope everything’s going well.

Zev

• Thanks for the heads-up! I’ll look into this.

• Dear Qiaochu,

Your course notes have disappeared. Does that mean that you had to take them down based on some Berkeley policy? That would be unfortunate.

• It appears to mean that there’s something wrong with the math servers; everyone else’s websites have also disappeared.