I’ve started to notate my graduate textbooks this year. I’ve found it helps immensely in understanding the material and it lets me give details to some of things the texts gloss over. I tend to go pretty in-depth with this by including explicit details for everything so that the text should be readable on its own without any other references to mathstack, other texts, online articles, etc. I’ve decided to update and post these notes online (see the link below), and plan to continue this through my undergraduate and graduate career.
The current texts I have up are for Bott & Tu’s Differential Forms and Algebraic Topology (chapter 1 sections 1-6) and Neukirch’s Algebraic Number Theory (Chapter 1 sections 1-8). Rosen’s Number Theory in Functions Fields is next (chapters 1-5). As I comb through the texts, the notes will be updated as well.
I’m posting for two reasons. The hope is that this will serve as a useful guide to people who are reading through these texts and may be confused at places. God knows I’ve been suck on things way too much and I hope others won’t have this issue. The second is that if anyone has notes of their own for these texts or other texts they would like to see posted online I would most likely be happy to do it. All in all, I want to get this out into the general public and see if it has any use.
If you like or dislike these please let me know, I’m always trying to improve. I’m planning to add examples to the notes in the near future as well.