Deep-Dive is just a poetic name to a compilation of notes that I'm writing while studying mathematics and related fields. They currently encompass the following topics:
- Category Theory
- Linear Algebra
- Group Theory
- Ring Theory
- Module Theory
- Classical Topology
- Algebraic Topology
- Abstract Homotopy Theory
- Graph Theory
- Manifold Theory
- Real Analysis
- Statistics, Probability and Machine Learning
I'm a category theory junky so expect a lot of abstraction and commutative diagrams. If you are into that, I think you may find these notes at the very least interesting for your taste.
If you want to have a peek at the actual document, you can find a certainly out-of-date compiled version in my website. If you want to hear more about the story behind these notes, you may take a look at this blog post.
None of these subjects are completed and will never be (for trivial reasons), however the notes already have about 700 pages.
If you happen to compile them and find them helpful or stupid in some way (and if you're willing to help), reach me out and I'll be quite happy to have some feedback.
I won't accept any pull-requests. Mind you, these are my personal notes for my own learning process.
- A LaTeX distribution (I've tested with TeXLive and MiKTeX already and both work).
- Make if you're on Linux.
- LaTeXMk for building.
- latexindent.pl for formatting.
git clone https://github.com/luizmugnaini/deep-dive
cd deep-dive
make build # single build
make watch # continuous build as files are changed
make format # format the tex files with latexindent.pl- Did you get some strange "font not loadable" or something along those lines?
You are probably lacking Japanese support in your latex installation (used
for the Yoneda functor symbol) you may give a try installing
ckj-fonts.