- When I took my Discrete Mathematics course, I began to keep a separate notebook to compile proofs that I found to be particularly clever or, I thought, illustrated a particular concept/approach clearly. It was partially inspired by Erdős' concept of The Book.
- I did something similar for "Leetcode" problems but in this notebook I would only document solutions I personally came up with for when I feel like having solved the problem gave me considerable "XP" if not outright leveling me up. They ended up mostly dynamic programming problems and clever applications of number theory---I never really felt like I grokked these topics even now so it was useful when I detected similarities to past problems.
- Lately I've decided to give signal processing a deeper shot and a grid notebook has been my invaluable companion for the task. The last two notebooks were very neatly organized but this one is more like lab/field notes but for mathematics. It's gritty and dirty in there. There isn't really much point learning signal processing only from books so I'm always in front of my computer (with a lecture video or an interactive Python script) when I'm working on this notebook. Being able to formulate hypotheses/intuition, writing down thoughts to be considered later, annotating graphs/proofs where things don't make sense to me yet---it has been an extremely liberating learning experience. I've only been on this endeavor for a few weeks but I can definitely say it has allowed me to interact with the material at a deeper level.
The only way my signal processing effort could be better was if I had a teacher whom I can ask my noted-down questions to. I know the suggestion is gonna come up and I'll be lying if I say it hasn't crossed my mind so I'm just gonna address it unprompted (pun intended): I don't bring my questions to a LLM because I'm not yet smart enough to detect bullshit in this field of study. I don't think setting-up my own agent to ingest my notes would make any sense because then I would have to structure my notes and the core reason why it's been so liberating/has enabled me to interact deeper with the material is because I gave myself the freedom to be unstructured.