How To Chose Textbooks to Self-study Math
I’ve been self-studying math and computer sciences for a while now, and I get way more suggestions for textbooks and courses than I know what to do with. I usually don’t end up trying them out. This means sometimes I’m missing out on amazing content.
What to do about this? My solution is One Textbook A Day (for one week at a time). First, whenever someone recommends a resource, add it to a list. I’ve personally accumulated quite a long list of math-related content. Lots of textbooks, a few lecture playlists, some fiction books. About 150 in total.
Then, randomly read one of the resources each day. I run a python script that outputs one of the entries. I try it out for ~45 minutes. I’m very focused when reading, and I’m not afraid to go on tangents to search up terms I don’t understand. Every time I learn something new. Most of the material on the list is way beyond my level. However, even when reading something beyond you, you can still learn a lot.
It feels like artificially growing a passion for a topic. Mostly what I read doesn’t fit. But other times I end up enjoying it so much that I add it permanently to my schedule.
Let me give an example. I wanted to teach myself differential geometry. While surfing Reddit I found a recommendation for Frederic Schuller’s lectures on the geometric anatomy of theoretical physics. I wanted to listen to them. But you know… just not right now. And that’s normally where most people would leave it. Slowly forgetting. However because of One Textbook A Day, I ended up listening to his lectures a few weeks later. And it was one of the best and most enjoyable sources I’ve read. I added it to my permanent schedule. And eventually, it became the basis for what is now The Feynman Mafia.
By doing this method I found many resources that I love, some of which you may recognize, and others that you won’t.
- 3blue1brown videos. Amazing on giving intuition for concepts you though we’re complicated
- Frederic Schuller’s lectures on the geometric anatomy of theoretical physics. The entire course is about having a perfectly precise understanding of spacetime.
- Physics, Topology, Logic and Computation: A Rosetta Stone. A nice resource that translates concepts from Category Theory to physics, topology, logic and computation.
- The Man Who Loved Only Numbers. A biography of Paul Erdos, one of the most interesting mathematicians.
- Learn you a Haskell for the great good! Introduction to Haskell, functional programming, and category theory. A very enjoyable book to go through.
- Arrows, Structures and Functors: The Categorical Imperative. Introduction to category theory introduces a whole new way of thinking about math. Makes you think a ton about simple things.
Also Do This to Massively Help The Process of Self-Learning
If you’re self-studying a topic, it’s an extremely good idea to find an advisor or mentor to whom you can discuss weekly progress and who can point you in the right direction. Finding somebody can feel impossible. The most important thing is showing people that you really care about the topic.
For example, most graduate students, Ph.D. students, postdocs, and professors are glad to provide guidance on what to read and will point out references. If you’ve worked your way through something that somebody recommends, then they’re much more likely to be willing to meet.
If you want more on my own story in finding friends to help me self-learn math, feel free to email me directly. This is probably one of the most important things to learn if you want to self-study a topic seriously.