A more intense, advanced approach to learning math (and physics) written out in a blog post.
From the introduction:
“‘How to learn math and physics’ — the title is deliberately provocative. Everyone has to learn their own way. I don’t know how you should learn math and physics. But presumably you came here looking for advice, so I’ll give you some…
Learning math and physics takes a whole lifetime. Luckily, it’s a lot of fun… if you have a reasonably patient attitude. A lot of people read pop books about quantum mechanics, black holes, or Gödel’s theorem, and immediately want to study those subjects. Without the necessary background, they soon become frustrated — or worse, flaky…
This webpage doesn’t have lots of links to websites. Websites just don’t have the sort of in-depth material you need to learn technical subjects like advanced math and physics — at least, not yet. To learn this stuff, you need to read lots of books. I will list some of my favorites below, and also some you can get free online.
But, you can’t learn math and physics just by reading books! You have to do lots of calculations yourself — or experiments, if you want to do experimental physics. Textbooks are full of homework problems, and it’s good to do these. It’s also important to make up your own research topics and work on those…
It’s also crucial to ask people questions and explain things to people — both of these are great ways to learn stuff. Nothing beats sitting in a cafe with a friend, notebooks open, and working together on a regular basis. Two minds are more than twice as good as one!”