Ratio of time reading and solving I am learning a lot of material on my own and I enjoying it but I have a constant problem: I really don't know how much time to spend actually reading theorems, corollaries and stuff and how much time to spend solving the exercises. I like both but at times I feel I spend too much time reading and postponing solving exercises on the excuse that "I must first build foundation". A friend of mine who is working on similar topics only reads definitions and theorems once and jumps into exercises and at times I feel he understands the stuff better than me. Help!
 A: What I usually do is this: I read theorems and proofs but with a pen and some paper. It is extremely hard to follow a proof (unless it is elementary) without writing something down. I usually try to simplify proofs, definitions, etc. as much as possible because I am dyslexic but apparently it is a good strategy for everyone. Try to focus on the key works. Richard Feynman used almost the same method. This is why almost every professor of physics in the world has a copy of Feynman lectures. I also use a lot of symbols when convenient e.g. $\exists$, $\forall$, $\Rightarrow$, $\Leftarrow$, $\Leftrightarrow$, etc. But doing a few exercises also helps because you understand the concepts better. For example, when you first see the definition of the floor of $x$ i.e. $\left\lfloor x \right\rfloor$, you might think it is obvious but you still need try a few values of $x$ to convince yourself. This way you will actually remember. Your friend will most definitely forget everything by the end of the semester, and you do not need to understand the proof of a theorem to do an exercise that uses that theorem.
