>Now, some xx years later, I'm resuming the study of math. What I do >now is read half a page, or maybe a page. Then, I stop, go back, and >challenge every line that I've read.
I think I try to read all my textbooks, not just the math ones, like that too. It's really the only way that anything in math can be understood. Even still, though, I feel that some things are not understandable no matter how slowly or how many times you read them.
It's so time-consuming. And since I'm a last-minute kind of guy, I'm not able to do it as often as I probably should.
>Then, for each step of the proof, I force myself >to actually state how and why it follows from the previous step. This >sometimes means that I need to look at the justification given in my >book, and say "but why is *that* true?" This leads to going back and >reviewing a previous result.
Right. I like to do all that myself too. But, it's just that much more frustrating when you do this and something *still* just doesn't click. I generally don't have problems following the steps of proofs that are already written out for me; but, when I sit down to solve them myself, it doesn't really work. Would anyone recommend just memorizing the entire proof? Like--write it over and over and over until it's stuck in your head? In the long run, could this help a person to finally grasp the proof completely (including the precise wording)? I *think* it might have helped me before, but only with proofs that I've seen in more than one course. The linear algebra proofs are all new to me this semester, so I'm not sure writing them out will help solve anything....