I just recently decided to go back to school. I had previously majored in piano performance and dropped out to work as a software engineer.
In high school, I did pretty well at math, I got a 5 on the Calc BC exam my sophomore year. I was also pretty young at the time. I've always been "good" at math.
Coming back to university, I've decided to major in math, as some of the software work I'd like to do requires mathematical chops that I don't currently have. Calc BC was the last calculus course I took, so now I'm in multi-variable, which is a cake-walk. On the other hand, I'm taking an upper-division number theory class which is seriously kicking my butt. Over the winter break (I didn't attend fall semester) I worked through about half of Velleman's how to prove it, to help prepare myself for "real" math classes. It feels totally insufficient. I wonder if I'm cut out for mathematical work. I can manage the "technical" aspect of doing math fairly well, but I can't help feel that I do a lot of bumbling where "real" math is involved.
I also feel like I have some mathematical gaps. While I've always been "good" at math, I think that my mathematical education has some definite holes in it.
So, I'm trying to plug my mathematical holes, but I'm spending 3 or 4 hours a day easily studying for number theory alone. It's getting to be a little bit ridiculous.
Does anyone have any advice? I wish there was a "SICP-like" book for Mathematics.