How do I get good at math?
I'm a freshman in college, and I've always done OK in math. I never had any good teachers in High school, and I always have done the bare minimum. Over the course of this year, I really came to understand how important math is and how much potential I have to enjoy it. I'm taking a discrete 2 course and I love it. (I'm a Computer Science major)
Even though I passed Calculus 3, I don't feel I understand Calculus. I have an excellent memory and was able to memorize formulas and apply them when I was supposed to. I don't understand anything though.
I came to the realization that I should put some effort into getting better at math. Over spring break, I went through almost all of Khan Academy's exercises just to make sure that I have a good grasp on the very basics. I'm going to finish them up in a couple of days.
what should I do next?
My plans are to start at the beginning of my Calculus book (Thomson's Early Transcendental) and work my way through the book (one part a day), reading everything and doing every problem. I don't know how good of a book this is though. I've done some googling and a lot of people recommend Spivak's and Apostle's Calculus books. Is it worth purchasing one of these (or something else) if I really want to comprehend the material? Are they good for self-teaching?
I usually have some sort of project like this going on (except never math based), and I'm completely willing to put time into this goal. Some direction would be nice though.