I recently finished catching myself up on my basic differential and integral calculus. I actually think I understand it better now than I did when I took calculus in high school and in university. I may be fooling myself 🙂 I finished reading and doing many exercises in Quick Calculus 2nd Ed. and I can highly recommend it for anyone who wants to brush up on their calculus. It’s fast-paced, focuses on core concepts and techniques, covers both theory and application, and does it all in a slim easy-to-consume volume. Of course, it doesn’t have the depth of something like Stewart’s Calculus which is a common textbook, and I’m peeking into that too, but it satisfies the requirements of getting back up to speed after a time away. I’m also continuing to use Khan Academy for further practice and depth, and will continue to do so probably throughout at least my first term back in school.
I’m also just at the start of brushing up on linear algebra, which I have very little interest in. I kinda have to force myself. I’ve got an old textbook called Linear Algebra with Applications. I also downloaded two linear algebra texts onto my iPhone, and I’ve still got a bunch of Khan Academy units to do… but I have to push myself harder because of my lack of interest. It’s not that I don’t see the applications… I do… it’s just that linear algebra has so many numbers!!!
That’s not a contradiction: I love mathematics, but I’m not a big fan of numerical manipulation (calculation). The difference is that mathematics is about seeing relationships, structures and concepts whereas calculation is simply about getting formulaic answers from numerical data. Calculation is boring to me (usually) because it doesn’t represent an intellectual challenge. As a result, I hate doing bookkeeping. On the other hand, I love designing complicated spreadsheets. And, back to mathematics, I like doing proofs and other activities that represent problem-solving and discovery. I love learning about cool relationships between mathematical structures and concepts. And the numbers don’t matter except incidentally.