Harvard's math curriculum, for freshmen, is divided into 4 classes beyond the BC Calculus level, Math 21, 23, 25 and 55. Math 21 is your classic plug-and-chug multivariable calculus and linear algebra course. The rest of the courses teach multivariable calculus and linear algebra in the context of proofs, along with some real analysis. I decided to take Math 21 this semester (don't ask me why, it was a horrible decision and it is why I am writing this post).
Anyways, I now realize that I need to learn proofs in order to use them in higher-level computer science classes. Plus, I might have an interest in higher mathematics in concepts such as real analysis, probability theory, optimization, etc. How should I go about learning proofs, specifically in the context of discrete math, linear algebra, and real analysis, so that I can apply my knowledge to computer science and the higher-level math in which I might be interested?
Thanks for your advice in advance. This is my first question on Math Stack Exchange, and I'm curious to see what the community is like!
Best Answer
Your question really resonated with me. I wish I could beam back in a time machine to give myself the following advice. Since I can't, I'll pass it along to you.
Finally, I want to echo Peter Smith's advice to study as many textbooks as you need to in order to get a clear explanation of the concept you want. I remember trying to understand a concept and getting something like 6 books from the library once, and only one of them did a decent job of explaining the concept. So lots of books is a good thing, not a bad thing.