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!