Where to go after calculus? Ok this is a bit of an unanswerable question, but hopefully someone will answer. As I have been going through college & high school there has been a kind of "path" through which you learn math. For example I went through basic math, prealgebra, algebra, precalc, calculus 1-3. My question is where to go after calculus three?(which is where I am at now btw). It looks to me like math really starts branching after calculus. I worried that I'll end up in classes that I can't fully understand because I didn't have the prerequisite knowledge. Do I go to linear algebra, real analysis, number theory, another branch ...? 
I'm working towards a degree in mathematics and would like to get the most out of every class, So if anybody would tell me what worked/didn't work for them I would be grateful.

I would strongly recommend you to read the book, "Differential Calculus For Normed Linear Banach Spaces" by Kalyan Mukherjee. Its published by the Hindustan Book Agency. I think it is one of those rare wonderful books which bridges the gap between calculus and manifold theory. It has beautiful sections on differentiating and Taylor expanding and integrating functions between arbitrary finite dimensional euclidean planes. He masterfully uses all this to motivate Lie Groups and calculates tangents to curves in Lie Groups. He further explains subtle things like differentiating matrix multiplication and determinant maps. 
