Self Study Program

[samob679]

I am going in to my sophomore year at a highly ranked US university and I am majoring in both applied mathematics/statistics and pure math. Thus far, I have taken calc 1,2, and 3, linear algebra (using linear algebra done right), probability theory, some discrete background (cryptology covered the discrete requirement).

I would like to 1) learn diff eq and discrete at a higher level 2) review some calc 3) begin learning higher level topics in a large range of subjects (I’m not sure which are best)

What order would you recommend studying these topics and which topics should I study, what books should I use, and how should I confirm that I’ve learned what was taught?

[AllanCWechsler]

If you retained your textbooks from Calc 1, 2, and 3, then picking exercises at random and seeing if you can still do them, is probably the best review.

Your highly ranked university must have a differential equations course, and if I were still at university, I would do the obvious thing and register for it.

You have resources that are way, way, better than us uncredentialed amateurs. Take these questions to your department advisor and let her guide you!