I'm an undergrad at a top US university and I'm currently taking an Introduction to Analysis class. I really really enjoy this class and it's actually getting me more interested in math in general. I feel like I'm able to understand the material really well, and often notice that I understand some of the nuances better than my classmates (let me also add that I'm not saying this to be arrogant, but simply to say that I think I'm doing pretty well conceptually). Yet, I find that I'm not able to do too well on exams and tests. It's not that I don't know the problems or don't know what to do in them, I'm just not able to produce my best work on test day.
Again, I want to add that I am actually putting time and work into this class and feel like I'm understanding the material, I just think I'm not approaching the tests correctly (in terms of preparation and how I actually do them). This is a general question, but has anybody else faced something similar? What would you recommend I do? Any other general pieces of advice on how to approach a rigorous math course?
For many such math courses, it is important to distinguish understanding and identification. Just because you know all of the material doesn't mean you can spot it in an obscure problem, and exams are often intentionally obscure in this way. Often, the tricks are similar based on the type of problem. For example, if a problem involves Concept X, then usually Theorems A, B, C are the most useful for that type of problem. Trying to apply these first will save you a lot of time on exams, since unlike homework it is important how quickly you find the right order in which to do things. Often, these are just the theorems used to solve similar problems in the homework.
Hopefully this helps!