So I have a couple of weeks to study what I want before heading back to college. I am debating whether to study multivariable calculus or to study how to write proofs in general.
For context, I have already taken two proof based courses: A bit of real analysis and proof-based linear algebra. I did rather poorly in real analysis, and I attribute this to the fact that I did not have a lot of experience writing analysis proofs beforehand. Even now though I don't feel that I can write great real analysis proofs. In contrast, I did rather well in linear algebra, and felt I understood it decently well with a bit of preparation. However, I found that a non-insignificant number of times during linear algebra I wrote down a proof that I convinced myself was good, and there was some issue that made it a false proof.
I hope it's clear how it can be confusing as to what I should study. It seems that I did well in linear algebra by looking at examples of proofs, but neither before nor after this practice do I feel comfortable with real analysis, and there are also clear weak spots that I have. I'm not sure which way to approach learning proofs.
My own personal question is what is appropriate to study in order to get better at writing proofs, multivariable calculus proofs, real analysis proofs, or reading a book that generally aids with proofs? To make this question more general so that it is appropriate for this medium, I guess I would ask, what is better for learning proofs thoroughly after some exposure - seeing examples of proofs and trying your own, or reading a book for teaching proofs and trying your own? The book I've had in mind while writing this is Bridge to Abstract Mathematics by Morash.
I hope this is appropriate to ask here. I don't know what better place to get this advice from than math.stackexchange.com.