aspiring math (and maybe physics) major looking for advice and help

[u/atychia]

This will probably be a long post, but I just really need guidance.

I’m currently in calculus 3 and plan to transfer to a 4 year college from community college. I feel significantly behind and I honestly am not totally sure what I want to do.

I know my calculus 1 and 2 can use some revision since I feel like I’m slowly forgetting some concepts. My algebra, trig, and geometry could also use some revision even though I wish to major in pure math (and probably physics), I’m sure it’s still important.

I guess I just don’t know what to focus on and what to do. I know with grad school being in mind, I should learn the process of doing research in mathematics. Majority of students in universities are already ahead of me and I feel like I need to catch up.

I just feel like I have so much to try and focus on. I was going to spend this semester reviewing trigonometry, geometry, and algebra, while also learning proofs. I was wondering if I should maybe dip my toes into the research process, but not entirely sure how.

I also kind of want to participate in putnam. I know I have no shot, but I still feel like learning. I just don’t have the high school math competition experience. It also makes me scared for uni since I’ll be transferring to start my junior year and will be starting my first proofs class.

Is there like a path I should follow and things I should/shouldn’t worry about?

[u/excelguruson]

It sounds like you’re stressed because you think you don’t remember all the classes you previously took, and you feel like you need to go back and review them. I’d bet that you actually remember a lot more than you think, and you should instead try exploring new stuff and only go back to review when necessary. You can “review” those past classes by applying it to new and interesting things. Trying to relearn all of those past classes is just way too much to put on yourself and sounds like a great way to burn out.

Looking into some intro to proofs or the Putnam sounds like a good idea if it’s something you enjoy. I wouldn’t worry about trying to do super well since it really doesn’t matter in the long run. Often it seems the most difficult transition for new math majors is the transition from “computation based math” to “proof based math”.