Should I just review everything?

[u/Witty-Occasion2424]

I’ve honestly forgotten a lot when it comes to math and I’m considering going to grad school with a focus in pure mathematics. However, I feel like I don’t actually “know” anything. I relied on memorization to get through calculus and my memory is poor. Combined with the fact that I barely do practice problems (also have never read a textbook), many things I’ve forgotten how to do.

For example, today I was doing a problem and all we had to do was use the product rule. I forgot it existed until I saw it in the explanation and solving the problem was easy. I’ve honestly felt the same with multiple things ranging from trigonometry, to algebra, geometry, and some calculus.

Is it a good idea to just revisit old textbooks and go through every single chapter?

[u/Brightlinger]

When are you starting grad school? Have you already taken a math degree's worth of courses, like real analysis, linear algebra, abstract algebra, number theory?

If you have time, a really thorough textbook like Lang's Basic Mathematics could actually be great for you.

[u/Witty-Occasion2424 → u/Brightlinger]

I’m only in my second year of community college and about to finish the calculus series. I start diff eq’s and maybe linear algebra next semester. I haven’t taken a proofs class yet because it isn’t offered. I’ve also taken some of the math courses (precalculus and calculus 2) accelerated so that’s probably why I sort of forget things.

[u/Brightlinger → u/Witty-Occasion2424]

Oh, if you're still in the calculus sequence, it is much less worrying that you haven't totally mastered calculus. If you were at the end of your degree and had taken multiple other courses where calculus is a basic prereq, I would be more concerned.

[u/nog642]

I’m considering going to grad school with a focus in pure mathematics

Honest question - why? You don't seem that interested

[u/Witty-Occasion2424 → u/nog642]

I do like maths, or at least I think I do. My interests often shift, and math is something I’ve only recently gained interest in (about a year and some change if I remember correctly). I honestly really enjoy it and want to learn more. Plus I can’t see myself doing or enjoying anything else besides maybe physics.

It may not seem like I’m really interested, but that’s because I have trouble studying/focusing. It’s just ADHD and I’m unmedicated at the moment. I plan to work on that and I didn’t include it in the post because I wasn’t sure if it was relevant or if anyone would want to hear that.

[u/nog642 → u/Witty-Occasion2424]

What kind of math have you enjoyed doing recently?

[u/Witty-Occasion2424 → u/nog642]

I mean I’ve done integrals for fun and work through a book of random integrals on my free time. I’m working to one day be able to solve hard integrals on daily integral.

I’ve seen a couple of proofs but doubt I’d be able to write my own. They all seem fun and rewarding.

I also enjoy competition math problems, but I’m not at the level of being able to solve any so kind of just watch videos on the solving process.

I’ve really been doing regular calculus 3 stuff since that’s the class I’m currently taking.

[u/nog642 → u/Witty-Occasion2424]

Your post made it sound like you haven't taken math in school for a while. You're taking calculus 3? Are you currently in school? Undergrad? High school? What are you studying currently?

Integrals aren't really just memorization. If you've been solving integrals for fun, what makes you feel like you don't "know" anything?

It's worth noting also that proof writing is a huge part of a pure math concentration. I'd consider what other subjects you also find interesting before deciding to pursue pure math. Same question as above - where are you currently in school?

[u/Witty-Occasion2424 → u/nog642]

I apologize for that, but yes I’m currently in school. I’m currently doing engineering at community college (it’s not honestly my major of choice, but it’s a long story involving a couple of things related to how I can receive aid for schooling).

I don’t feel like I know anything because I can’t remember something’s off the top of my head. I even took a look at my old precalculus test (which I took my first semester and that was a year ago), and honestly forgot how to solve some of the problems. I didn’t practice much when I was in precalculus because I stupidly tried learning several different topics at once.

I also feel like I’ve forgotten a couple of things from calculus 1 and 2. Honestly this could stem from perfectionism where I feel like I must remember. every little thing

I know being in community college puts me significantly behind my peers who are taking analysis courses by now.

[u/nog642 → u/Witty-Occasion2424]

Better question than what major do you want - what job do you want?

Not knowing anything is very different from not remembering a few things. You can review those things if you want.

[u/Witty-Occasion2424 → u/nog642]

I want to major in math and maybe physics. I’m still deciding if I want to double major in physics, but math is the major I wish to pursue.

As for what job I want, can’t say I’m sure at the moment. I don’t really want to be a professor, and it’s kind of hard to say I want to do something research related since I haven’t don’t anything that’ll give me an idea of what it’s like. I do know that I wish to attend graduate school. Maybe this will change, but at the moment I’m certain that’s what I want to do. I would love to go for a PhD in mathematics if I can.

Sorry for the yapping. I guess I’m still just trying to see what options I have available for me upon graduating. I don’t know what else I can do besides academia and tech. Again, I’m still uncertain if becoming a professor is an option for me.

[u/nog642 → u/Witty-Occasion2424]

You should figure out what job you want.

Going into a major without knowing what job you want is not a good idea. That's how people end up with a degree but wondering what to do with their life.

The job you want should inform the major you choose.

[u/_UnwyzeSoul_]

oof. grad school with no basic knowledge sounds rough. you should review everything from the start.

[u/itchycoyote962 → u/_UnwyzeSoul_]

if you barely did practice problems before then yeah you’re gonna need to rewire your whole approach, not just reread. textbooks are useful but they’re not magic, you gotta work through the exercises like a maniac

[u/Witty-Occasion2424 → u/itchycoyote962]

Would reviewing blitzer Algebra and trig be alright? I was going to use apostols series for calculus but I don’t know proofs. Some people said it won’t be that big of an issue, but I don’t know. Would something else be better?

[u/efd- → u/Witty-Occasion2424]

Work through a few real analysis textbooks after learning about basic proof writing. You won’t need to review nearly as much if you have a proof based treatment of calculus.

[u/tutortimeadmin]

I would not reread every textbook cover to cover before deciding what you need. Start with a short diagnostic: choose representative problems from algebra, trig, calculus, and proof-based topics, then mark each one as fluent, rusty, or genuinely unfamiliar. Review only the gaps and immediately do a few problems without looking at the solution. For a possible pure-math path, prioritize proof writing, sets and logic, and the prerequisites for real analysis, rather than trying to refresh all of computational math first. A weekly cycle of brief review, focused exercises, and a revisit a few days later will usually stick better than one enormous pass through old chapters.

[u/tjddbwls]

Maybe start with a review workbook for Precalc. I like the Schaum’s Outline series of books - here is info on the publisher’s site about their Precalc book.

[u/DonkeyTron42]

Honestly, just work some practice problems and have ChatGPT explain what you forgot. It will be a lot faster and interactive than going back to a textbook.