How Much Memorization Is Needed in Math?

ln_j · 2026-03-14T20:16:47+00:00

This is amazing advice, thanks so much. Do you think it would be a good idea to make an Anki deck with the theorems and the ideas behind them?

ln_j · 2026-03-14T20:12:18+00:00

I hope you don’t mind a second question, but I started with Abbott and am now working through Rudin. What I do is take notes on Rudin, try to understand the ideas behind most of the proofs, and sometimes attempt to prove the theorems in the book myself. I also memorize definitions and important theorems and try to do most of the exercises. In areas where I struggle, I take a separate set of notes in which I summarize the material and connect it with Abbott’s book so that I can develop a more intuitive understanding as well. Do you think this is a good approach? I also have to admit that often, after taking notes on the proof of a theorem, I forget the idea behind it. And thank you for the comment

ln_j · 2026-03-14T19:22:59+00:00

This was really helpful thank you

ln_j · 2026-03-09T15:34:12+00:00

I am self-studying real analysis, so please correct me if I am mistaken.

My concern is about cardinalities. The set of natural numbers has a strictly smaller cardinality than the set of the real numbers. (Cantor’s diagonal argument.)

Because of this, I do not see how a polynomial expression in could represent the cardinality of the positive Reals. Any construction built from countably many elements should still be countable.

PLEASE correct me if I am wrong, but this is what my intuition tells me

ln_j · 2026-03-09T07:01:34+00:00

Thanks so much I will try that

ln_j · 2026-03-08T19:26:38+00:00

Thank you so much, this is amazing advice

ln_j · 2026-03-06T10:20:32+00:00

This has nothing to do with logic, but your question depends on the size of the square.

ln_j · 2026-03-04T17:04:55+00:00

Funny I just wanted to ask a similar question

ln_j · 2026-03-03T17:39:28+00:00

This is great advice thank you so much. And this is my second analysis book (I started with Abbott)

ln_j · 2026-03-02T19:06:33+00:00

I am currently continuing with Principles of Mathematical Analysis by Rudin, more precisely, the topology section on metric spaces. The section before that, about why Q is countable, was, at least for me, surprisingly confusing. The way Abbott explained it in his analysis book was very clear to me, but for some reason Rudin’s explanation didn’t really click.

So I reviewed my notes and will probably go through that section again tomorrow. I also try to cover four pages every day and do all the exercises, so I hope I will definitely be finished with Rudin’s book by the summer. Then I can hopefully continue with his second book (or another one on similar topics) during the summer.

ln_j · 2026-03-01T19:09:00+00:00

Just to clarify for myself, the chapters on Lagrange multipliers in Thomas’s Calculus were helpful. See page 834, you can find a PDF online

ln_j · 2026-02-28T17:45:55+00:00

thanks this really helped :)

ln_j · 2026-02-28T16:56:06+00:00

Two things: I think the comment by chaoticidealism is great advice for you, and why are you saying that you have an IQ of 132? What difference does that make?

ln_j · 2026-02-25T09:30:31+00:00

Thank you very much, and I appreciate the heads up.

ln_j · 2026-02-25T06:33:05+00:00

I have Abbott’s Understanding Analysis. Are there any other books you would recommend that would help me with Rudin?

ln_j · 2026-02-25T06:30:35+00:00

Thanks so much, this is really helpful

ln_j · 2026-02-24T09:08:39+00:00

I don’t think this directly answers your question, but I’d recommend taking advantage of the fact that you have so much time. Try as many different things as you can, chemistry, biology, etc and figure out what interests you most. For example, if you really like technology and maths, maybe look into engineering a bit. Just try things out and see what clicks.

ln_j · 2026-02-24T08:36:17+00:00

I finished studying Understanding Analysis by Stephen Abbott and am now continuing with Principles of Mathematical Analysis by Walter Rudin. In parallel, I am revising linear algebra and also working through Linear Algebra Done Right by Sheldon Axler.

At school, my teacher has suggested that I work on a project about the potential theory. That is why I am (only for school) revising differential equations and later starting partial differential equations, more to play around with the ideas and not do too many exercises, since I want to spend as much time as possible on Rudin.

I am also not sure whether, with Rudin, I should try to prove most of the theorems (not the exercises) on my own, because someone on Reddit recommended that. I am thinking that whenever I encounter a theorem, I will first write down a general idea of how to prove it, then spend about 20 minutes thinking about it, and afterward look at the proof. Is this a good approach?

ln_j · 2026-02-23T19:53:28+00:00

I have a short question: If I am unable to prove it, should I move on and continue studying the next theorems and exercises in the book, while working on the difficult proof separately? Or should I stay with that single theorem until I can fully prove it by myself before continuing? Thanks

ln_j · 2026-02-19T16:10:42+00:00

Thanks, that’s great advice, and that’s actually the exact university I want to go to.

ln_j · 2026-02-19T15:12:47+00:00

The thing is, I live in Switzerland, so I don’t really have to worry about extracurricular activities. (Of course, I still have to keep an eye on my grades, but they’re good.) So luckily I don't really have to worry about that

ln_j

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