[digital_ghoul]

I took my first real analysis course last semester, and I made flashcards with pen and paper for every single non trivial definition, theorem, lemma, and corollary that we covered in lecture.

Analysis definitions and theorems get really complicated with intricate and difficult to follow logical chains, and there are a lot to remember.

These definitions and results don’t mean much on their own without exploring their neighbourhoods by proving relevant things, and I could have learned these definitions and results by just doing proofs. But being absolutely sure I could recite every theorem and definition definitely helped me on the final exam.

I think if you’re learning algorithms (like find the area under a curve) in a calculus course for example, flashcards might have more limited value, as in that case problems are relatively short and you’re better off just running through your set of algorithms a ton of times by doing problems.

I also took a group theory course last semester and I memorized every definition and result from lecture via flashcard, but didn’t practice using them enough by writing proofs. I ended up with like 2 or 3 out of 10 complete proofs and the rest half finished on the final exam because I had the right starting points, but not enough practice using what I knew in unexpected ways. Still passed somehow.

[jvvw]

I am a fan of Anki for lots of things but it always puzzled me people trying to learn analysis and group theory by memorising lots and lots of parts of their lecture notes.

I would test myself on the main steps of some of the proofs before exams but that was the nearest I got to memorisation. It felt like if you needed to memorise definitions then you hadn't used them enough. Even 30 years later, not having done maths for most of that time, I could still tell you the most of the definitions and could still do an epsilon-delta proof - they feel like conceptual things rather than memory things.

Perhaps I was in a way doing spaced repetition just by trying to solve lots of problems and looking things up if I didn't know them but it didn't feel like a memorisation process, more a process of trying to really really understand the mathematics.

[PandaRider]

> I ended up with like 2 or 3 out of 10 complete proofs and the rest half finished on the final exam because I had the right starting points, but not enough practice using what I knew in unexpected ways.

I feel ya. I memorised definitions for my algorithms course as well and also experienced diminishing rewards of using SRS flashcards (especially when the conceptual questions get more novel).

Like what you say, we have to practice using the factual knowledge enough by writing proofs.

The next generation of flashcards would probably use AI to generate concise questions on writing proofs.

[1] A Little Randomness May Not Be Enough - https://www.scotthyoung.com/blog/2014/11/07/srs-for-concepts...

Thank you for sharing your experiences!

[BeetleB]

> I took my first real analysis course last semester,

> These definitions and results don’t mean much on their own without exploring their neighbourhoods

Were these epsilon-neighborhoods?

[digital_ghoul]

I couldn’t resist :)