If you’ve saved some of your favorite links, please share!
I like CheCheDaWaff’s comments on r/Anki; see here for a decent place to start. In particular, for proofs, I’ve shifted toward adding “prove this theorem” cards rather than trying to break the proof into many small pieces. (The latter adheres more to the spaced repetition philosophy, but I found it just doesn’t really work.)
Richard Reitz has a Google doc with a bunch of stuff.
I like this forum comment (as a data point, and as motivation to try to avoid similar failures).
One thing I should mention is that a lot of the above links aren’t written well. See this Quora answer for a view I basically agree with.
I couldn’t stop thinking about it
I agree that thinking about this is pretty addicting. :) I think this kind of motivation helps me to find and read a bunch online and to make occasional comments (such as the grandparent) and brain dumps, but I find it’s not quite enough to get me to invest the time to write a comprehensive post about everything I’ve learned.
So… I just re-read your brain dump post and realized that you described an issue that I not only encountered but the exact example for which it happened!
so i might remember the intuition behind newton’s approximation, but i won’t know how to apply it or won’t remember that it’s useful in proving the chain rule.
I indeed have a card for Newton’s approximation but didn’t remember this fact! That said, I don’t know whether I would have noticed the connection had I tried to re-prove the chain rule, but I suspect not. The one other caveat is that I created cards very sparsely when I reviewed calculus so I’d like to think I might have avoided this with a bit more card-making.
I want to highlight a potential ambiguity, which is that “Newton’s approximation” is sometimes used to mean Newton’s method for finding roots, but the “Newton’s approximation” I had in mind is the one given in Tao’s Analysis I, Proposition 10.1.7, which is a way of restating the definition of the derivative. (Here is the statement in Tao’s notes in case you don’t have access to the book.)
I like CheCheDaWaff’s comments on r/Anki; see here for a decent place to start. In particular, for proofs, I’ve shifted toward adding “prove this theorem” cards rather than trying to break the proof into many small pieces. (The latter adheres more to the spaced repetition philosophy, but I found it just doesn’t really work.)
Richard Reitz has a Google doc with a bunch of stuff.
I like this forum comment (as a data point, and as motivation to try to avoid similar failures).
I like https://eshapard.github.io
Master How To Learn also has some insights but most posts are low-quality.
One thing I should mention is that a lot of the above links aren’t written well. See this Quora answer for a view I basically agree with.
I agree that thinking about this is pretty addicting. :) I think this kind of motivation helps me to find and read a bunch online and to make occasional comments (such as the grandparent) and brain dumps, but I find it’s not quite enough to get me to invest the time to write a comprehensive post about everything I’ve learned.
So… I just re-read your brain dump post and realized that you described an issue that I not only encountered but the exact example for which it happened!
I indeed have a card for Newton’s approximation but didn’t remember this fact! That said, I don’t know whether I would have noticed the connection had I tried to re-prove the chain rule, but I suspect not. The one other caveat is that I created cards very sparsely when I reviewed calculus so I’d like to think I might have avoided this with a bit more card-making.
I want to highlight a potential ambiguity, which is that “Newton’s approximation” is sometimes used to mean Newton’s method for finding roots, but the “Newton’s approximation” I had in mind is the one given in Tao’s Analysis I, Proposition 10.1.7, which is a way of restating the definition of the derivative. (Here is the statement in Tao’s notes in case you don’t have access to the book.)
Ah that makes sense, thanks. I was in fact thinking of Newton’s method (which is why I didn’t see the connection).