# Lanrian comments on Lessons I’ve Learned from Self-Teaching

• I’m really surprised at how big your cards are! When I did anki regularly, I remember getting a big ugh-feeling from cards much smaller than yours, just because there were so many things that I had to consciously recapitulate. It was also fairly common that I missed some little detail and had to choose between starting the whole card over from scratch (which is a big time sink since the card takes so much time at every repeat) or accept that I might never remember that detail.

I’m super curious about your experience of e.g. encountering the function question. Do you try to generate both an example and a formalism, or just the formalism? Do you consciously recite a definition in words, or check some feeling of remembering what the definition is, or mumble something in your mind about how a function is a set of ordered pairs? Is the domain/​range-definitions just there as a reminder when you read it, or do you aim to remember them every time? Do you reset or accept if you forget to mention a detail?

• I’m really surprised at how big your cards are! When I did anki regularly, I remember getting a big ugh-feeling from cards much smaller than yours, just because there were so many things that I had to consciously recapitulate. It was also fairly common that I missed some little detail and had to choose between starting the whole card over from scratch (which is a big time sink since the card takes so much time at every repeat) or accept that I might never remember that detail.

First, the Lebesgue integration card is one of my is one of my largest; I selected it to show Isusr how I might handle a non-decomposable question. I recommend that new Anki users be careful not to do this kind of thing: find a way to decompose, whenever possible!

I generally tolerate missing details that I would have worked out were I actually expanding the mental sketch into formal writing; for example, if I make an arithmetical error but perform the correct kinds of calculations, I count that. If I make a sign error that I wouldn’t make if I had been writing it out pencil and paper, I’ll usually count it. If I think momentum is a scalar quantity or something crazy, though, I fail that card.

I want to penalize the kind of error that I’m unlikely to fix with unaided reflection, or instinctive errors (like my gut sense for a concept just being wrong).

I guess I use Anki to recall the “felt sense” of a proof sketch, and I don’t sweat the details. Here’s another long card I have:

Believe it or not, I can decompose this proof into a sequence of ~five “urges”, each of which I can (but generally don’t) unpack into actual math if pressed.

That said, this card was a PITA to learn, even with my level of experience. It took a lot of ’fail’s to get right consistently. Again: if one is thinking about using Anki for the first time, do not do this kind of thing! It’s hard to pull off at first, knowing if your mistake was worth redoing; if you make yourself recite the whole card above, you’ll be reviewing it forever.

I’m super curious about your experience of e.g. encountering the function question. Do you try to generate both an example and a formalism, or just the formalism? Do you consciously recite a definition in words, or check some feeling of remembering what the definition is, or mumble something in your mind about how a function is a set of ordered pairs? Is the domain/​range-definitions just there as a reminder when you read it, or do you aim to remember them every time? Do you reset or accept if you forget to mention a detail?

Imagining that card, I first imagine the motivation before superimposing the formal definition “on top” of it to capture the relevant part of the situation. I remember the phenomenon of apple exchange, and then overlay the function to describe what happens. Then I recite the formal definition.

I don’t make myself remember to label the “domain” or “range”, because that’s not fair game—it wasn’t on the prompt. Those should go on separate cards. (I’d only learn one of those at a time, for similarity reasons)

• Interesting. I have used multiple different approaches with Anki. Last year I had to learn all pre-university math to enter uni, and I decided to use Anki which worked out pretty well. For a lot of the problems it’s about remembering what steps to take in general. So I put in practice problems so I could remember the steps. The numbers don’t matter, they could’ve been anything.

I also tend to put in definitions, rules, theorems, standard and harder derivatives and primitives.

Now I’m in uni and I used Anki for learning linear algebra, I mostly tended towards clozes.

For linear algebra I tended to put in all theorems and facts, tried to keep them short so they’re easier to remember and then do complementary exercises handed out by the course. Being an autodidact myself, I must say that if the course is done right it can make learning a lot easier. Sadly many of the courses weren’t as good as the linear algebra course.