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Oscar_Cunningham comments on Open Thread, June 16-30, 2012 - Less Wrong
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I'm trying to memorise mathematics using spaced repetition. What's the best way to transcribe proofs onto Anki flashcards to make them easy to learn? (ie what should the question and answer be?)
When it comes to formulate Anki cards it's good to have the 20 rules from Supermemo in mind,
The important thing is to understand before you memorize. You should never try to memorzize a proof without understanding it in the first place.
Once you have understood the proof think about what's interesting about the proof. Asks questions like: "What axioms does the proof use?" "Does the proof use axiom X?" Try to find as many questions with clear answers as you can. Being redundant is good.
If you find yourself asking a certain question frequently invent a shorthand for them. axioms(proof X) can replace "What axioms does the proof use?"
If you really need to remember the whole proof then memorize it step by step.
Proof A:
Do A
Do B
becomes 2 cards:
Proof A:
Proof A:
Do A
[...]
If you have a long proof that could mean 9 steps and 9 cards.
Thanks!
I've been doing something similar (maths in an Anki deck), and I haven't found a good way of doing so. My current method is just asking "Prove x" or "Outline a proof of x", with the proof wholesale in the answer, and then I run through the proof in my head calling it "Good" if I get all the major steps mostly correct. Some of my cards end up being quite long.
I have found that being explicit with asking for examples vs definitions is helpful: i.e. ask "What's the definition of a simple ring?" rather than "What's a simple ring?".
"def(simple ring)" is more efficient than "What's the definition of a simple ring?"
I find that having proper sentences in the questions means I can concentrate better (less effort to work out what it's asking, I guess), but each to their own.
If you have 50 cards that are in the style "def(...)" than it doesn't take any effort to work out what it's asking anymore.
Rereading "What's the " over a thousand times wastes time. When you do Anki for longer periods of time reducing the amount of time it takes to answer a card is essential.
A method that I've been toying with: dissect the proof into multiple simpler proofs, then dissect those even further if necessary. For instance, if you're proving that all X are Y, and the proof proceeds by proving that all X are Z and all Z are Y, then make 3 cards: * One for proving that all X are Z. * One for proving that all Z are Y. * One for proving that all X are Y, which has as its answer simply "We know all X are Z, and we know all Z are Y."
That said, you should of course be completely certain that memorizing proofs is worthwhile. Rule of thumb: if there's anything you could do that would have a higher ratio of awesome to cost than X, don't do X before you've done that.