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I am studying real analysis and trying to convert some of the rather wordy theorems into flashcards. Some of the theorems have names and so it's easy to make a flashcard that just asks that I state the main hypotheses of the theorem and the conclusions. Further, I can make flash cards that state the hypotheses for a particular theorem and asks me to follow through with the statement of the conclusion; or ones that state a given conclusion and asks me the hypotheses under which the conclusion holds.

My problem is that I am most stuck with theorems that are not named, are relatively long or that have relatively uninformative hypotheses for instance, "Let $f:A\rightarrow B$ be a continuous function, then ...". A hypothesis like that can easily apply to dozens of theorems.

Does anybody have any experience with making flashcards for learning mathematics or any ideas about how to overcome these problems?

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Since it's for your convenience, it may help to give those unnamed theorems names you would remember... –  J. M. Aug 11 '11 at 15:14
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If a theorem doesn't have a name, give it one. Be creative and make it meaningful to you. Personal mnemonics make recall easier on tests anyway. –  anon Aug 11 '11 at 16:01
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For some theorems, try splitting them into 2 cards, to test yourself both on the hypotheses as well as the conclusion. For example, compare these two: (1) Let $f:X\rightarrow Y$ be a continuous map of metric spaces, with $X$ compact. What can you say about $f$?...and also (2) What conditions could I impose to ensure that a map $f$ on metric spaces is uniformly continuous? –  John M Aug 11 '11 at 16:13

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up vote 4 down vote accepted

IMHO flashcards are more for knowledge based subject, rathen than skills based. IMHO Math is skills based, so, as long as you want to do this with flash cards - you have to be tricky.

Try to turn this stuff into problemsolving puzzles. For example "How to solve this and that", maybe some practical example, or something related. As you have to create connections, it works like mnemonics so you have double effects. But, remember - prepare memory hooks carefully to have access to this knowledge as you will need it.

Btw. Are you going to print them out, or use a kind of software with flashcards, supporting spaced repetition ? IMHO Anki looks interesting - what is your choice?

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I agree completely, except there are plenty of knowledge based questions too like definitions and simply being able to remember various formulas that be may part of a theorem like the Fundamental theorem of calculus. –  Henry B. Aug 15 '11 at 10:16

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