Hey guys,
Do any of you know of any ways to memorise mathematical proofs? The major System lacks mathematical symbol and developping a PAO system with all the symbols seems like it will take a very long time to develop, probably more than it’ll save me. Anything else I could use (I’m open to new methods or already developped systems, almost anything at this point)
Thanks a lot in advance!
PS: The goal isn’t to just memorise formulaes but the whole structure of the proof
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Not saying it’s the only option, but it’s one option…
The best way is by understanding as much as possible.
I have a degree in Mathematics, at a university where the course is particularly rigorous. My final year involved a lot of proof memorization—some of them (Arzelà-Ascoli Theorem, for example) taking more than a page handwritten with my compact handwriting.
At the time, I thought it was a bit of a waste of time. Why assess memorization so much, when they could assess problem-solving?!
Now, I realize that those of us who understood the concepts could memorize them much more easily, as a short series of abstract steps (e.g. “proof by induction on the number of vertices; remove edges until you get a minimal spanning tree”), while students who didn’t understand the concepts well enough would need to memorize many more steps of the proof—possibly including entire formulas, verbatim sentences etc. in the extreme case. Of course, that would be much more time-consuming (and unreliable), and these students wouldn’t have the capacity to memorize enough for a good mark.
So, the first thing I’d do is to separate the proof into some big stages. Can you figure out how to write some of these stages just using your intelligence? If so, great! For those where you can’t, you’ll need to break it down further.
Lastly, for anything that really doesn’t stick (like e.g. the 3 main stages you identify for the proof, or the special “magic” algebra step on line 16 where you multiply by (x – 1)/(x – 1) that you’d never think of yourself), then that’s where you can use a mnemonic technique to help. Maybe in a short memory palace or other sequential data encoding, since the steps in the proof usually do need to go in order.
Hope that helps, and makes your studying simpler! The hard work is of course “understanding” better. That comes with practice, exploring different types of questions, and trying to determine why the author of the proof had to do each part.
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I didn’t think of breaking it down by stages, this should help a lot. Memorizing only the “unique” stuff through mnemonics might make using them worth it. Thanks a ton!
I’ll look through it, it looks interesting evenwithout considering the math aspect, but since I don’t have an image system yet it might take a while. Thanks!
Agree with @Daniel_360. I have a background in Applied Math and have in my time learned a lot of proofs. A proof is a logical argument involving relationships between ideas. As such the parts must fit together. There are tight associations between the steps and this provides strong memory support. IMO first devote yourself to mastering the proof and then use mnemonics to capture the elements that you still have trouble with.
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