How to “memorize” a theorem

Comments · 88

• JJ

  @JJGhostHunters · 3 years ago

  Just finished a grueling PhD program in electrical and computer engineering.  When you said there were "optional" enrichment courses that you pretty much had to complete, it reminded me of the 3 published papers that were never mentioned in my curriculum and turned out to be "required" before submitting my final dissertation.

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• EL

  @eliasmai6170 · 3 years ago

  i don't really memorize theorems.  i do a lot of the exercises which make use of the theorems so that by the end, the theorem sticks in my mind.

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• IS

  @IsomerSoma · 3 years ago (edited)

  I do diagrams of how the theorems (and structures in general) relate to each other and what their application is. By developing such a network of relations they not only stick, but you know the chain of theorems and concepts leading up to a theorem too. Almost no repetition needed. Adding some visuals makes such a network even stickier. Making such a diagram is quite hard as one has to chunk efficiently, intuitively and logically, one has to figure out what the most important relationships are and how to spatially arange all of this.<br><br>Do what you do if you want, but imo what you seem to be doing doesnt seem to be efficient. The order memorizing then understanding and finally getting big picture is skewed. Having some idea of the big picture first makes learning the details <b>greatly</b> more efficient.

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• GU

  @GusMXRacing · 3 months ago

  With math, since the theorems themselves are true, it hurts not to memorize them. You can understand later, and it will be easier if you have it downloaded on you before you try to explain.

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• AS

  @asbjrnandersen4765 · 3 years ago

  You really do need to memorize things at least in my experience. Most of my math exams were exams where you draw a random theorem which you then need to prove to the professor. Only way to prepare for such an exam is literally remembering the proofs....

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• BL

  @blinderfleck1625 · 3 years ago

  balls, a lot of balls haha

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• II

  @IITIIT-o2m · 4 months ago

  Really love long form in depth informative videos ❤❤❤<br>This was so down to earth and real, I loved It 😊😂

• PY

  @Pygmygerbil88 · 1 year ago

  Micheal penn is absolute gem of a professor he teaches all aspects of math abstract algebra set theiry analysis linear algebra even number theory .<br>When he teaches he periodically takes a peep at the solution before wrting it down even the best matgematicians dont memorize every line of the proofs

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• JO

  @JoaoSilva-yz4zq · 3 years ago

  I would like to add, in case you did not know, that Fatou&apos;s Lemma, the Dominated Convergence Theorem and the Monotone Convergence Theorem are all equivalent results. In other words, any of the these three results can be proved using any of the others.

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• SO

  @soyoltoi · 3 years ago

  In order to understand, you first have to have it in your head. If you can efficiently upload it into your head first, then you can set yourself up for successful understanding as you make connections between these theorems and concepts afterwards or as you go.

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• AL

  @Alex-fh4my · 3 years ago (edited)

  I think the idea here is that when you first see a proof it can be difficult to &quot;store&quot; all of it in your short term memory. If you can&apos;t store the whole thing, you have to look at it piece by piece, which doesn&apos;t let you see the full picture. This way you at least commit the proof to memory, and then once its in your mind you can play around with it and manipulate it until you understand the bigger picture.<br><br>Typically though its much easier to remember something if it is tied to other ideas conceptually, instead of just an arbitrary abstract sequence of symbols (extract meaning vs. rote learn). But in the case of something like this I think the approach is fair, since its hard to build the conceptual understanding in a single time step

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• CA

  @cainmorano4956 · 2 years ago

  You don&apos;t memorize, you Internalize. When you were a kid, like you said, you memorized. But now you work with a lot of content and eventually you start to remember and cold recall facts. More importantly you intuitively see relationships among the written symbols and understand the how and why across a broad network of ideas.

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