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2

This is not a direct answer to your question, but it is literature that addresses at least one aspect of the issue you raise. Keith Devlin wrote an article entitled, "The Symbol Barrier": Link. The point of his article is to argue that video games can help overcome "the greatest obstacle to good mathematical learning." But setting video ...


1

For most people, including myself, there is pretty much no chance that you’ll remember most of the things you’ll see and do in math-land the first time ‘round. It’s just an inevitable relic of the fact that mathematics is... well... hard, and it isn’t something that the human brain was designed to do. The fact that you’ve gotten as far as you have is an ...


3

You don't describe engaging in conceptual chunking. You mention the Sylow theorems as an example and I will also use them as an example. It is easy enough to memorize the theorem statements. If you do not chunk the material in the proofs, then I challenge any claim that you understand the proofs. (Fix a positive prime integer, $p$.) The Sylow theorems ...


2

I believe you should follow these steps: Understand what the theorem says, with some applications of it (which also means to do the exercises, also show your work to TAs) Try to prove it yourself and get stuck quickly Work through the proof and try to understand it Take a fresh sheet of paper and now try again to do the proof When you get stuck (which you ...


16

For context, I have a lot of experience self-learning mathematics. I spent a summer learning additional algebra, point-set topology, linear algebra, and analysis (to extend my undergraduate degree) before entering my current graduate program. This was sufficient to skip a literal year in the program. I am now well into the program and have to self-teach ...


22

Memorization per se should not be the primary focus. When I learn something new, I type up notes on the computer in a reverse-indented outline format. Then as time goes on and my understanding improves, I edit the notes to reflect that. When I work an exercise or read a paper, I refer back to my notes. Memorization, to the extent that it happens, is just a ...


3

I think it is important to do some drill EVEN (maybe especially) with advanced concepts. This is because the concepts may be more strange and abstract. So you need to do some basic work to get familiarity with it. Quantum mechanics (or E&M) are rather non-intuitive and you just need to work with them. Not everything is as much an "aha" ...


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It's so unclear. I cannot follow what your idea is. I understand what you're saying the result of your idea might be, learning the material better even when there's so much to learn in a limited amount of time. I am unable to figure out what your idea is that you think might lead to that result. In theory, I could try to learn more about the things you ...


0

Your list seems like overkill to me. As far as geometry, Kiselev is basically a rehash of Euclid, so I don't see the point in studying both. Just pick one. I don't think you need the solid geometry parts of either. If using Euclid: -- Euclid contains stuff like number theory done in an ancient style that is now only of historical interest, so if using Euclid,...


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