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This question is similar to the question posted here.

I seem to forget a lot the details I learnt before. I don't claim myself to be a math genius; rather, all the work I am able to do is only because of my sheer tenacity and hardwork -- studying all day and night for instance. I'm sure other more capable math students would do the same amount of work in a matter of a few hours, and retain it for a long time.

More specifically, one of the things I clearly lack is the ability to put material together. For instance, I was going through an introductory unit on manifolds and I came across a question that asked to prove that $O(n)$ is a manifold! I have no clue how to start integrating the information. If I were to go back to my linear algebra book, do everything (revise) again and come back, perhaps I'll be able to do this question. That's one of my main concerns: on their own, I can cover most of a textbook, but I find it very hard to flip flop between different concepts in a textbook, flip flop between different texts on the same topic and different texts on different topics.

  1. Is natural?

  2. How does one usually go about improving on this front? For instance, I have taken a course a course in point-set Topology. But if you were to ask me to prove the Finite Intersection Property, or recall the proof of thereof, on the spot, I won't be able to do this. That's why I feel like going back to my Topology book and revising it?

  3. Could it be the case that I'm blowing up this issue out of proportion? I feel as if this problem will increase as I go on to more advanced material. It's more abstract in the first place; even if I forget some tricks in Calculus, for instance, I can always go back and recall them. This won't be that easy for more advanced material.

  4. I find it very, very hard to retain information. Be it physics or mathematics. I go through a text 10 times in a semester for the exams; and after the exams, I am unable to recall the information at will.

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  • $\begingroup$ Look at the information you actually have retained. I'm guessing it's stuff you've used over and over again. For example, I'm guessing you can factor $x^2-5x-6$ quite easily. Why? Because you've done similar problems many times, often in doing more advanced mathematics. Perhaps you really only understand algebra after you use it a lot, for example in calculus. The going back and learning again is necessary for most people. $\endgroup$ – Arby Apr 5 '17 at 6:39
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  1. Yes this is totally natural.

  2. Yes you can review topology and it'll be helpful. If you want to see how much you've improved by virtue of taking the course, working through your topology textbook might be a great idea. This ties into my answer to the next question.

  3. Yes your probably blowing this out of proportion. Memorizing specific proofs is not something you'll really ever be expected to do except by professors who write bad mathematics exams. The point of writing so many proofs and doing so many exercises is to train you in the process of doing them, not make you memorize them. I would suggest that the following metric might be helpful: when you took the course, you probably made extensive use of the TA, other students, and outside material. If you were to take the course again, do you think you would need as much support to write the proofs? If the answer is "no," then taking the course improved your ability to work mathematically and write proofs, which is the goal.

  4. If you think that you have some kind of impairment, you might want to consider talking to a psychologist and the student disabilities services office.

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