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I know that normally, after attending class and understand the theorem and proofs, we will go directly to the problem and solve a couple of them, strengthening the concepts. Clearly, this is the best way to study and this is why in the US they always give a homework assignments to keep track of the study.

But it seems this way doesn't really work for me. The main problem is always, I found it's hard for me to do the problem directly after the class as I need more time to absorb the materials (In some sense, I might need to prove a theorem 5 times on my own to really understand what that theorem is all about.) So I don't usually do any homework on my own, instead, I focus on understanding the material first and do extra homework 2 weeks before exams.

This causes a big problem, that I don't have enough time to think about the homework assignment and end up "discussing problems" (mimicking solutions) with the others during the week. Also, I feel more comfortable just having a solid understanding of the whole course before moving on to doing questions, say two weeks before final exams.

Is there any way to solve this problem? Due to US system, there are always homework assignment and mid term and I cannot avoid them.

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    $\begingroup$ It helped me to learn in a "big picture first" style. Get the big picture then learn just what you need to solve whatever problem you need to solve. "Get comfortable feeling uncomfortable." Taking the course is only your first iteration of learning this material. You can revisit the important ideas many times in the future. Especially the ideas that are relevant to your research. Grokking this material is the work of a lifetime. $\endgroup$ – littleO Feb 7 at 12:57
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    $\begingroup$ Unfortunately, unless you are a mathematical prodigy, your strategy will lead to disaster. Doing the problems will not only help you understand the theory, but often also prepare you for the next steps in the theory. So what you have to ask yourself if you really do understand the theory without doing the problems, or is your understanding superficial. 1/2 $\endgroup$ – Oбжорoв Feb 7 at 13:08
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    $\begingroup$ But I do understand what you say, because I have the same; it often takes some time for me to understand the theory and I have to go through the details several times before i really understand it. What I have found useful is to wait a few days and then go through it again and then start solving problems. Solving problems is like playing an instrument or doing sports. Start slowly, practice a lot, and realise it is not always fun. Most surely do not wait until a few weeks before your exams to start them ! $\endgroup$ – Oбжорoв Feb 7 at 13:11
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    $\begingroup$ This is silly - you know the solution, you want another solution that doesn't take as much work. Sorry, doing the homework (roughly when assigned, not waiting for the midterm) is the only way. $\endgroup$ – David C. Ullrich Feb 7 at 13:53
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One recommendation is to get a study partner or form a study group of 2 or 3 dedicated individuals. Working with others can get you unstuck quicker and reveal more incites into the problems from different angles; hence allowing for conceptual understanding rather than rote learning.

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You don't really need to 100% understand the proof of the theorem (or the theory itself) when solving problems. I don't know how hard are your homeworks but sometimes it is good to go to the problem headfirst. Take a theorem(s) as blackbox into which you put some assumptions and you get some consequences and try to proceed with the homework.

Of course, you usually won't solve the whole homework this way but you will put the theory in use. And it is easier to spot the places where you need a deeper understanding of theory.

I personally find it more useful for me to get over a problem set multiple times then to go over the proofs of theorems in theory multiple times. Also some theory is not to be understood immediately. That's just how math works. But seeing it in "practice" (on homework problems) helps you realize the connections.

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