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How do you effectively study mathematics? How does one read a maths book instead or just staring at it for hours?

(Apologies in advance if the question is ill-posed or too subjective in its current form to meet the requirements of the FAQ; I'd certainly appreciate any suggestions for its modification if need be.)

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    Do the exercises, then come up with your own exercises. The best exercises are the ones which test your understanding of two different books. (These are the ones you have to come up with.)2011-02-20
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    I definitely agree with the advice of "coming up with your own exercises". It is certainly the best way to learn mathematics. Let me also add the advice of "coming up with your own proofs of results in the text". If you find it difficult to come up with your own exercises, then it is also a good idea to search online or look at many different books to find good exercises.2011-06-25
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    @Quiaochu Yuan: What did you do if you could not solve ''your own exercise''? Normally, I got alot of my own problems when I study a new mathematical theory, and I could not answer them. Then I try to abandon them and come back in a beautiful day :D2012-03-29
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    Your question is probably appropriate for the nearly-in-beta-SE http://area51.stackexchange.com/proposals/64216/mathematics-learning-studying-and-education. Check out the proposal and commit to it if you're interested. Then we can get it off the ground and get the site in beta!2014-03-03

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