I am currently reading Algebra by Michael Artin (for self study). I'm finding the book pretty interesting, but I'm still not sure how I should study the book. For example, should I try to prove every theorem as I read the book or should I just read the proof for the theorems? Also, when I take notes, I usually just write down all the theorems, proposition, lemmas, etc. Is this a good way to take notes? And one last question: how should I deal with seemingly impossible exercises? I have experiences with proofs from Olympiad math, and from learning Calculus (rigorously), but there seem to be some exercises that takes a very long time to figure out.

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    $\begingroup$ I cannot tell what in this question is specific to Artin's book. You have to develop your best way of reading a book, and of taking notes —what is good for me is mostly irrelevant for you! Also, yes: some exercises do take a lot of time. $\endgroup$ – Mariano Suárez-Álvarez Sep 17 '14 at 23:37

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