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What is expected on graduate school for students when learning a topic in a course? To read and fully undertand the proofs of theorems on the respective book, then make some exercises; or to read only the theorems but do a lot of exercises? or maybe both both?

HeMan
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    I think you are expected to defeat Skeletor – Will Jagy Feb 18 '18 at 03:38
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    Definitely understand, and for the most part memorize, the statements of the theorems. Make sure you can come up with examples, showing why the parts of the hypotheses are needed. Fully understand and test yourself on the easy proofs -- those that you can do pretty much in your head. For the rougher proofs, be selective, else you'll burn out, but the ones with ideas likely to be reusable, those you should master. As far as exercises, definitely do lots of them, at varying levels of difficulty, and without too much repetition. Your ability to do exercises confirms your knowledge. – quasi Feb 18 '18 at 03:45

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Read and understand the theorems; be able to state, apply and prove the theorems; do exercices to master the techniques; and learn to apply the ideas of the course to solve more complex problems.

Olivier
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