How do you choose what exercises and proofs to see through? There's so much math to learn that if you proved everything you came across, you might not reach your learning goals. Also, some problems seem more interesting than others, some are too elementary and some would take days.
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2As a corollary: what books/authors give the most insightful exercises (i.e. a motivated student should be doing a higher percentage from these b/as than others) – Eric Stucky Aug 05 '13 at 03:30
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1@EnjoysMath: If you can do the harder problems, you can skip the easier ones. You do as many as it takes to be able to do the deeper ones. – Amzoti Aug 05 '13 at 03:31
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3Dear Enjoys, It's hard to answer this question when you've given no indication of what level of exercises etc. that you are asking about. You write that some problems would take days; you should bear in mind that some of us here have spent good parts of our lives studying certain problems, and that Ph.D. students in mathematics do sometimes spends days and weeks on just one or two pages (or less) of a difficult piece of mathematics. In short, it's very hard to answer this question without more context about your level and your learning goals. Regards, – Matt E Aug 05 '13 at 04:12
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I try to either prove or find a proof for any theorems used in a subject I am trying to learn. This way, I understand why a theorem is true and I can remember the theorem far more easily than just memorizing the theorem.
Sujaan Kunalan
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I agree with Sujaan Kunalan. Learning and understanding the proof (not memorizing the proof but understanding the idea behind it) helps you remember a theorem because then you really understand it on a deeper level and when you don't remember the theorem it is always good practice to quickly derive it (which is not hard if you remember the idea behind the proof). Deriving it yourself also helps you remember it even better than the first time.
Pratyush Sarkar
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