What are the best methods for learning proofs? I'm tasked with learning two dozen proofs about the properties of continuous functions and real numbers in a week well enough to be able to present them. Like Taylor's Formula, the fundamental theorem of calculus, and Bolzano-Weierstrass theorem. What is the best way to do it? My main problem is that there are no exercises to practice on.

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    $\begingroup$ So basically you are supposed to learn most of the main theorems from a course in real analysis in a single week? There is a reason why such a course normally takes a quarter/a semester, so you might want to clarify what exactly you are supposed to do in this single week. Furthermore, it might be good to know your background, e.g. are you a freshman who never did (university level) math, or are you an experienced mathematician and just need to re-read the proofs to remember them from your time as a student? $\endgroup$ – Dirk Dec 4 '17 at 13:16
  • $\begingroup$ I'm only an amateur. But I know the math from the course I just haven't understood these abstract results. :) The proofs are easy but getting them to stick in memory is hard. :) $\endgroup$ – Björn Lindqvist Dec 4 '17 at 21:51
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    $\begingroup$ I'm not sure if this is really a math education question as the answer is known: "do a lot of proofs and have them reviewed." If you don't have time for go through every premise in the statement of the theorem and find an example where the theorem doesn't hold if that premise is dropped. Then find the line in the proof that would preclude your example. That will at least give you an idea of the shape of the ideas involved in the proof. Why do you have to do this? $\endgroup$ – Nate Bade Dec 5 '17 at 17:25

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