I am currently studying abstract algebra. When I study new concepts, I manage to understand what it means. But when it comes to prove something, I lose my direction. It is not the case that I don't know what the statement means, but rather I have no idea to prove it. Can anyone give me some suggestions so that I can deal with proofs?
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closed as not a real question by rschwieb, Micah, Dennis Gulko, Davide Giraudo, tomasz Apr 6 '13 at 15:11
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At first read proofs, read a lot of proofs. So you learn how to write up a proof.
And another really important point is, know your definitions. Often proofs are just the definition and some minor steps, but to see those minor steps you don't need to know only one definition but every equivalent one. The more tools you have the higher is the chance you will be able to prove something.
If it isn't possible to see the general proof try some special cases. Calculate some examples on your own, maybe you see a system how it is working.
And be honest, reread your proof and check if every step follows from the one you made before. If you are not sure about it, maybe there is something fishy. Give yourself some time.