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I have an exam on P-Adic integers (and a bit on Galois Theory) that my professor said would be very computational, but he never does any examples of the theorems he proves in class. He said the exam would be mostly, if not entirely computational, and I am trying to hypothesize what kinds of questions the professor could ask so that I can practice doing computations instead of proofs all the time!

(IN P-Adics we have covered Hensel's lemma and Ostrowski's theorem, I know how to apply Helsel's lemma but I don't really understand Ostrowski's theorem... Those are the only 2 theorems my prof even gave names and we don't have a textbook to reference either so it is really hard to describe what we have covered so far...)

(IN Galois Theory we have discussed splitting fields and normal extensions but I don't really know what they are, examples of them, or any types of computational questions that could be asked about them, if any at all, primitive elements... and a little bit more...)

Any types of questions you think could be asked about these 2 topics would be wonderfully appreciated, or links to sources where I could read more about them. Again, no textbook, only photocopies of handwritten notes (oh, yeah, and my prof doesn't really speak english that well either...)

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Well, if you can get your instructor to login here and answer this question, you'll be in business. Anyone else's answer would be speculative at best. Probably a lot of mathematicians who are familiar with this material (like me) are leery of telling you "the wrong" things to study. – Pete L. Clark Mar 22 '11 at 2:44
Note though that F.Q. Gouvea's book on p-adic numbers has a very hands-on, computational approach. You could do worse than flip through it and familiarize yourself with some of the examples and constructions therein. – Pete L. Clark Mar 22 '11 at 2:44

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