The topics and that I think may be most important out of those we've studied would include induction, relations, equivalence classes, and functions. Specifically, regarding relations, I know that it is important to know if they are reflexive, symmetric, and transitive. Concerning functions, it is important to know if they are injective, surjective, and bijective. There are a couple of noteworthy theorems regarding this in my notes. Also, I think that the theorems about congruence modulo n and equivalence relations are very important.
I am expecting a similar format for this exam as the one used in Exam 1. True/False questions, Multiple Choice, and Free Response, which include proofs. Speaking of proofs, I feel like I need a much better understanding of how to construct proofs. Is there a certain formula or are there guidelines I can follow when doing an induction proof or when I am trying to prove a function is injective, surjective, or bijective. I think that I get stuck with how to start and how to finish, not to mention what to put in between. Really, I sometimes freeze up when thinking about how to write proofs because I don't know how to proceed. I am more used to solving problems - first, take the derivative, then plug it into the formula, then simplify, then solve the integral, etc. I'm not sure if there are clear-cut guidelines for proof construction, but that would be helpful to me.
A problem I would need to see worked out would be, for example, is "Prove that n! > 2^n for every integer n >3." I missed this one on the homework.
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