I'm sure that the cardinality of sets will be very important. The proofs are difficult for me, so I plan to study hard to understand how to prove that a set is denumerable or uncountable. I would expect to see this topic on the exam.
Also, I plan to see the Division algorithm and the Euclidean algorithm. Fortunately, this seemed to make a little more sense than Chapter 10 and the cardinality of sets.
An important theorem is the Schroder-Bernstein Theorem. I would think that we would have to be able to prove that two sets are numerically equivalent. That appeared in the homework and I kind of struggled with it with regards to when to use it and quote it exactly.
It seems that the questions on the test, at least the proofs and free response, are similar in some ways to homework questions, which is nice. I feel that if you can do your homework well, then you should know it well enough to perform on the test without the textbook or notes.
As for the definitions, we went over many, as usual. Denumerable, countable, uncountable - it will be good to know these on the test. I need to memorize the definitions exactly as I wrote them down from class notes. I've found that I lose points on exams when I don't provide the exact definition from text/notes, even though what I've written on the test for a definition is correct. I suppose it wasn't the "correct" correct answer. Definition memorization will be a part of my preparation.
I would please like to see a problem showing how one set has a larger cardinality than another.
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