- Which topics and theorems do you think are the most important out of those we have studied?
As I prepare for this test, I have a couple different feelings about what is most important. I really enjoy tangible problems - examples that I can see worked out. I really enjoy direct proofs, contrapositive proofs, contradiction proofs, counterexamples, etc. I think each of those are truly important. But I believe the most important thing that we have studied is the syntax for writing sentences. I think writing sentences using quantifiers (both existential and universal) and understanding how to negate these - that is the most important topic we have covered. I think this because with a solid understanding of how to take a result that you need to prove and change it into a sentence with P, Q, R, etc. then you can more effectively see and apply other proofs.
- What kinds of questions do you expect to see on the exam?
I expect to see problems that are similar in style, difficulty, and content as to those that we had on the homework. I think there will be more applications of proofs (direct, contrapositive, contradiction, existence, etc.) because those proofs show that you know how to do a multitude of things.
- What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
I think before the exam I would just like to go through a handful of problems and talk about strategies for noting how to recognize which proof to use in different scenarios. I plan on going through all of the homework problems, recognizing patterns of how to go about proving different results. I feel good about many of the definitions and notation. I just want to make sure I know how to recognize results, and then how I can plan on proving them.
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