(First of all, I'd like to apologize again for doing this last week. Second of all, I'd like to really thank you for helping me yesterday via e-mail with those questions. You really helped a lot. The second I read your hint about number 4, I was so embarrassed because I knew exactly what to do... I think my brain is just fried because, believe it or not, I've been studying/preparing for this test all week. I've typed up a study guide from everything you listed on your study guide (don't worry, I know it's not exhaustive) but I thought that might be a good place to start. So... without much further ado, let's get started.)
1. Which topics and theorems do you think are the most important out of those we have studied?
It seems to me that the theme of this exam, as I said last week, would be prime numbers. Specifically, the infinitude of primes. It seems that everything we have done this section has come back around to proving that there are an infinite number of primes.
2. What kinds of questions do you expect to see on the exam?
You know, I really am not sure. Mostly I'm scared. Hopefully we'll see some very similar to the ones on the homework (at least, the questions on the homework assignments that I completed successfully... So just look up my grade and don't ask anything from any of the assignments where I have a zero.)
3. 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 in class on Friday.
Characters. Characters. Characters. I'm really praying that you don't put much emphasis on them. They are the bane of my existence. But, I'm guessing they'll be somewhere on the test. So, I really need to work on those. I'm still not sure that I understand EXACTLY what the Method of Infinite Descent is. I skimmed over the section that you recommended, but I probably need to READ it very closely and slowly. However, of everything listed on the study guide, I have been unable to find (I could probably figure it out, after some more studying) in the book, or in my notes, the proof of the second part of the Orthogonality Relations II. I'm just really nervous because it seems that that is one of the proofs that we need to be able to prove, and I don't want to mess this one up. Stupid characters.
4. Are there topics you are especially interested in studying during the rest of the semester? What are they?
I say this with no desire for offense at all. I doubt you'd take any, but I'll just warn you. But, when I was deciding to take this class, graph theory, or combinatorix (?) for my math ed major, I really really wanted to take combinatorix (?) because I'm so interested in that stuff. But, I was nervous that I wouldn't get in, and I wanted my last semester here (wahoo!!!) to be lighter than the rest. So I settled (I know, I'm so mean) for Number Theory. I know I could take combinatorix next semester, but that would require extra money and time I don't have. So I would love to see some more of that. But, I also know that isn't what this class is for. So, I'll try to get over it.
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