Midterm 2 Study Prep

1. Which topics and theorems do you think are the most important out of those we have studied?
Well, looking back at my notes, it seems like the biggest theme here is: the Infinitude of Primes. It seems to me that there has been one proof after the other how many primes there are. So, I think that any theorems relating to that are going to be the most important.

2. What kinds of questions do you expect to see on the exam?
Like I said in the first part, I'm guessing that we will be expected to proof that there are an infinite number of primes of various forms. Hopefully, we'll get lots of questions about continuous fractions -- I like those. :) Also, perhaps we'll need to be able to calculate certain Mersenne numbers, or Fermat numbers or whatever.

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.
Well, I've got to say, with very few exceptions, I started getting desperately lost around quadratic reciprocity. I'm thinking that part of that is that I'm missing some real basic understandings somewhere early on, so I feel like I need to return to some of the basics before really delving into the understanding of these sections. But that's what this weekend is for. In terms of a question I'd like to see answered, I guess if you're going to be including anything about characters, I'd like to see the type of question that would be, and how you'd go about answering it. That is, without a doubt, my weak spot for this section. I feel like we just did one theorem after another with out any problems really being solved (I admit, the homework was so whelming to me that I didn't finish any of those assignments). I'd like to see a question relating to those that is solvable (not necessarily a proof).

4.Are there topics you are especially interested in studying during the rest of the semester? What are they?
As I've mentioned before, I'm really just trying to survive and not drown in number theory. I'm interested in any topic that won't make me feel like a complete idiot. Help me Bro. Jenkins. You're my only hope.