Test 1 Review Due September 29, 2011

1. Which topics and theorems do you think are the most important out of those we have studied?
It seems to me that The Fundamental Theorem of Arithmetic will be important (I mean, it does have the word "Fundamental" in it. Also the Phi Function, Chinese Remainder Theorem, and Quadratic Reciprocity all seem to be big ideas that were built upon other smaller ideas we've discussed.

2. What kinds of questions do you expect to see on the exam?
I expect us to have to solve a system of congruences (using the chinese remainder theorem) as well as finding if a number is a quadratic residue mod whatever using that mess. Also, I'm guessing there will be some questions about rings and probably a proof or two about primes.

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.
As is pretty obvious, my frustration over the homework that was due Monday seemed to put a damper on what I thought had been pretty good progress. I've pretty much given up for this week (with every intention to pick myself up at the start of next week...) But, I am still really confused about the whole Quadratic Reciprocity thing. I thought I understood how to flip and solve and yadda yadda at the end of class, but then I started to do the homework and got confused and frustrated. I'm mostly confused because from the theorems in that chapter (and with the jacobi stuff) it seemed that your numbers had to be, at the very least, odd. Then you were saying something about using the chinese therorem to break things up and whatever.... I revisited the chinese theorem, and I was still pretty confused. So, I need to understand that stuff better, and I'd like to see an example done, like the one in the homework, where the numbers weren't necessarily prime, and one of them was even -- so you had to use the CRT. After that it'll just be up to me to decide how much I'll be watching conference, and how much I'll be studying... sigh... what a spiritual dilemma....