Section 2.2

1)

I don’t follow the proof of the division algorithm. I don’t understand what a1 and b1 were in the proof of lemma 2.2.1. Where did the s come from in Lemma 2.2.2? Overall I had a hard time following most of the proofs that were given in this section.

2)

I like the proof of theorem 2.2.2. Even though I didn't follow every aspect of the proof the general idea of the contradiction to get r = 0 was interesting. I really enjoy applying the Euclidean algorithm to solve for linear combinations.

Section 2.1

1)

“Notice that the additive part of any ring forms an abelian group.” The example at the end of page 8 about zero divisors was a bit confusing. I thought I understood what it means to have a zero divisor but that example confused me. I didn't understand the beginning of page 9 when it states that y – x exists in D+. I didn't understand the proof for the lemma 2.1.3.

2)

One of the things I really liked about studying rings and groups was how they applied to the real world. For example how they were applied to Rubik’s cubes and Sudoku puzzles. I also liked the review on proof by induction.

Introduction

I'm a senior and a math education major. I plan on teaching mathematics in a middle or high school. I have taken 290, 313, 314, 300, 334, 362, and 371. I am taking this class because I needed to take it for my major and it was the only one that fit into my schedule. I don't really know what types of things I am going to learn in this class. I just hope I understand it.

The math professor that I enjoyed the most taught the class by letting us solve problems in class that taught the principles she wanted us to learn. I felt like I was really learning something and understanding it. She didn't overwhelm me with theorems or terms and show me why it worked, but let me discover it on my own. She also paced the class so that even though we may not have covered a lot of material, what I did learn stayed with me.

Something unique about me: When I was 2 years old, I inhaled a peanut and collapsed a lung.

The times that would work best for me are Tuesday mornings or T/TH after 3pm.