2.3, Due on January 14

Difficult:
For the most part, I felt like I pretty much understood this section, which is a pretty big surprise for me! However, the part that I found to be most difficult was in the proof of Corollary 2.9. In the last part of the proof when the authors are proving uniqueness, they have this great idea to multiply both ends of the equation by u. This made sense, but the reason I found it to be so difficult was because I would never be able to think of doing something like that. I see why it works, but when I am doing proofs, I never think of doing something like this. Multiplying through by the number I want to both sides of the equation is not something that I ever think to do. This step in the proof was difficult for me to understand only because it is not something that I ever think of doing.

Connection:
I really liked the method used to solve the equation ax=b in Z mod n using the Euclidean algorithm to find a linear combination. Then using the solutions in the linear combination, you can find the solution to ax=b. I like being able to use algebra skills that I am already familiar with to solve new mathematics that I encounter in this course. Even though modular algebra is a newer, more difficult concept to me, I feel like I better understand the material when I can apply concrete ideas that I already know how to use.