Section 5.2, due on October 6

The hardest part of this material for me is distinguishing between the field F, F[x], and the ring F[x]/(p(x)). I have to keep reminding myself that elements of F[x]/(p(x)) are classes of polynomials and not just polynomials. Theorem 5.7 was also confusing to me because of my confusion with trying to distinguish between F and F[x]/(p(x)).

The most interesting part of this material was Theorem 5.8. It was a little confusing to me, but it seemed like a cool fact. I was a little confused about the difference between Theorem 5.7 and Theorem 5.8, but when I figured out how they were different I thought this was also interesting. This section also makes me wonder what types of things the ring F[x]/(p(x)) is used for and why its structure is so much more rich then the set of congruence classes modulo n.