Section 9.4

Difficult: It was hard for me to understand Theorem 9.31. I don't get what this theorem is saying or how it will be important. The proof doesn't really make much sense to me either, and I don't understand how it proves the theorem.

Reflective: I think it's interesting that so much can be done with integral domains, and I think the concept of a field of quotients is really interesting. It makes sense to think of the rationals as a field of quotients of the integers.

Section 8.4-8.5

Difficult: The most difficult thing for me to understand in these sections was the proofs of the Sylow Theorems, especially the proof of the second Sylow theorem. I don't understand some of the steps they take in the proofs.

Reflective: I think the idea of conjugacy is really interesting, especially conjugacy classes. It's interesting how they fit into the classification of groups problem, and the proofs of the Sylow Theorems.

Section 8.3

Difficult: I am having a hard time understanding the second example on page 264. I am having a hard time following their steps to get to the point where they applied Corollary 8.16.

Reflective: I think it's really interesting that there are so many properties that can be found from finite groups. This section was really interesting to me because I think that the Sylow theorems are interesting, and I look forward to seeing how we will use them.