8.5, due on December 7

I felt like this section was easier than some of the others recently (it helped that a page and a half of the section was describing dihedral groups that we have already learned about). I didn't understand the first proof (theorem 8.27). I didn't know how they obtained the equation they call the class equation and I was unsure if the Ci's were just divisors of G or what they were. I also didn't really understand the proof of theorem 8.34. It was really long and I wasn't exactly sure how they used all these assumptions to construct the multiplication table. I would be helpful to go through that proof again.

I had one other question which was about the group Q, the quaternion group. I missed one or two days and I'm wondering if we talked about it on one of those days. I don't know what it is or why it exists and has no similar groups in other orders except of order 12 (is the reason there is a T group similar to the reason there is a Q group? It was a little disheartening that the chapter ends by telling us that there are 267 different groups of order 64 and that there was no way to know the number of distinct groups of order n. How do mathematicians find the maximum number of distinct groups for very large groups?

Looking over the study exam for the final made me feel a little overwhelmed. I feel like it is all important and that means I have a lot of stuff to memorize. I really need to review the stuff on rings because it has been a while since we covered that material. I also don't fully feel comfortable using the theorems from this chapter to prove things. I want to go over the practice problems from the study guide especially numbers 8, 9, 12, 17, and 18.

I have learned so much from this class. I don't know what will be specifically important to me in my future because I don't know what I want to do with my math degree. But I think that the improvement that I have made in being able to prove things will be really helpful in future classes, especially theory of analysis which freaked me out because I couldn't remember how to do proofs at all.