Section 7.2

Difficult: The hardest part of this section for me was when the author started to talk about the order of an element. I mostly understand it, but it was a little difficult to follow the proof for Theorem 7.8. I always have to go back to the definition of finite order to understand what the theorems are talking about. Because I had a hard time understanding Theorem 7.8, Corollary 7.9 was hard to follow as well. I think seeing more examples of finite order would help me.

Interesting: I am now seeing that basic properties of groups have been included in many of my previous classes. For example, in linear algebra, we talked about the inverse of two matrices (AB) being equal to "B inverse" times "A inverse." Now it makes sense and I can see the connection to a real example. It is also interesting that many of the things that we assumed in calculus and other math classes are now being defined and proved. I can compute and operate in certain ways because the number systems or algebraic systems that we work with are groups, rings, and fields.