Section 3.3, Due on Januray 25

Part I: What was the most difficult part of the material to you?

 The most difficult part of the reading for me was the statement and proof for Corollary 3.13. I am really confused about the idea of the image and how it relates to S. I understand that the image is f(r) for any r that is from R, but it is hard for to me relate this idea in the proof since I is just stated to be the image, when I could say that I want to see f(r) to be the subset of S, right?

Part II: Write something reflective about the reading. 

I really liked the example in the book about how to find a function that is an isomorphism and it had integers mod 12 and the cross product of integers mod 3 and 4. It built up so well to each step and to the final product, yet it seems super complex because there are so many subscripts and numbers with functions, cross products, and integers. It could be easy to get lost but you just have to look at each step carefully and it makes sense.