3.3, due on September 19

I felt like the first part of section 3.3 was relatively easy to understand. However, some of the examples began to confuse me because I feel a little shaky on some of my rings like matrices and Cartesian products of congruence classes. I am also somewhat confused by why the homomorphic examples on page 72 are not injective or not surjective (and how to show that they are the other one). I did not understand the definition of image and think that an example would clarify that for me. Lastly, I was really confused by the example on page 75 about the ring Z8 and why it's not isomorphic of Z4 x Z2.

In graph theory, we are talking about isomorphism so I really enjoyed that the description of isomorphism on the first two pages of this section were the same as how we described it in graph theory (relabeling the elements). I keep having the feeling that somehow these two classes are more connected than I currently understand and that really intrigues me (although maybe they aren't connected at all and it's just wishful thinking that graph theory has meaning). I also really enjoyed that we were shown techniques for finding if rings are isomorphic and for finding that they are not. It's funny that in graph theory it's typically easier to find a way that graphs are nonisomorphic than showing that they are isomorphic whereas in this section it seems like it's easier to find the isomorphism than the difference between the ring. Although possibly that might change with practice.