6.2 (through pg 147), due February 25

So I'm pretty confused these days, but it seems to me the first part of this reading is mostly just coming up with different terms/notation to describe things we have already discussed and learned about in a way that will help us to draw new connections...? This is kinda cool I guess because we have another way to make connections and new ways to talk about ideas that we've already learned. The most confusing thing for me is the third example because I didn't understand why they were adding ( 1 + I ) + (1 + I ). I'm also still a little confused by cosets and how it is that if I is the ideal of polynomials with even constant terms, then there are two distinct cosets. I think I'm not thinking about them in the right way.