1. I am still struggling with finding the cosets and how many there are and what they are etc., so I think I am going to struggle with this section because it deals more with cosets and the multiplication of and addition of them, but I can't even find them to use them yet. So there is no way that I can do addition and multiplication tables of cosets when I can't even figure out what the cosets are. So this is the most difficult part of this section -- the fact that cosets still make no sense to me.
2. It is interesting that R/I is a ring. I had no idea from the last section that this would be coming. I can see how a coset is like a congruence class, but to have R/I - the set of cosets - be a ring, well, that is just really cool. I like seeing how things that make no sense in one section (like R/I) are connecting to a big principle (like rings) that we have been working on all semester. I like when weird things turn out to have a purpose. It is cool.
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