1. I know that "nothing" isn't an acceptable answer for this part of the question, but there wasn't really anything difficult for me about this material. Cosets were difficult for me when I first learned about them in Math 344, but they behave exactly the same way with respect to ideals as they do to vector subspaces, and the notation is the same.
2. It was interesting to see how the concepts and theorems we have been using for principal ideals in Z and F[x] generalize nicely to quotient spaces with arbitrary ideals. It's always cool to see connections like that between different mathematical ideas.
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