Difficult- I don't think I understand how to form the extension field of F or where that comes from. Another part that confuses me is how x^2 + 1 has in Z7 has 49 elements. I don't see how it could. But the notion that a polynomial in Zp with degree k in a filed F[x] has p^k elements is interesting.
Reflective- I think the most interesting part of this lecture is example 5.3.2 which shows [x] is a root of that polynomial in the extension field K even though it is irreducible in Z2. I literally said cool out loud when I read this. This lecture is really interesting and I like it.
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