5.3, due February 18

• Difficult: In Theorem 5.10 it says that p(x) is irreducible in F[x]. But why is that necessary? A field didn't JUST have prime numbers, so why does this one have just irreducible polynomials? It doesn't make sense to me. Also, I have no idea what an extension field is. I've read that part a bajilion times, and it's still jibberish. Looking forward to the explanation in class.
• Reflective: Hm... For once, it's actually the reflective part that's hard. "What was the most interesting part of the material?" Um... well... I didn't understand what an extension field was, and that's pretty much what it was all about. So... "How does this material connect to something else you have learned in mathematics?" well, so far as I can tell it doesn't! "How is this material useful/relevant to your intellectual or career interests?" I'm not sure. I wish someone would tell me how AA is going to help me teach high school math.