1. The most difficult thing for me is thinking of x as a specific element of the ring rather than a variable. It makes sense logically, but I'm just not used to it yet. The example with pi does help with that.
2. I thought it was really cool how well the division algorithm in F[x] correlates with the division algorithm in Z. Both are fairly simple theorems that are extremely useful later. I haven't read ahead in the book, but I've heard hints of some interesting ideas that are coming - cosets of functions modulo a polynomial, etc. I'm looking forward to it.
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