Difficult:
The difficulty of this section started at the very beginning. For some reason the very first paragraph was confusing to me. Ironically, understood mostly everything else from that point on. It took me a second, but I soon quickly understood what they meant by a polynomial function when I started to think of it as the same polynomial functions that I have been dealing with since I was in junior high. From there I came to understand the distinction between the intermediate x and the variable x. I also understood the concepts of roots, seeing as it is not a novel concept in math. As soon as they began to discuss these polynomial functions in terms of fields, it became more difficult. Fortunately, I was able to understand fairly well at first but it gradually got more difficult towards the end of the section. In particular I did not fully understand the proof of Corollary 4.16. Consequently, Corollaries 4.17 and 4.18 were not completely clear as well. But other than that, I pretty much understood the overall picture that this section was trying to depict.
Reflective:
I find it very interesting and almost humorous that they found the need to really make sure that we understood the difference between the intermediate x and the variable x, seeing as the intermediate x deals with polynomials in the polynomial ring R[x] and the variable x deals with polynomials in the ring R. Oh my goodness! Heave forbid we get them confused! I guess I understand the need for a distinction, because they are different, it just seemed like something obvious to a math major. But, nevertheless, as is expected in a Math major, I appreciate the attention to detail and the extreme thoroughness. :)
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