The proof of The Division Algorithm was very difficult for me to follow. As mentioned in the text, the theorem is quite easy to understand because I've used it so often in my life, but indeed the proof is not obvious. Maybe it has to do with the fact that it is a proof about something so fundamental, I'm not sure. It's like trying to describe the taste of salt. How do you start? What do you say? I don't know, maybe it's not exactly like that, but The Division Algorithm, with the quotient and remainder, is something that seems so easy that no proof is required. But, of course, a proof is required! It was a hard one for me to understand.
Number theory seems like it will be interesting. I don't know a lot about it, but the introduction to the chapter seemed to hype it up quite nicely, praising it for its appeal, clarity, simplicity, and elegance. I look forward to learning about it. I don't really think it will tie in too strongly to some of my career goals in statistics, but I like the way that Prof Jenkins explained the study of some of the material in this class. To paraphrase: 'It might not save the world, but it's cool and interesting, so we study it.' I feel like that is a great way to think about it for me.
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