5.3

1. There wasn't too much difficult in this section. I am amazed at how similar irreducible polynomial quotient rings and Z mod p for some prime behave. Seriously, the fact that it is a field, and the implications of all that, well, it was unexpected to me.

2. I have this problem where I ask "why?" all the time. First it was "why are we learning this?" That was quickly mitigated as I renewed my faith in the BYU mathematics department--realized that they wouldn't teach things that one didn't need. It then shifted to, "Why was this developed?" Newton invented the Calculus (or discovered it, if you prefer) to model the laws of nature. I understand a little about the application of fields to cryptography and even to computation in general, but is the development of these ideas really that recent? (By recent, I mean early 1900s). Sometimes I have this suspicion that we are learning things that, while true, aren't immediately applicable, but they'll be assets when the fallout comes and we have to decide who gets to stay in the shelter and who doesn't. Kind of like that desert island game. I'm kidding. Kind of.