3.2

1. The most difficult thing for me in this section is keeping symbol manipulation separate from the logical validity of the operations. It seems interesting to me that behaviors of systems can be dictated by defined symbols and operations. I probably don't understand it, though, to be saying that. I think it's also interesting that kids are taught symbol manipulation through school and teachers struggle to teach how it is applied--there's just too much to go over and most kids just aren't willing to put forth the effort into something if it doesn't come easy. As a math tutor, I see this consistently and is the rule, not the exception.

2. I am taking Theory of Analysis (315) right now and the book started with fields. The author, who doesn't mince words, went through a similar process as this book to establish laws for fields, groups, etc., albeit with way fewer words. It's nice to see some mathematical convergence since for so long it seems there is just new topic after new topic.