I don't know about anyone else, on the O.U course M208; but I am finding the topics of Group Theory and Analysis, so far apart from each other, in terms of mathematical flavours; that I am beginning to feel like Analysis is not dissimilar to a wonderfully stodgy, bread and butter pudding (quintessential, robust and ever so yummy); whilst Group Theory feels like more of a Monday lunchtime, fish-paste sandwich.
They are just so different; that I find myself wondering how it can be possible to love both areas of mathematics. I mean, Group Theory kind of feels a little bit like messing around with puzzles in the back of the Sunday newspapers. Don't misunderstand me here; I don't mean that Group Theory is easy, by any stretch. Rather, it just feels like messing around with stuff, for its own sake. This approach is supported by my day school tutor, who said this weekend, "don't ask why Group Theory is that way; just have fun with it, and enjoy it for its own sake".
Analysis, on the other hand, is just breathtakingly beautiful. You only have to thumb through the unit books of AA1 and beyond, to see that Analysis can be studied both for the pleasure of enjoying the pure aspect of its construction - and also for practical applications, that can present themselves at the end of the subject.
So far, I'm with Analysis, all the way; although I am yet to properly taste Linear Algebra. So, who knows? I might have time to clean my palette, before opening a new bottle of dessert wine, to wash down that second bowl of pudding.
Hello, I just found this post while searching for something else, and I had to add a comment.
ReplyDeleteAnalysis and group theory join up in the end - groups are a really useful abstract concept for thinking about the symmetries of things, which you want to do when trying to classify spaces, topologies, and so on.
The group theory you get taught in an introductory module does seem pointless unless it's given some historical context, but it's really useful to know a couple of years down the line when you start spotting group structures all over the place.