...Prove Their Worth...

"Problems worthy of attack
prove their worth
by hitting back." - Piet Hein

A kind of running diary and rambling pieces on my struggles with assorted books, classes, and other things, as they happen. You must be pretty bored to be reading this...

Tuesday, June 25, 2002

I've caught the flu, and I feel like a used kleenex. What's more, it's likely an imported flu (from Russia, most likely). Joy.



In more pleasant news, I was reading Spivak while on The Throne, and I think I'm actually not completely off my rocker in my initial impression of bundles. They are, apparently, 'just' a fancy way of saying you've got a tangent vector space to a manifold. The 'tangent bundle' turns out to be somewhat fancier still - it's something like a set of equivalence classes of bundles on the manifold, or something. I haven't digested that part yet. Hmm... I think I'll write up my digested version of tangent bundles once I work through them, for posterity and humor value.



Strichartz's book is neat. So is Needham's book (except I'd use a stronger descriptor than neat -- perhaps comic-book-guy-style "Best. Math. Book. Ever."?). I'm done with Needham's fantastic chapter on winding numbers and topology. The short-range plan is now to finish Strichartz's chapter on differentiation, and Spivak's chapter on tangent bundles. Then, I'm going to get my exercise on, and try to crank through some problem sets in all three books before continuing in any of them. Exercises are irreplaceable in firming up one's grasp of material, and at least the one's in Needham are actually fun.



Sadly, exercises are also hard work, and I'm a lazy bum. Motivation to do the 'homework' is one of the things that is especially challeging in autodidaction. On the other hand, in my specific case, there is a silver lining. See, I get to pick what problems I do, when I do them, and so on. Not some teacher with masochistic tendencies and an undying devotion to engineering plug-and-chug busywork. I pick the good stuff (and yes, I can see this being a problem, as it's questionable whether I can tell what the good stuff is.) And I don't get graded. And I'm not competing with anyone for a curve or anything like that. Which makes all makes the idea of self-assigned work easier to swallow and stick with, provided the work is interesting, and I can feel myself making progress. I've a nasty character flaw in getting easily frustrated.

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