...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...

Thursday, June 13, 2002

So I've jumped back to Visual Complex Analysis. Having spent the last few days with Strichartz, the difference is striking. Needham actually gives intuition in spades, motivates his arguments, is fun to read, and all-around blows Strichartz clean out of the water on everything except rigour. And to be honest, I don't give a crap about rigour for rigour's sake. I know, in a vague intellectual way, that rigour is necessary and even useful, but I don't have any feel for it. I definetly need to find a companion book for Strichartz that will have motivational stuff in it. Hopefully, the book by Abbott I mentioned earlier will fit the bill - I'll try to find it in the local book super-store this weekend.

I've temporarily skipped Needham's chapter on non-Euclidean geometry, and I'm reading the chapter after that, on topology and winding numbers. I did this reluctantly, as I've long dreamed of learning about crazy geometries, but I also want to learn about complex integration, for which the topology and winding number stuff is a prerequisite, while the non-Euclidean geometry chapter isn't. However, I can't resist intellectual candy, and so I've made a compromise: I'll read the non-Euclidean chapter during bathroom breaks, as I do some of my best thinking there, as explained in detail in past posts, and I'll read the winding number stuff in my out-of-bathroom time. Fun!

Talking about fun, the winding numbers chapter is spectacularly entertaining. I think I've said it before, but I'll say it again: "Tristan Needham's Visual Complex Analysis is the Best Math Textbook Ever." If you have even the slightest interest in mathematics, and especially geometry, and have studied basic calculus, get this book. You're very unlikely to regret it.


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