27 December 2007

A couple articles from the Princeton Companion to Mathematics

Differential forms and integration (10 pp.), from the forthcoming Princeton Companion to Mathematics. (From Terence Tao, who has also written other articles for the PCM. I think it would have been rather nice to receive such an article at the outset of the class in which I learned about this stuff, as it would have helped to give some context; although one can often get context from a textbook, it's difficult to do so because all the little explanatory bits are often mingled with the details. The PCM articles I've seen do not suffer from this flaw; indeed, one might describe a lot of them as what the preface of a textbook covering the same material should be.

In a less theoretical, and less general, vein, here's Frank Kelly's The Mathematics of Traffic in Networks, also from the PCM, which I learned about from a post from Tao last week. One thing this mentions is the paradox that under certain conditions, adding roads to a road network can make trips slower, even though each driver tries to minimize their own time spent on the road. (Fortunately, my life is arranged so that I walk almost everywhere; thus at the moment I only appreciate the weirdness of traffic on a theoretical level. But I know it won't always be like that.) I'd be interested to see if this paradox occurs in actual road networks or only in the contrived example that Kelly gives.

The PCM will sell for about $100, so I probably won't buy it when it comes out. But I suspect I will spend some time browsing it when our library gets it.


Fibo said...

NICE Blog :)


Aaron said...

I like Tao's article on differential forms! I've been trying to learn differential forms since September, and I've been having a pretty rough time of it. Tao's article isn't much easier to understand than any of the books I've read, but it is substantially shorter, which is nice.