*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.

## 2 comments:

NICE Blog :)

HAPPY NEW YEAR :)

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

issubstantially shorter, which is nice.Post a Comment