13 November 2008

In which I buy the Princeton Companion to Mathematics

I cashed in 5.793 kilograms of assorted coins today at the bank. That's $115.19, for a density of $19.88 per kilogram; I know the weight because the bank's coin counting machine gave a receipt that had the numbers of each type of coin I received. I then immediately proceeded to the bookstore and purchased the The Princeton Companion to Mathematics (That was $106 with sales tax; perhaps I should have bought it from Amazon.com, where it's cheaper. Oh well, it's too late now. But at ten cents a page it's still a good deal.) I told myself I wouldn't buy it, but I'm doing some private tutoring on the side, and so there's a bit of extra money floating around, and I couldn't help myself...

I want to compliment the design of it; the side of the book which faces out on the shelf has "The Princeton Companion to" in small letters and then "Mathematics" in large letters, perhaps giving the impression that the book contains all of mathematics. This is not true, but from the portions of it I've seen online and the part I've read so far, it seems to admirably solve the optimization problem of squishing down mathematics to an object that only weighs five pounds. That's less than the coins I hauled to the bank to get the cash I paid for it! For links to various reviews, see this entry from Tim Gowers' blog. Gowers is the editor, and also wrote substantial parts of the book, although it has many other contributors; you can play the party game "how many of these names do I recognize?" I was interested to see that I recognize many more than I would have when I started grad school.

Yes, I'm actually trying to read it cover-to-cover. Like many mathematicians, there are a bunch of things that people seem to assume I'm familiar with, but I only heard about very briefly in some course in my first year of grad school in which I was holding on by the skin of my teeth. Indeed, this is one of the uses that's recommended in the introduction! I will resist the urge to turn this blog into a Companion to the Princeton Companion to Mathematics.


Anonymous said...

My copy arrived a few weeks ago (I did get it from Amazon at the remarkable price of AU$75). I've dipped into a few times since then but, unfortunately, I don't think I'll get a chance to read it cover-to-cover, mainly because my first daughter, Ada, arrived around the same time and is cornering more of my attention than mathematics. (I'm pretty sure glad to be able to say that, though it's hard to say with the lack of sleep and all.)

I would be very interested to read about any particularly good articles from the Companion here in your blog. Maybe you could do a mini-Companion to the Companion for the probability related articles?

Anonymous said...

Ooh, I think I had heard of this before but now I really want it. I just looked at the table of contents and started drooling.

MFamulare said...

Long time lurker here...

Which bank do you use? I'm trying to find one that'll count my ~6 kg of coins for me without charging 9%.

Mark Dominus said...

I would not be sorry to see your companion articles to the Princeton Companion to Mathematics.

Michael Lugo said...

@intrinsicallyknotted: I didn't think I was going to buy it either. But I was in the bookstore Wednesday and I saw it and started drooling. Then I was at home Thursday and saw the big jar of change, which I figured was about $100, and I connected the dots.

@mike: in the Philadelphia area, Commerce Bank has long had this service; they're now TD Bank, as of a few weeks ago. It looks from the TD Bank web page that all TD branches (not just the ones that used to be Commerce) do this.

CarlBrannen said...

Having been in the pinball business for some years, pretty much any bank will accept your change if you roll it for them; and they will typically provide you with the rolls for free.

Of course I had a quarter counting machine that rolled them for me. It required constant repairs and shipped in the odd quarter every now and then.

Because of my long experience counting big piles of money, my faith in mathematics decreased considerably. Some of the rules that seem to apply to small sums do not apply at all to large sums.

In particular, if you count the coins in two piles and compute their total values you get two integers (i.e. muliples of 0.01). If you combine the two piles into a single pile and count that, you won't necessarily get the sum of the two values.

Unfortunately, the differences are not typically positive so there doesn't seem to be a way to extract free money from the environment this way. :(

Michael Lugo said...


that's a good point. But rolling the money takes time, so it might be worthwhile to seek out a bank that offers free coin-counting. (I'm not sure what my speed at coin-counting is, because I have always sought out such machines.)

Peter Krumins said...

I just got it! (happy smiling face)

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