The Pleasures of Counting

Rating:
Summary: A superb book - well worth reading & re-reading
Review: I came across this book on the 'new acquisitions' shelf of our library. It looked interesting, so I spent a lunch break browsing through a couple of chapters. Come the time to go back to work, and I put my name down on the circulation list.
By the end of the week, I had crossed out my name, leaving the comment: 'I have just bought my own copy'.

This is a great book to dip into on a wet evening. The chapters can stand alone, though many themes recur throughout the book. Each chapter combines a well-written narrative, examples that expand on the underlying mathematics, and numerous sidebars of the highest quality. I particularly liked the one about the extrovert mathematician.

Dr Korner's aim with this book is to lure unsuspecting teenagers into enjoying mathematics. He uses the technique of showing lots of real-world applications, most of which can be readily grasped (and some that are totally gripping). These range from tracing the source of a cholera epidemic, through submarine warfare and Enigma codebreaking, to understanding how the cells that form the walls of blood vessels know when to divide, so as to make the blood vessel just the right size. In most cases the mathematics involved is fairly straightforward: enough to challenge, without intimidating. Some of the mathematical material is developed in the narrative, more in the examples. Just about every page has enough text per equation to ensure readability.

There is a good annotated bibliography, and plenty of references, among which I found many books I had already read and enjoyed. However, the references lack ISBNs.The book - my copy is the paperback - is well laid-out and presented, with a clear typeface and robust binding. It should stand up well to the repeated use it is likely to get.
Buy this book!

Rating:
Summary: a wonderful introduction to the magic of mathematics
Review: If you know a bright teen interested in mathematics or engineering, GIVE THEM THIS BOOK!If you were once a bright teen interested in mathematics and engineering, give yourself this book. This is not an introduction to math. This is an introduction to *using* math to see things you might otherwise miss. Korner is a story-teller (he must be a wonderful lecturer). He covers his subject by telling stories of significant problems and the math that conquered them. The openning chapter tells the story of Dr. Snow's use of statistics to recognize the source of a London cholera epidemic, an epidemic stopped by removing the pump-handle of a London water pump. The subsequent chapters tell the story of operations research in World Wars I and II. In World War I, to counter the threat of German U-boats, was it better to use convoys, or individual ships? Convoys would mean delays --- gathering the ships to start, the convoy could proceed no faster than the slowest ship, and then overload the docks and railroads when they arrived. Which would you choose, and why? Having made your decision, how would you explain it to a math-leery naval officer? Later chapters tell the story of Alan Turing and breaking the enigma codes. This book is challenging, but great fun.

Rating:
Summary: worthwhile read, with some disfiguring flaws
Review: No question, this is a five star book, it is a nice tutorial overview of applied maths, the high point being a presentation of Turing's analysis of the Enigma cypher at Bletchley, which I had never read before.

I was surprised at some of the things cited (the first chapter on operational research in the first world war is not, shall we say, deep) and some of those that do not get cited, but de gustibus non disputandem est. And I would have to say that in general the contents were surprising in the best way, by being ofbeat, and that is good.

Nevertheless, I have a list of quibbles; here are some:

First, he makes some foolishly dismissive - to be kind - remarks about economics, which reveal only that he does not seem to know a lot about the subject.

Second, he makes some foolish jokes about masters and servants; he glosses his description of Halmos's Naive set theory as a gentlemans guide by explaining that a gentleman should know how to drive, but probably prefers to let his chauffeur do it most of the time. He makes similar remarks about valets and algorithms (an algorithm is something that your valet could perform). One gets the feeling he would have been on the prosecution side at the Chaterley trial.

When I was doing my PhD, I remember one of the other students attempted to cultivate a gentleman's attitude to the computer on which he did his research. This was not as endearing a pose as he thought.

Third, maybe less aristocratic disdain about foundations would have improved the final dialogue about the axiomatic method, where complex technical issues are simply brushed under the rug without mention. Yes, the standard axioms for addition and multiplication, plus induction, do define the natural numbers up to isomorphism, but not in a standard first-order language. Surely such a point is germain to the discussion (or reason to have another discussion instead, if you do not want to confuse a beginner with end extensions and non-standard models).

But a nice book, and I look forward to reading bits of it more carefully sometime soon.