Nonplussed!: Mathematical Proof of Implausible Ideas

by Julian Havil

Book Overview

Math--the application of reasonable logic to reasonable assumptions--usually produces reasonable results. But sometimes math generates astonishing paradoxes--conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than...

• Format: Hardcover
• Language: English
• ISBN: 0691120560
• ISBN13: 9780691120560
• Release Date: April 2007
• Publisher: Princeton University Press
• Length: 216 Pages
• Weight: 1.05 lbs.
• Dimensions: 0.8" x 6.0" x 9.3"

Customer Reviews

Fascinating

This book will delight readers who like to get their hands into their math. Havil sticks to mostly elementary concepts, avoiding highly abstract fields that would lose most readers. When a subject could go too far afield, Havil warns about it and presents only the part the reader needs to know, citing original source references for the interested reader. He gives complete, understandable proofs of some startling statements--proofs that leave you understanding exactly how you got there. The great thing is that you can choose to work through these problems for yourself, verifying each step, or you can just follow along with his proofs and take on faith any simple algebraic rearrangements that he may have skipped over. Compared to Havil's earlier classic on Euler's Gamma Function, this one's a bit easier to read, with numerous short sections on a variety of topics. One minor complaint is that I found some typesetting errors. One, ironically, occurs on page 49 where he uses the notation "!n" (the number of derangements of n objects) when actually he meant "n!" (the number of permutations of n objects). It's ironic because only two paragraphs later Havil warns that !n can be easily confused with n!, whereupon he adopts a new notation for !n. In the delightfully bizarre but challenging chapter on John Conway's Fractran, there are a few typos that might confuse that minority of readers who will actually try to go line-by-line through the explanation of the Fractran machine (p. 172), but if you're one of those people, discovering the errors will anyway prove your mastery.

A real brain teaser

The book of Julian Havil is certainly not easy reading. Perhaps I am a dummy, but at several pages I had to read over a paragraph several times before understanding its real meaning, but the result was always worth the trouble. The calculations itself are explained thoroughly and his way of highlighting different sidesteps are often eye-openers. People loving Martin Gardner's articles in Scientific American, will certainly appreciate this book.