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1 Burnside Mathematics- Games and Puzzles

This title in other editions

Impossible? Surprising Solutions to Counterintuitive Conundrums

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Impossible? Surprising Solutions to Counterintuitive Conundrums Cover

 

Synopses & Reviews

Publisher Comments:


In Nonplussed , popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable, and all of it mathematically irrefutable.

Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly. why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion. How is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible?

Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.

Synopsis:

"Julian Havil's Impossible? is a superb discussion of problems easily understood by a high schooler, yet with solutions so counterintuitive as to seem impossible. Topics include the notorious Monty Hall three-door problem, the Gamow-Stern elevator paradoxes, the Kruskal count card trick, Cantor's 'paradise' of alephs, and the mind-blowing Banach-Tarski paradox, all analyzed in depth by a master who does not hold back equations that provide elegant proofs. There are surprises on almost every page."--Martin Gardner

"This book is a fascinating and thoroughly enjoyable read. Havil offers an engaging collection of counterintuitive results and seemingly impossible problems. Some of the material is truly astonishing, and the author conveys his sense of surprise very effectively. Each problem ultimately yields to careful and well-presented analysis. The history of many of the results is discussed, and further references are provided."--Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles

"I thought it impossible for Julian Havil to exceed Nonplussed!, his previous collection of perplexing math puzzlers. And yet he has done just that with the sequel Impossible?, an accomplishment that has left me nonplussed."--Paul J. Nahin, author of An Imaginary Tale

Synopsis:

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable--and all of it mathematically irrefutable.

Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly--why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion--how is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible?

Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.

About the Author

Julian Havil is a master at Winchester College, England, where he has taught mathematics for more than thirty years. He is the author of "Nonplussed!: Mathematical Proof of Implausible Ideas" and "Gamma: Exploring Euler's Constant" (both Princeton).

Table of Contents

Acknowledgments xi

Introduction 1

Chapter 1: It's Common Knowledge 3

Chapter 2: Simpson's Paradox 11

Chapter 3: The Impossible Problem 21

Chapter 4: Braess's Paradox 31

Chapter 5: The Power of Complex Numbers 39

Chapter 6: Bucking the Odds 50

Chapter 7: Cantor's Paradise 68

Chapter 8: Gamow-Stern Elevators 82

Chapter 9: The Toss of a Coin 88

Chapter 10: Wild-Card Poker 103

Chapter 11: Two Series 113

Chapter 12: Two Card Tricks 131

Chapter 13: The Spin of a Needle 146

Chapter 14: The Best Choice 165

Chapter 15: The Power of Powers 176

Chapter 16: Benford's Law 190

Chapter 17: Goodstein Sequences 201

Chapter 18: The Banach-Tarski Paradox 210

The Motifs 217

Appendix 221

Index 233

Product Details

ISBN:
9780691131313
Subtitle:
Surprising Solutions to Counterintuitive Conundrums
Author:
Havil, Julian
Publisher:
Princeton University Press
Location:
Princeton
Subject:
Mathematics
Subject:
Probability & Statistics - General
Subject:
Applied
Subject:
Statistics
Subject:
Problem solving -- Miscellanea.
Subject:
Mathematics - General
Subject:
Popular science
Copyright:
Publication Date:
April 2008
Binding:
Hardback
Grade Level:
College/higher education:
Language:
English
Illustrations:
75 line illus.
Pages:
264
Dimensions:
9 x 6 in

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Related Subjects


Reference » Science Reference » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Games and Puzzles
Science and Mathematics » Mathematics » General

Impossible? Surprising Solutions to Counterintuitive Conundrums Used Hardcover
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Product details 264 pages Princeton University Press - English 9780691131313 Reviews:
"Synopsis" by ,

"Julian Havil's Impossible? is a superb discussion of problems easily understood by a high schooler, yet with solutions so counterintuitive as to seem impossible. Topics include the notorious Monty Hall three-door problem, the Gamow-Stern elevator paradoxes, the Kruskal count card trick, Cantor's 'paradise' of alephs, and the mind-blowing Banach-Tarski paradox, all analyzed in depth by a master who does not hold back equations that provide elegant proofs. There are surprises on almost every page."--Martin Gardner

"This book is a fascinating and thoroughly enjoyable read. Havil offers an engaging collection of counterintuitive results and seemingly impossible problems. Some of the material is truly astonishing, and the author conveys his sense of surprise very effectively. Each problem ultimately yields to careful and well-presented analysis. The history of many of the results is discussed, and further references are provided."--Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles

"I thought it impossible for Julian Havil to exceed Nonplussed!, his previous collection of perplexing math puzzlers. And yet he has done just that with the sequel Impossible?, an accomplishment that has left me nonplussed."--Paul J. Nahin, author of An Imaginary Tale

"Synopsis" by ,

In Nonplussed!, popular-math writer Julian Havil delighted readers with a mind-boggling array of implausible yet true mathematical paradoxes. Now Havil is back with Impossible?, another marvelous medley of the utterly confusing, profound, and unbelievable--and all of it mathematically irrefutable.

Whenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly--why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion--how is this possible? What does the game show Let's Make A Deal reveal about the unexpected hazards of decision-making? What can the game of cricket teach us about the surprising behavior of the law of averages? These are some of the counterintuitive mathematical occurrences that readers encounter in Impossible?

Havil ventures further than ever into territory where intuition can lead one astray. He gathers entertaining problems from probability and statistics along with an eclectic variety of conundrums and puzzlers from other areas of mathematics, including classics of abstract math like the Banach-Tarski paradox. These problems range in difficulty from easy to highly challenging, yet they can be tackled by anyone with a background in calculus. And the fascinating history and personalities associated with many of the problems are included with their mathematical proofs. Impossible? will delight anyone who wants to have their reason thoroughly confounded in the most astonishing and unpredictable ways.

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