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Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction

Popular Science

By: Paul J Nahin

400 pages, 4 halftones, 98 line drawings, 6 tables

Princeton University Press

Hardback | Sep 2011 | #194239 | ISBN-13: 9780691144252
Availability: Usually dispatched within 5 days Details
NHBS Price: £19.95 $25/€24 approx

About this book

How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What's the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in "Number-Crunching".

Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today's powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished. Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler's ruin problems.

Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions. Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, "Number-Crunching" will appeal to anyone interested in understanding how these three important fields join forces to solve today's thorniest puzzles.

Great stories. Interesting and challenging problems. Instructive MATLAB code. Lots of physics. That's my in-a-nutshell assessment... Nahin takes on the subject of using computers to solve difficult problems, many in physics, that couldn't be solved before computers... This is one of those books that one can read as a spectator, enjoying the scenery, taking in the landscape, appreciating the rich stories--my relationship with the book--or one can dive in, study the many equations, run the code, and have a personal experience of how problems that were unsolvable just a few decades ago have succumbed to computers. -- Sol Lederman, Wild About Math


Contents

Introduction x

Chapter 1: Feynman Meets Fermat 1
Chapter 2: Just for Fun: Two Quick Number-Crunching Problems 16
Chapter 3: Computers and Mathematical Physics 27
Chapter 4: The Astonishing Problem of the Hanging Masses 82
Chapter 5: The Three-Body Problem and Computers 131
Chapter 6: Electrical Circuit Analysis and Computers 218
Chapter 7: The Leapfrog Problem 288
Chapter 8: Science Fiction: When Computers Become Like Us 297
Chapter 9: A Cautionary Epilogue 328

Appendix
(FPU Computer Experiment MATLAB Code) 335
Solutions to the Challenge Problems 337

Acknowledgments 371
Index 373
Also by Paul J. Nahin 377

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Biography

Paul J. Nahin is the author of many best-selling popular math books, including "Mrs. Perkins's Electric Quilt", "Digital Dice", "Chases and Escapes", "Dr. Euler's Fabulous Formula", "When Least Is Best", and "An Imaginary Tale". He is professor emeritus of electrical engineering at the University of New Hampshire.

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