The Joy of X: A Guided Tour of Math, from One to Infinity - Hardcover

Strogatz, Steven

Hardcover

ISBN 10: 0547517653 ISBN 13: 9780547517650

Publisher: Houghton Mifflin Harcourt, 2012

Synopsis

A world-class mathematician and regular contributor to the New York Times hosts a delightful tour of the greatest ideas of math, revealing how it connects to literature, philosophy, law, medicine, art, business, even pop culture in ways we never imagined

Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.

Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in p, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for theNew York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.

Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight inThe Joy of x.

About this title

About the Author

Steven Strogatz is a professor of applied mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he blogs about math for the New York Times and been a frequent guest on National Public Radio’s RadioLab. In 2007 he received the Communications Award, a lifetime achievement award for the communication of mathematics to the general public. He lives in Ithaca, New York with his wife and two daughters.

Reviews

When Strogatz invites grade-schoolers to construct Möbius strips with scissors, crayons, and tape, he is not expecting them to discover revolutionary new mathematical principles. But he does expect them to experience the kind of intellectual joy that sustains a lifetime of mathematical inquiry. Readers share that joy by joining Strogatz on a high-spirited romp through complex numbers, standard deviations, infinite sums, differential equations, and other mathematical playgrounds. The math arrives in such delightful episodes—a hike through a snow-covered field, for example, or an excited dinner conversation over symbols scribbled on a napkin—and is so often connected to poetry, sports, and popular TV shows that even math phobes will find themselves swept up in the fun. (Who knew that The Sopranos could help us fathom calculus?) To be sure, Strogatz occasionally points well-schooled readers to the rigorous analyses identified in his endnotes. But even those reluctant to venture into deeper waters will finish this book with a new relish for mathematics as a thrilling adventure, not a dreary chore. --Bryce Christensen

Excerpt. © Reprinted by permission. All rights reserved.

PREFACE

I have a friend who gets a tremendous kick out of science, even though he’s an artist. Whenever we get together all he wants to do is chat about the latest thing in psychology or quantum mechanics. But when it comes to math, he feels at sea, and it saddens him. The strange symbols keep him out. He says he doesn’t even know how to pronounce them.

In fact, his alienation runs a lot deeper. He’s not sure what mathematicians do all day, or what they mean when they say a proof is elegant. Sometimes we joke that I should just sit him down and teach him everything, starting with 1 + 1 = 2 and going as far as we can.

Crazy as it sounds, that’s what I’ll be trying to do in this book. It’s a guided tour through the elements of math, from preschool to grad school, for anyone out there who’d like to have a second chance at the subject—but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.

We’ll discover how Michael Jordan’s dunks can help explain the fundamentals of calculus. I’ll show you a simple—and mind-blowing—way to understand that staple of geometry, the Pythagorean theorem. We’ll try to get to the bottom of some of life’s mysteries, big and small: Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How many people should you date before settling down? And we’ll see why some infinities are bigger than others.

Math is everywhere, if you know where to look. We’ll spot sine waves in zebra stripes, hear echoes of Euclid in the Declaration of Independence, and recognize signs of negative numbers in the run-up to World War I. And we’ll see how our lives today are being touched by new kinds of math, as we search for restaurants online and try to understand—not to mention survive—the frightening swings in the stock market.

By a coincidence that seems only fitting for a book about numbers, this one was born on the day I turned fifty. David Shipley, who was then the editor of the op-ed page for the New York Times, had invited me to lunch on the big day (unaware of its semicentennial significance) and asked if I would ever consider writing a series about math for his readers. I loved the thought of sharing the pleasures of math with an audience beyond my inquisitive artist friend.

“The Elements of Math” appeared online in late January 2010 and ran for fifteen weeks. In response, letters and comments poured in from readers of all ages. Many who wrote were students and teachers. Others were curious people who, for whatever reason, had fallen off the track somewhere in their math education but sensed they were missing something worthwhile and wanted to try again. Especially gratifying were the notes I received from parents thanking me for helping them explain math to their kids and, in the process, to themselves. Even my colleagues and fellow math aficionados seemed to enjoy the pieces—when they weren’t suggesting improvements (or perhaps especially then!).

All in all, the experience convinced me that there’s a profound but little-recognized hunger for math among the general public. Despite everything we hear about math phobia, many people want to understand the subject a little better. And once they do, they find it addictive.

The Joy of x is an introduction to math’s most compelling and far-reaching ideas. The chapters—some from the original Times series—are bite-size and largely independent, so feel free to snack wherever you like. If you want to wade deeper into anything, the notes at the end of the book provide additional details and suggestions for further reading.

For the benefit of readers who prefer a step-by-step approach, I’ve arranged the material into six main parts, following the lines of the traditional curriculum.

Part 1, “Numbers,” begins our journey with kindergarten and grade-school arithmetic, stressing how helpful numbers can be and how uncannily effective they are at describing the world.

Part 2, “Relationships,” generalizes from working with numbers to working with relationships between numbers. These are the ideas at the heart of algebra. What makes them so crucial is that they provide the first tools for describing how one thing affects another, through cause and effect, supply and demand, dose and response, and so on—the kinds of relationships that make the world complicated and rich.

Part 3, “Shapes,” turns from numbers and symbols to shapes and space—the province of geometry and trigonometry. Along with characterizing all things visual, these subjects raise math to new levels of rigor through logic and proof.

In part 4, “Change,” we come to calculus, the most penetrating and fruitful branch of math. Calculus made it possible to predict the motions of the planets, the rhythm of the tides, and virtually every other form of continuous change in the universe and ourselves. A supporting theme in this part is the role of infinity. The domestication of infinity was the breakthrough that made calculus work. By harnessing the awesome power of the infinite, calculus could finally solve many long-standing problems that had defied the ancients, and that ultimately led to the scientific revolution and the modern world.

Part 5, “Data,” deals with probability, statistics, networks, and data mining, all relatively young subjects inspired by the messy side of life: chance and luck, uncertainty, risk, volatility, randomness, interconnectivity. With the right kinds of math, and the right kinds of data, we’ll see how to pull meaning from the maelstrom.

As we near the end of our journey in part 6, “Frontiers,” we approach the edge of mathematical knowledge, the borderland between what’s known and what remains elusive. The sequence of chapters follows the familiar structure we’ve used throughout—numbers, relationships, shapes, change, and infinity—but each of these topics is now revisited more deeply, and in its modern incarnation.

I hope that all of the ideas ahead will provide joy—and a good number of Aha! moments. But any journey needs to begin at the beginning, so let’s start with the simple, magical act of counting.

Edition details

• Publisher: Houghton Mifflin Harcourt
• Publication date: 2012
• Language: English
• ISBN 10: 0547517653
• ISBN 13: 9780547517650
• Binding: Hardcover
• Edition number: 1
• Number of pages: 316