The Joy of X

by Strogatz, Steven

• ISBN13: 9780547517650
• ISBN10: 0547517653
• Format: Hardcover
• Copyright: 2012-10-02
• Publisher: Houghton Mifflin Harcourt

Summary

In 2010, award-winning professor Steven Strogatz wrote a series for the New York Timesonline called "The Elements of Math." It was a huge success. Each piece climbed the most emailed list and elicited hundreds of comments. Readers begged for more, and Strogatz has now delivered. In this fun, fast-paced book, he offers us all a second chance at math.Each short chapter of The Joy of Xprovides an "Aha!" moment, starting with why numbers are helpful, and moving on to such topics as shapes, calculus, fat tails, and infinity. Strogatz explains the ideas of math gently and clearly, with wit, insight, and brilliant illustrations. Assuming no knowledge, only curiosity, he shows how math connects to literature, philosophy, law, medicine, art, business, even pop culture and current events. For example, 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? Strogatz is the math teacher you wish you'd had, and The Joy of X is the book you'll want to give to all your smart and curious friends.

Table of Contents

Preface	p. ix
Numbers
From Fish to Infinity	p. 3
An introduction to numbers, pointing out their upsides (they're efficient) as well as their downsides (they're ethereal)
Rock Groups	p. 7
Treating numbers concretely-think rocks-can make calculations less baffling.
The Enemy of My Enemy	p. 15
The disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so… negative
Commuting	p. 23
When you buy jeans on sale, do you save more money if the clerk applies the discount after the tax, or before?
Division and Its Discontents	p. 29
Helping Verizon grasp the difference between .002 dollars and .002 cents
Location, Location, Location	p. 35
How the place-value system for writing numbers brought arithmetic to the masses
Relationships
The Joy of x	p. 45
Arithmetic becomes algebra when we begin working with unknowns and formulas.
Finding Your Roots	p. 51
Complex numbers, a hybrid of the imaginary and the real, are the pinnacle of number systems.
My Tub Runneth Over	p. 59
Turning peril to pleasure in word problems
Working Your Quads	p. 67
The quadratic formula may never win any beauty contests, but the ideas behind it are ravishing.
Power Tools	p. 75
In math, the function of functions is to transform.
Shapes
Square Dancing	p. 85
Geometry, intuition, and the long road from Pythagoras to Einstein
Something from Nothing	p. 93
Like any other creative act, constructing a proof begins with inspiration.
The Conic Conspiracy	p. 101
The uncanny similarities between parabolas and ellipses suggest hidden forces at work.
Sine Qua Non	p. 113
Sine waves everywhere, from Ferris wheels to zebra stripes
Take It to the Limit	p. 121
Archimedes recognized the power of the infinite and in the process laid the groundwork for calculus.
Change
Change We Can Believe In	p. 131
Differential calculus can show you the best path from A to B, and Michael Jordan's dunks help explain why.
It Slices, It Dices	p. 139
The lasting legacy of integral calculus is a Veg-O-Matic view of the universe.
All about e	p. 147
How many people should you date before settling down? Your grandmother knows-and so does the number e.
Loves Me, Loves Me Not	p. 155
Differential equations made sense of planetary motion. But the course of true love? Now that's confusing.
Step Into the Light	p. 161
A light beam is a pas de deux of electric and magnetic fields, and vector calculus is its choreographer.
Data
The New Normal	p. 175
Bell curves are out. Fat tails are in.
Chances Are	p. 183
The improbable thrills of probability theory
Untangling the Web	p. 191
How Google solved the Zen riddle of Internet search using linear algebra
Frontiers
The Loneliest Numbers	p. 201
Prime numbers, solitary and inscrutable, space themselves apart in mysterious ways.
Group Think	p. 211
Group theory, one of the most versatile parts of math, bridges art and science.
Twist and Shout	p. 219
Playing with Möbius strips and music boxes, and a betterway to cut a bagel
Think Globally	p. 229
Differential geometry reveals the shortest route between two points on a globe or any other curved surface.
Analyze This!	p. 237
Why calculus, once so smug and cocky, had to put itself on the couch
The Hilbert Hotel	p. 249
An exploration of infinity as this book, not being infinite, comes to an end
Acknowledgments	p. 257
Notes	p. 261
Credits	p. 307
Index	p. 309
Table of Contents provided by Ingram. All Rights Reserved.

Excerpts

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.