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The Joy of X
A Guided Tour of Mathematics, from One to Infinity
Steven Strogatz
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eBook - ePub
The Joy of X
A Guided Tour of Mathematics, from One to Infinity
Steven Strogatz
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About This Book
Award-winning Steven Strogatz, one of the foremost popularisers of maths, has written a witty and fascinating account of maths' most compelling ideas and how, so often, they are an integral part of everyday life. Maths is everywhere, often where we don't even realise. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the unitiated - connect pop culture, literature, art, philosophy, current affairs, business and even every day life. In The Joy of X, Strogatz explains the great ideas of maths - from negative numbers to calculus, fat tails to infinity - with clarity, wit and insight. He is the maths teacher you never had and this book is perfect for the smart and curious, the expert and the beginner.
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Topic
MatemáticasSubtopic
Matemáticas generalContents
Preface
Part One NUMBERS
1. From Fish to Infinity
An introduction to numbers, pointing out their upsides (they’re efficient) as well as their downsides (they’re ethereal)
2. Rock Groups
Treating numbers concretely — think rocks — can make calculations less baffling.
3. The Enemy of My Enemy
The disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so . . . negative
4. Commuting
When you buy jeans on sale, do you save more money if the clerk applies the discount after the tax, or before?
5. Division and Its Discontents
Helping Verizon grasp the difference between .002 dollars and .002 cents
6. Location, Location, Location
How the place-value system for writing numbers brought arithmetic to the masses
Part Two RELATIONSHIPS
7. The Joy of x
Arithmetic becomes algebra when we begin working with unknowns and formulas.
8. Finding Your Roots
Complex numbers, a hybrid of the imaginary and the real, are the pinnacle of number systems.
9. My Tub Runneth Over
Turning peril to pleasure in word problems
10. Working Your Quads
The quadratic formula may never win any beauty contests, but the ideas behind it are ravishing.
11. Power Tools
In maths, the function of functions is to transform.
Part Three SHAPES
12. Square Dancing
Geometry, intuition, and the long road from Pythagoras to Einstein
13. Something from Nothing
Like any other creative act, constructing a proof begins with inspiration.
14. The Conic Conspiracy
The uncanny similarities between parabolas and ellipses suggest hidden forces at work.
15. Sine Qua Non
Sine waves everywhere, from Ferris wheels to zebra stripes
16. Take It to the Limit
Archimedes recognized the power of the infinite and in the process laid the groundwork for calculus.
Part Four CHANGE
17. Change We Can Believe In
Differential calculus can show you the best path from A to B, and Michael Jordan’s dunks help explain why.
18. It Slices, It Dices
The lasting legacy of integral calculus is a Veg-O-Matic view of the universe.
19. All about e
How many people should you date before settling down? Your grandmother knows — and so does the number e.
20. Loves Me, Loves Me Not
Differential equations made sense of planetary motion. But the course of true love? Now that’s confusing.
21. Step Into the Light
A light beam is a pas de deux of electric and magnetic fields, and vector calculus is its choreographer.
Part Five DATA
22. The New Normal
Bell curves are out. Fat tails are in.
23. Chances Are
The improbable thrills of probability theory
24. Untangling the Web
How Google solved the Zen riddle of Internet search using linear algebra
Part Six FRONTIERS
25. The Loneliest Numbers
Prime numbers, solitary and inscrutable, space themselves apart in mysterious ways.
26. Group Think
Group theory, one of the most versatile parts of maths, bridges art and science.
27. Twist and Shout
Playing with Möbius strips and music boxes, and a better way to cut a bagel
28. Think Globally
Differential geometry reveals the shortest route between two points on a globe or any other curved surface.
29. Analyze This!
Why calculus, once so smug and cocky, had to put itself on the couch
30. The Hilbert Hotel
An exploration of infinity as this book, not being infinite, comes to an end
Acknowledgments
Notes
Credits
Index
Note on the Author
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 maths, 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 maths, 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 maths 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.
Maths 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 maths, 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 maths for his readers. I loved the thought of sharing the pleasures of maths 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 maths 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 maths to their kids and, in the process, to themselves. Even my colleagues and fellow maths 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 maths among the general public. Despite everything we hear about maths 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 maths’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 e...