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The Joy of x: A Guided Tour of Math, from One to Infinity

Steven Strogatz

Table of Contents

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 math, 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 math, 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