Preface ix
Part 1 Numbers
1. From Fish to Infinity 3
An introduction to numbers, pointing out their upsides (they're efficient) as well as their downsides (they're ethereal)
2. Rock Groups 7
Treating numbers concretely-think rocks-can make calculations less baffling.
3. The Enemy of My Enemy 15
The disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so … negative
4. Commuting 23
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 29
Helping Verizon grasp the difference between .002 dollars and .002 cents
6. Location, Location, Location 35
How the place-value system for writing numbers brought arithmetic to the masses
Part 2 Relationships
7. The Joy of x 45
Arithmetic becomes algebra when we begin working with unknowns and formulas
8. Finding Your Roots 51
Complex numbers, a hybrid of the imaginary and the real, are the pinnacle of number systems
9. My Tub Runneth Over 59
Turning peril to pleasure in word problems
10. Working Your Quads 67
The quadratic formula may never win any beauty contests, but the ideas behind it are ravishing.
11. Power Tools 75
In math, the function of functions is to transform.
Part 3 Shapes
12. Square Dancing 85
Geometry, intuition, and the long road from Pythagoras to Einstein
13. Something from Nothing 93
Like any other creative act, constructing a proof begins with inspiration.
14. The Conic Conspiracy 101
The uncanny similarities between parabolas and ellipses suggest hidden forces at work.
15. Sine Qua Non 113
Sine waves everywhere, from Ferris wheels to zebra stripes
16. Take It to the Limit 121
Archimedes recognized the power of the infinite and in the process laid the groundwork for calculus.
Part 4 Change
17. Change We Can Believe In 131
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 139
The lasting legacy of integral calculus is a Veg-O-Matic view of the universe.
19. All about e 147
How many people should you date before settling down? Your grandmother knows-and so does the number e.
20. Loves Me, Loves Me Not 155
Differential equations made sense of planetary motion. But the course of true love? Now that's confusing.
21. Step Into the Light 161
A light beam is a pas de deux of electric and magnetic fields, and vector calculus is its choreographer.
Part 5 Data
22. The New Normal 175
Bell curves are out. Fat tails are in.
23. Chances Are 183
The improbable thrills of probability theory
24. Untangling the Web 191
How Google solved the Zen riddle of Internet search using linear algebra
Part 6 Frontiers
25. The Loneliest Numbers 201
Prime numbers, solitary and inscrutable, space themselves apart in mysterious ways
26. Group Think 211
Group theory, one of the most versatile parts of math, bridges art and science
27. Twist and Shout 219
Playing with Möbius strips and music boxes, and a better way to cut a bagel
28. Think Globally 229
Differential geometry reveals the shortest route between two points on a globe or any other curved surface
29. Analyze This! 237
Why calculus, once so smug and cocky, had to put itself on the couch
30. The Hilbert Hotel 249
An exploration of infinity as this book, not being infinite, comes to an end
Acknowledgments 257
Notes 261
Credits 307
Index 309