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