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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 | |