Part 1. Numbers. From fish to infinity : an introduction to numbers, pointing out their upsides (they're efficient) as well as their downsides (they're ethereal) ; Rock groups: Treating numbers concretely--think rocks--can make calculations less baffling ; The enemy of my enemy : the disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so negative ; Commuting : when you buy jeans on sale, do you save more money if the clerk applies the discount after the tax, or before? ; Division and its discontents : helping Verizon grasp the difference between .002 dollars and .002 cents ; Location, location, location : how the place-value system for writing numbers brought arithmetic to the masses -- Part 2. Relationships. The joy of x : arithmetic becomes algebra when we begin working with unknowns and formulas ; Finding your roots : complex numbers, a hybrid of the imaginary and the real, are the pinnacle of number systems ; My tub runneth over : turning peril to pleasure in word problems ; Working your quads : the quadratic formula may never win any beauty contests, but the ideas behind it are ravishing ; Power tools : in math, the function of functions is to transform -- Part 3. Shapes. Square dancing : geometry, intuition, and the long road from Pythagoras to Einstein ; Something from nothing : like any other creative act, constructing a proof begins with inspiration ; The conic conspiracy : the uncanny similarities between parabolas and ellipses suggest hidden forces at work ; Sine qua non : Sine waves everywhere, from Ferris wheels to zebra stripes ; Take it to the limit : Archimedes recognized the power of the infinite and in the process laid the groundwork for calculus.
Part 4. Change. 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 ; It slices, it dices : the lasting legacy of integral calculus is a Veg-O-Matic view of the universe ; All about e : how many people should you date before settling down? Your grandmother knows, and so does the number e ; Loves me, loves me not : differential equations made sense of planetary motion. But the course of true love? Now that's confusing ; Step into the light : a light beam is a pas de deux of electric and magnetic fields, and vector calculus is its choreographer -- Part 5. Data. The new normal : Bell curves are out. Fat tails are in ; Chances are : the improbable thrills of probability theory ; Untangling the Web : how Google solved the Zen riddle of Internet search using linear algebra -- Part 6. Frontiers. The loneliest numbers : prime numbers, solitary and inscrutable, space themselves apart in mysterious ways ; Group think : group theory, one of the most versatile parts of math, bridges art and science ; Twist and shout : playing with Möbius strips and music boxes, and a better way to cut a bagel ; Think globally : differential geometry reveals the shortest route between two points on a globe or any other curved surface ; Analyze this! : Why calculus, once so smug and cocky, had to put itself on the couch ; The Hilbert Hotel : an exploration of infinity as this book, not being infinite, comes to an end.
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