The joy of X : a guided tour of math, from one to infinity
(Book)

pt. 1. 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 -- pt. 2. 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 -- pt. 3. 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 --

pt. 4. 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

pt. 5. 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

pt. 6. 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.