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Table of Contents
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.
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.