The joy of x: a guided tour of math, from one to infinity

Preface

Part 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

Part 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.

Part 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.

Part 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.

Part 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

Part 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

Acknowledgments

Notes

Credits

Index

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.