Table of Contents for Joy of X : A Guided Tour of Math, from One to Infinity


Preface ix
Part One NUMBERS
1 From Fish to Infinity
3(4)
An introduction to numbers, pointing out their upsides (they're efficient) as well as their downsides (they're ethereal)
2 Rock Groups
7(8)
Treating numbers concretely---think rocks---can make calculations less baffling
3 The Enemy of My Enemy
15(8)
The disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so... negative
4 Commuting
23(6)
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
29(6)
Helping Verizon grasp the difference between .002 dollars and .002 cents
6 Location, Location, Location
35(10)
How the place-value system for writing numbers brought arithmetic to the masses
Part Two RELATIONSHIPS
7 The Joy of x
45(6)
Arithmetic becomes algebra when we begin working with unknowns and formulas
8 Finding Your Roots
51(8)
Complex numbers, a hybrid of the imaginary and the real, are the pinnacle of number systems
9 My Tub Runneth Over
59(8)
Turning peril to pleasure in word problems
10 Working Your Quads
67(8)
The quadratic formula may never win any beauty contests, but the ideas behind it are ravishing
11 Power Tools
75(10)
In math, the function of functions is to transform
Part Three SHAPES
12 Square Dancing
85(8)
Geometry, intuition, and the long road from Pythagoras to Einstein
13 Something from Nothing
93(8)
Like any other creative act, constructing a proof begins with inspiration
14 The Conic Conspiracy
101(12)
The uncanny similarities between parabolas and ellipses suggest hidden forces at work
15 Sine Qua Non
113(8)
Sine waves everywhere, from Ferris wheels to zebra stripes
16 Take It to the Limit
121(10)
Archimedes recognized the power of the infinite and in the process laid the groundwork for calculus
Part Four CHANGE
17 Change We Can Believe In
131(8)
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
139(8)
The lasting legacy of integral calculus is a Veg-O-Matic view of the universe
19 All about e
147(8)
How many people should you date before settling down? Your grandmother knows---and so does the number e
20 Loves Me, Loves Me Not
155(6)
Differential equations made sense of planetary motion. But the course of true love? Now that's confusing
21 Step Into the Light
161(14)
A light beam is a pas de deux of electric and magnetic fields, and vector calculus is its choreographer
Part Five DATA
22 The New Normal
175(8)
Bell curves are out. Fat tails are in
23 Chances Are
183
The improbable thrills of probability theory