CHAPTER ONE: Fun and Games: An introduction to rigorous thought
CHAPTER TWO: Number Contemplation
Section 2.1. Counting [Pigeonhole principle].
Section 2.2. Numerical Patterns in Nature: [Fibonacci numbers].
Section 2.3. Prime cuts of numbers [Prime numbers].
Section 2.4. Crazy clocks and checking out bars [Modular arithmetic].
Section 2.5. Secret Codes and How to Become a Spy [RSA public key cryptography].
Section 2.6. The irrational side of numbers [Irrational numbers].
Section 2.7. Get real [The real number line].
CHAPTER THREE: Infinity
Section 3.1. Beyond Numbers [An introduction to one-to-one correspondence].
Section 3.2. Comparing the Infinite [Examples of one-to-one correspondences].
Section 3.3. The Missing Member [Cantor's diagonalization proof that |N|<|R|].
Section 3.4. Travels Toward the Stratosphere of Infinities [Power set theorem].
Section 3.5. Straightening up the circle [Geometrical correspondences].
CHAPTER FOUR: Geometric Gems
Section 4.1. Pythagoras and his hypotenuse [Blaskara's elegant proof].
Section 4.2. A view of an art gallery [A view-obstruction question from computational geometry].
Section 4.3. The sexiest rectangle [The Golden Rectangle].
Section 4.4. Soothing symmetry and spinning pinwheels [Aperiodic tilings].
Section 4.5. The Platonic Solids Turn Amorous [Symmetry and duality in the Platonic Solids].
Section 4.6. The shape of reality? [Non-Euclidean geometries].
Section 4.7. The Fourth Dimension [Geometry through analogy].
CHAPTER FIVE: Contortions of Space
Section 5.1. Rubber sheet geometry [Topological equivalence by distortion].
Section 5.2. The Band That Wouldn't Stop Playing [Möbius Band and Klein Bottle].
Section 5.3. Circuit training. [The Euler circuit theorem].
Section 5.4. Feeling edgy? [The Euler characteristic].
Section 5.5. Knots and links [A little knot theory].
Section 5.6. Fixed Points, Hot Loops, and Rainy Days [The Brouwer Fixed Point Theorem].
CHAPTER SIX: Fractals and Chaos
Section 6.1. Images [A gallery of fractals].
Section 6.2. The infinitely detailed beauty of fractals [Creating fractals through repeated processes].
Section 6.3. Between dimensions [Fractal dimension].
Section 6.4. The mysterious art of imaginary fractals [Julia and Mandelbrot Sets].
Section 6.5. The Dynamics of Change [Repeated applications of simple processes].
Section 6.6. Predetermined chaos [Deterministic chaos].
CHAPTER SEVEN: Taming Uncertainty
Section 7.1. Chance surprises [Unexpected scenarios involving chance].
Section 7.2. Predicting the future in an uncertain world [Probability].
Section 7.3. Random thoughts [Coincidences].
Section 7.4. Down for the count [Systematic counting].
Section 7.5. Dizzling, Defending, and Doctoring [Probability of Precipitation, game theory, Bayesian probability]
CHAPTER EIGHT: Meaning from Data
Section 8.1. Stumbling Through a Minefield of Data [Pitfalls of statistics].
Section 8.2. Getting Your Data to Shape Up [Organizing, describing, and summarizing data]
Section 8.3. Looking at Super Models [Mathematically described distributions]
Section 8.4. Go Figure [Making inferences from data, hypothesis testing]
Section 8.5. War, Sports, and Tigers [Cause and effect and correlation, Simpson's Paradox, famous applications of inference]
CHAPTER NINE: Deciding Wisely
Section 9.1. Great Expectations [Expected value]
Section 9.2. Risk [Deciding personal and public safety]
Section 9.3. Money Matters [Compound interest]
Section 9.4. Peril at the polls [voting]
Section 9.5. Cutting cake for greedy people [fair division]