**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]