Introduction: How to read mathematics. An example of mathematical writing-the birthday paradox -- Our reader tackles the birthday paradox -- Challenges -- 1. Mathematical discovery in the classroom. A simple lesson -- The math teacher as conductor -- The effective teacher -- Challenges -- 2. Don't reach for your calendar (Yet). A magic trick -- Clever calculations -- Pythagorean triples -- Challenges -- 3. Have another piece of pie, Zeno? A simpler way -- Euclid, proofs, and writing mathematics -- Challenges -- 4. Thinking like a mathematician- Lessons from a medieval rabbi. Rabbi Levi ben Gershon and his sums -- The number of squares and rectangles in a grid -- The triangle puzzle-a model mathematics problem -- Challenges -- 5. What is mathematics good for? Knock hockey -- Basketball -- Rates of growth -- Challenges -- 6. Three averages. Average I. The Arithmetic Average -- Average II. The Harmonic Average -- Average III. The Geometric Average -- Exploring averages -- Challenges -- 7. Algorithms- the unexpected role of pure mathematics. A solution to the two jug puzzle -- Euclid's Algorithm -- Other methods for calculating greatest common divisors -- The efficiency (or speed) of an algorithm -- The Egyptian Mutliplication Algorithm -- The fast Modular Exponential Algorithm -- Greatest Common Divisors, algorithms, and e-commerce -- E-commerce and cryptography -- The rest of the story-the RSA Algorithm -- Challenges -- 8. Pythagoras' theorem and |