Rediscovering Mathematics is a guide to more effective mathematical education, offering topics and puzzles that can inspire a renewed interest in mathematics among students and enthusiasts. Suitable for anyone wanting to expand their view of mathematics, the book's topics are linked by the theme of mathematical learning through investigation, challenge, and discovery. This book can be used as a text for training mathematics teachers at all levels, and is recommended for anyone interested in mathematics and how mathematics should be taught. Containing dozens of illustrations, tables, and exercises, the book focuses on problem solving and understanding, subsuming learning by memorization. Topics range from number theory and applications, to secure Internet communication, to probability in sports and gambling.

• Includes nearly 200 end-of-chapter exercises • Frequent challenges with hints and solutions are offered throughout • The focus on learning through problem-solving and understanding is enhanced by linking mathematical topics to everyday-life scenarios

### Contents

Acknowledgements; A guide for the reader; Introduction - how to read mathematics; 1. Mathematical discovery in the classroom; 2. Don't reach for your calculator (yet); 3. Have another piece of pie, Zeno?; 4. Thinking like a mathematician - lessons from a medieval Rabbi; 5. What's mathematics good for?; 6. Three averages; 7. Algorithms - the unexpected role of pure mathematics; 8. Pythagoras' Theorem and math by pictures; 9. Memorizing versus understanding; 10. Games and gambling; 11. Soccer balls and counting tricks; 12. Pizza Pi and area; 13. Back to the classroom; Resources for rediscovering mathematics; Further reading; Index.