Mathematics Galore! The First Five Years of the St. Mark's Institute of Mathematics Classroom Resource Materials Series

The author of this book believes that there is too much rote learning and not enough creative exploration in mathematical education. To remedy this he has produced a book that promotes intellectual play and adaptability of thought by engaging the reader in mathematical activities. Twenty-six chapters examine a wide variety of mathematical teasers and problems and the mathematics behind them is explained and proved via natural and accessible means. This is an excellent recreational maths book that also serves as a source of inspiration for teachers of mathematics. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, and enjoy for yourself the bounty of additional research questions and intriguing puzzles that lie within.

Introduction; Newsletters and commentaries; 1. Arctangents; 2. Benford's Law; 3. Braids; 4. CLIP Theory; 5. Dots and dashes; 6. Factor trees; 7. Folding fractions and conics; 8. Folding patterns and dragons; 9. Folding and pouring; 10. Fractions; 11. Integer triangles; 12. Lattice polygons; 13. Layered tilings; 14. The middle of a triangle; 15. Partitions; 16. Personalized polynomials; 17. Playing with Pi; 18. Pythagoras's Theorem; 19. On reflection; 20. Repunits and primes; 21. The Stern–Brocot Tree; 22. Tessellations; 23. Theon's ladder and squangular numbers; 24. Tilings and theorems; 25. The Tower of Hanoi; 26. Weird multiplication; Appendices: 1. Numbers that are the sum of two squares; 2. Pick's theorem; 3. The Möbius function; 4. The Borsuk-Ulam theorem; 5. Galilean ratios; 6. A candy-sharing game; 7. Bending Buffon's needle; 8. On separating dots; Indexes: 1. Index of terms; 2. Index of topics; 3. Classic theorems proved.

James Tanton is the founding director of the St Mark's Institute of Mathematics, an outreach program designed to promote joyful and effective mathematics education. He is a full-time high school teacher at St Mark's School, Southborough, MA, and he conducts mathematics graduate courses for teachers through Northeastern University's School of Education.