Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Foreword: The Synergy of Pure and Applied Mathematics, of the Abstract and the Concrete ix
4. Introduction xvii
5. Why Math Works 1
6. Is Mathematics Discovered or Invented? 8
7. The Unplanned Impact of Mathematics 21
8. An Adventure in the Nth Dimension 30
9. Structure and Randomness in the Prime Numbers 43
10. The Strangest Numbers in String Theory 50
11. Mathematics Meets Photography: The Viewable Sphere 61
12. Dancing Mathematics and the Mathematics of Dance 79
13. Can One Hear the Sound of a Theorem? 93
14. Flat-Unfoldability and Woven Origami Tessellations 113
15. A Continuous Path from High School Calculus to University Analysis 129
16. Mathematics Teachers’ Subtle, Complex Disciplinary Knowledge 135
17. How to Be a Good Teacher Is an Undecidable Problem 141
18. How Your Philosophy of Mathematics Impacts Your Teaching 149
19. Variables in Mathematics Education 163
20. Bottom Line on Mathematics Education 173
21. History of Mathematics and History of Science Reunited? 176
22. Augustus De Morgan behind the Scenes 186
23. Routing Problems: A Historical Perspective 197
24. The Cycloid and Jean Bernoulli 209
25. Was Cantor Surprised? 216
26. Why Is There Philosophy of Mathematics at All? 234
27. Ultimate Logic: To Infinity and Beyond 255
28. Mating, Dating, and Mathematics: It’s All in the Game 262
29. Contributors 273
30. Notable Texts 281
31. Acknowledgments 285
32. Credits 287