The Myth of Leibniz’s Proof of the Fundamental Theorem of Calculus

Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Introduction xi
4. Mathematics and Teaching 1
5. In Defense of Pure Mathematics 17
6. G. H. Hardy: Mathematical Biologist 27
7. The Reasonable Ineffectiveness of Mathematics 32
8. Stacking Wine Bottles Revisited 48
9. The Way the Billiard Ball Bounces 66
10. The Intersection Game 77
11. Tonight! Epic Math Battles: Counting vs. Matching 86
12. Mathematicians Chase Moonshine’s Shadow 96
13. The Impenetrable Proof 105
14. A Proof That Some Spaces Can’t Be Cut 114
15. Einstein’s First Proof 122
16. Why String Theory Still Offers Hope We Can Unify Physics 132
17. The Pioneering Role of the Sierpinski Gasket 140
18. Fractals as Photographs 149
19. Math at the Met 155
20. Common Sense about the Common Core 187
21. Explaining Your Math: Unnecessary at Best, Encumbering at Worst 196
22. Teaching Applied Mathematics 203
23. Circular Reasoning: Who First Proved That C Divided by d Is a Constant? 224
24. A Medieval Mystery: Nicole Oresme’s Concept of Curvitas 238
25. The Myth of Leibniz’s Proof of the Fundamental Theorem of Calculus 249
26. The Spirograph and Mathematical Models from Nineteenth- Century Germany 261
27. What Does “Depth” Mean in Mathematics? 268
28. Finding Errors in Big Data 291
29. Programs and Probability 300
30. Lottery Perception 311
31. Why Acknowledging Uncertainty Can Make You a Better Scientist 316
32. For Want of a Nail: Why Unnecessarily Long Tests May Be Impeding the Progress of Western Civilization 321
33. How to Write a General Interest Mathematics Book 331
34. Contributors 345
35. Notable Writings 355
36. Acknowledgments 373
37. Credits 375