Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics

Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Introduction ix
4. Mathematical Products 1
5. The Largest Known Prime Number 7
6. A Unified Theory of Randomness 10
7. An “Infinitely Rich” Mathematician Turns 100 24
8. Inverse Yogiisms 28
9. Ramanujan in Bronze 37
10. Creating Symmetric Fractals 45
11. Projective Geometry in the Moon Tilt Illusion 54
12. Girih for Domes: Analysis of Three Iranian Domes 64
13. Why Kids Should Use Their Fingers in Math Class 76
14. Threshold Concepts and Undergraduate Mathematics Teaching 82
15. Rising above a Cause-and-Effect Stance in Mathematics Education Research 93
16. How to Find the Logarithm of Any Number Using Nothing but a Piece of String 99
17. Rendering Pacioli’s Rhombicuboctahedron 106
18. Who Would Have Won the Fields Medal 150 Years Ago? 121
19. Paradoxes, Contradictions, and the Limits of Science 130
20. Stairway to Heaven: The Abstract Method and Levels of Abstraction in Mathematics 145
21. Are Our Brains Bayesian? 172
22. Great Expectations: The Past, Present, and Future of Prediction 182
23. Contributors 193
24. Notable Writings 199
25. Acknowledgments 221
26. Credits 223