Soifer, Alexander
The Mathematical Coloring Book
Part I. Merry-Go-Round
1. A Story of Colored Polygons and Arithmetic Progressions
Alexander Soifer
Part II. Colored Plane
2. Chromatic Number of the Plane: The Problem
Alexander Soifer
3. Chromatic Number of the Plane: An Historical Essay
Alexander Soifer
4. Polychromatic Number of the Plane and Results Near the Lower Bound
Alexander Soifer
5. De Bruijn–Erdos Reduction to Finite Sets and Results Near the Lower Bound
Alexander Soifer
6. Polychromatic Number of the Plane and Results Near the Upper Bound
Alexander Soifer
7. Continuum of 6-Colorings of the Plane
Alexander Soifer
8. Chromatic Number of the Plane in Special Circumstances
Alexander Soifer
9. Measurable Chromatic Number of the Plane
Alexander Soifer
10. Coloring in Space
Alexander Soifer
11. Rational Coloring
Alexander Soifer
Part III. Coloring Graphs
12. Chromatic Number of a Graph
Alexander Soifer
13. Dimension of a Graph
Alexander Soifer
14. Embedding 4-Chromatic Graphs in the Plane
Alexander Soifer
15. Embedding World Records
Alexander Soifer
16. Edge Chromatic Number of a Graph
Alexander Soifer
17. Carsten Thomassen’s 7-Color Theorem
Alexander Soifer
Part IV. Coloring Maps
18. How the Four-Color Conjecture Was Born
Alexander Soifer
19. Victorian Comedy of Errors and Colorful Progress
Alexander Soifer
20. Kempe–Heawood’s Five-Color Theorem and Tait’s Equivalence
Alexander Soifer
21. The Four-Color Theorem
Alexander Soifer
22. The Great Debate
Alexander Soifer
23. How Does One Color Infinite Maps? A Bagatelle
Alexander Soifer
24. Chromatic Number of the Plane Meets Map Coloring: Townsend–Woodall’s 5-Color Theorem
Alexander Soifer
Part V. Colored Graphs
25. Paul Erdos
Alexander Soifer
26. De Bruijn–Erdos’s Theorem and Its History
Alexander Soifer
27. Edge Colored Graphs: Ramsey and Folkman Numbers
Alexander Soifer
Part VI. The Ramsey Principle
28. From Pigeonhole Principle to Ramsey Principle
Alexander Soifer
29. The Happy End Problem
Alexander Soifer
30. The Man behind the Theory: Frank Plumpton Ramsey
Alexander Soifer
Part VII. Colored Integers: Ramsey Theory Before Ramsey and Its AfterMath
31. Ramsey Theory Before Ramsey: Hilbert’s Theorem
Alexander Soifer
32. Ramsey Theory Before Ramsey: Schur’s Coloring Solution of a Colored Problem and Its Generalizations
Alexander Soifer
33. Ramsey Theory before Ramsey: Van der Waerden Tells the Story of Creation
Alexander Soifer
34. Whose Conjecture Did Van der Waerden Prove? Two Lives Between Two Wars: Issai Schur and Pierre Joseph Henry Baudet
Alexander Soifer
35. Monochromatic Arithmetic Progressions: Life After Van der Waerden
Alexander Soifer
36. In Search of Van der Waerden: The Early Years
Alexander Soifer
37. In Search of Van der Waerden: The Nazi Leipzig, 1933–1945
Alexander Soifer
38. In Search of Van der Waerden: The Postwar Amsterdam, 1945
Alexander Soifer
39. In Search of Van der Waerden: The Unsettling Years, 1946–1951
Alexander Soifer
Part VIII. Colored Polygons: Euclidean Ramsey Theory
40. Monochromatic Polygons in a 2-Colored Plane
Alexander Soifer
41. 3-Colored Plane, 2-Colored Space, and Ramsey Sets
Alexander Soifer
42. Gallai’s Theorem
Alexander Soifer
Part IX. Colored Integers in Service of Chromatic Number of the Plane: How O’Donnell
Unified Ramsey Theory and No One Noticed
43. Application of Baudet–Schur–Van der Waerden
Alexander Soifer
44. Application of Bergelson–Leibman’s and Mordell–Faltings’ Theorems
Alexander Soifer
45. Solution of an Erdos Problem: O’Donnell’s Theorem
Alexander Soifer
Part X. Predicting the Future
46. What If We Had No Choice?
Alexander Soifer
47. A Glimpse into the Future: Chromatic Number of the Plane, Theorems and Conjectures
Alexander Soifer
48. Imagining the Real, Realizing the Imaginary
Alexander Soifer
Part XI. Farewell to the Reader
49. Two Celebrated Problems
Alexander Soifer
Keywords: MATHEMATICS / General MAT000000
- Author(s)
- Soifer, Alexander
- Publisher
- Springer
- Publication year
- 2009
- Language
- en
- Edition
- 1
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (PDF)
- 9780387746425