The New Mathematical Coloring Book Mathematics of Coloring and the Colorful Life of Its Creators
The New Mathematical Coloring Book (TNMCB) includes striking results of the past 15-year renaissance that produced new approaches, advances, and solutions to problems from the first edition. A large part of the new edition “Ask what your computer can do for you,” presents the recent breakthrough by...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer US
2024, 2024
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| Edition: | 2nd ed. 2024 |
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| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 57. A Stroke of Brilliance: Matthew Huddleston's Proof
- 58. Geoffrey Exoo and Dan Ismailescu or 2 Men from 2 Forbidden Distances
- 59. Jaan Parts on Two-Distance 6-Coloring
- 60. Forbidden Odds, Binaries, and Factorials
- 61. 7-and 8-Chromatic Two-Distance Graphs
- XII. Predicting the Future
- 62. What If We Had No Choice?
- 63. AfterMath and the Shelah–Soifer Class of Graphs
- 64. A Glimpse into the Future: Chromatic Number of the Plane, Theorems and Conjectures
- XIII. Imagining the Real, Realizing the Imaginary
- 65. What Do the Founding Set Theorists Think About the Foundations?
- 66. So, What Does It All Mean?
- 67. Imagining the Real or Realizing the Imaginary: Platonism versus Imaginism
- XIV. Farewell to the Reader
- 68. Two Celebrated Problems
- Bibliography
- Name Index
- Subject Index
- Index of Notations
- 29. Edge Colored Graphs: Ramsey and Folkman Numbers
- VI. The Ramsey Principles
- 30. From Pigeonhole Principle to Ramsey Principle
- 31. The Happy End Problem
- 32. The Man behind the Theory: Frank Plumpton Ramsey
- VII. Colored Integers: Ramsey Theory Before Ramsey and Its AfterMath
- 33. Ramsey Theory Before Ramsey: Hilbert’s Theorem
- 34. Ramsey Theory Before Ramsey: Schur’s Coloring Solution of a Colored Problem and Its Generalizations
- 35. Ramsey Theory Before Ramsey: Van der Waerden Tells the Story of Creation
- 36. Whose Conjecture Did Van der Waerden Prove? Two Lives Between Two Wars: Issai Schur and Pierre Joseph Henry Baudet
- 38. Monochromatic Arithmetic Progressions or Life After Van der Waerden
- 39. In Search of Van der Waerden: The Early Years
- 40. In Search of Van der Waerden: The Nazi Leipzig, 1933–1945
- 41. In Search of Van der Waerden: Amsterdam, Year 1945
- 42. In Search of Van der Waerden: The Unsettling Years, 1946–1951
- Epigraph: To Paint a Bird
- Foreword for the New Mathematical Coloring Book by Peter D. Johnson, Jr
- Foreword for the New Mathematical Coloring Book by Geoffrey Exoo
- Foreword for the New Mathematical Coloring Book by Branko Grunbaum. Foreword for The Mathematical Coloring Book by Peter D. Johnson, Jr., Foreword for The Mathematical Coloring Book by Cecil Rousseau
- Acknowledgements
- Greetings to the Reader 2023
- Greetings to the Reader 2009
- I. Merry-Go-Round.-1. A Story of Colored Polygons and Arithmetic Progressions
- II. Colored Plane
- 2. Chromatic Number of the Plane: The Problem
- 3. Chromatic Number of the Plane: An Historical Essay
- 4. Polychromatic Number of the Plane and Results Near the Lower Bound
- 5. De Bruijn–Erdős Reduction to Finite Sets and Results Near the Lower Bound
- 6. Polychromatic Number of the Plane and Results Near the Upper Bound
- 7. Continuum of 6-Colorings of the Plane
- 8. Chromatic Number of the Plane in Special Circumstances
- 9. MeasurableChromatic Number of the Plane
- 10. Coloring in Space
- 11. Rational Coloring
- III. Coloring Graphs
- 12. Chromatic Number of a Graph
- 13. Dimension of a Graph
- 14. Embedding 4-Chromatic Graphs in the Plane
- 15. Embedding World Series
- 16. Exoo–Ismailescu: The Final Word on Problem 15.4
- 17. Edge Chromatic Number of a Graph
- 18. The Carsten Thomassen 7-Color Theorem
- IV.Coloring Maps
- 19. How the Four-Color Conjecture Was Born
- 20. Victorian Comedy of Errors and Colorful Progress
- 21. Kempe–Heawood’s Five-Color Theorem and Tait’s Equivalence
- 22. The Four-Color Theorem
- 23. The Great Debate
- 24. How Does One Color Infinite Maps? A Bagatelle
- 25. Chromatic Number of the Plane Meets Map Coloring: The Townsend–Woodall 5-Color Theorem
- V. Colored Graphs
- 26. Paul Erdős
- 27. The De Bruijn–Erdős Theorem and Its History
- 28. Nicolaas Govert de Bruijn
- 43. How the Monochromatic AP Theorem Became Classic: Khinchin and Lukomskaya
- VIII. Colored Polygons: Euclidean Ramsey Theory
- 44. Monochromatic Polygons in a 2-Colored Plane
- 45. 3-Colored Plane, 2-Colored Space, and Ramsey Sets
- 46. The Gallai Theorem
- IX. Colored Integers in Service of the Chromatic Number of the Plane: How O’Donnell Unified Ramsey Theory and No One Noticed
- 47. O'Donnell Earns His Doctorate
- 48. Application of Baudet–Schur–Van der Waerden
- 48. Application of Bergelson–Leibman’s and Mordell–Faltings’ Theorems
- 50. Solution of an Erdős Problem: The O’Donnell Theorem
- X. Ask What Your Computer Can Do for You
- 51. Aubrey D.N.J. de Grey's Breakthrough
- 52. De Grey's Construction
- 53. Marienus Johannes Hendrikus 'Marijn' Heule
- 54. Can We Reach Chromatic 5 Without Mosers Spindles?
- 55. Triangle-Free 5-Chromatic Unit Distance Graphs
- 56. Jaan Parts' Current World Record
- XI. What About Chromatic 6?