The New Mathematical Coloring Book : Mathematics of Coloring and the Colorful Life of Its Creators
The New Mathematical Coloring Book : Mathematics of Coloring and the Colorful Life of Its Creators
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Author(s): Soifer, Alexander
ISBN No.: 9781071635964
Pages: xlviii, 841
Year: 202403
Format: Trade Cloth (Hard Cover)
Price: $ 303.59
Dispatch delay: Dispatched between 7 to 15 days
Status: Available

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-Erdos 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.


Measurable Chromatic 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 Erdos.- 27. The De Bruijn-Erdos Theorem and Its History.- 28. Nicolaas Govert de Bruijn.- 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.- 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 Erdos 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?.- 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.


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