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Soifer, Alexander

The Mathematical Coloring Book

The Mathematical Coloring Book

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ISBN: 9780387746425
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Table of contents

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, 1945166
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)
Publisher
Springer
Publication year
2009
Language
en
Edition
1
Category
Natural Sciences
Format
Ebook
eISBN (PDF)
9780387746425

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