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The Mathematical Coloring Book

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Cover of 'The Mathematical Coloring Book'

Table of Contents

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    Book Overview
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    Chapter 1 A Story of Colored Polygons and Arithmetic Progressions
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    Chapter 2 Chromatic Number of the Plane: The Problem
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    Chapter 3 Chromatic Number of the Plane: An Historical Essay
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    Chapter 4 Polychromatic Number of the Plane and Results Near the Lower Bound
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    Chapter 5 De Bruijn–Erdős Reduction to Finite Sets and Results Near the Lower Bound
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    Chapter 6 Polychromatic Number of the Plane and Results Near the Upper Bound
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    Chapter 7 Continuum of 6-Colorings of the Plane
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    Chapter 8 Chromatic Number of the Plane in Special Circumstances
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    Chapter 9 Measurable Chromatic Number of the Plane
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    Chapter 10 Coloring in Space
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    Chapter 11 Rational Coloring
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    Chapter 12 Chromatic Number of a Graph
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    Chapter 13 Dimension of a Graph
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    Chapter 14 Embedding 4-Chromatic Graphs in the Plane
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    Chapter 15 Embedding World Records
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    Chapter 16 Edge Chromatic Number of a Graph
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    Chapter 17 Carsten Thomassen’s 7-Color Theorem
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    Chapter 18 How the Four-Color Conjecture Was Born
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    Chapter 19 Victorian Comedy of Errors and Colorful Progress
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    Chapter 20 Kempe–Heawood’s Five-Color Theorem and Tait’s Equivalence
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    Chapter 21 The Four-Color Theorem
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    Chapter 22 The Great Debate
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    Chapter 23 How Does One Color Infinite Maps? A Bagatelle
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    Chapter 24 Chromatic Number of the Plane Meets Map Coloring: Townsend–Woodall’s 5-Color Theorem
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    Chapter 25 Paul Erdős
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    Chapter 26 De Bruijn–Erdős’s Theorem and Its History
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    Chapter 27 Edge Colored Graphs: Ramsey and Folkman Numbers
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    Chapter 28 From Pigeonhole Principle to Ramsey Principle
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    Chapter 29 The Happy End Problem
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    Chapter 30 The Man behind the Theory: Frank Plumpton Ramsey
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    Chapter 31 Ramsey Theory Before Ramsey: Hilbert’s Theorem
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    Chapter 32 Ramsey Theory Before Ramsey: Schur’s Coloring Solution of a Colored Problem and Its Generalizations
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    Chapter 33 Ramsey Theory before Ramsey: Van der Waerden Tells the Story of Creation
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    Chapter 34 Whose Conjecture Did Van der Waerden Prove? Two Lives Between Two Wars: Issai Schur and Pierre Joseph Henry Baudet
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    Chapter 35 Monochromatic Arithmetic Progressions: Life After Van der Waerden
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    Chapter 36 In Search of Van der Waerden: The Early Years
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    Chapter 37 In Search of Van der Waerden: The Nazi Leipzig, 1933–1945
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    Chapter 38 In Search of Van der Waerden: The Postwar Amsterdam, 1945 166
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    Chapter 39 In Search of Van der Waerden: The Unsettling Years, 1946–1951
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    Chapter 40 Monochromatic Polygons in a 2-Colored Plane
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    Chapter 41 3-Colored Plane, 2-Colored Space, and Ramsey Sets
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    Chapter 42 Gallai’s Theorem
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    Chapter 43 Application of Baudet–Schur–Van der Waerden
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    Chapter 44 Application of Bergelson–Leibman’s and Mordell–Faltings’ Theorems
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    Chapter 45 Solution of an Erdős Problem: O’Donnell’s Theorem
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    Chapter 46 What If We Had No Choice?
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    Chapter 47 A Glimpse into the Future: Chromatic Number of the Plane, Theorems and Conjectures
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    Chapter 48 Imagining the Real, Realizing the Imaginary
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    Chapter 49 Two Celebrated Problems
Attention for Chapter 36: In Search of Van der Waerden: The Early Years
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