The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators / Edition 1by Branko Grunbaum, Alexander Soifer
This book is dedicated to problems involving colored objects, and to results about the existence of certain exciting and unexpected properties that occur regardless of how these objects are colored. In mathematics, these results comprise the beautiful area known as Ramsey Theory. Wolfram’s Math World defines Ramsey Theory as "the mathematical study of… See more details below
This book is dedicated to problems involving colored objects, and to results about the existence of certain exciting and unexpected properties that occur regardless of how these objects are colored. In mathematics, these results comprise the beautiful area known as Ramsey Theory. Wolfram’s Math World defines Ramsey Theory as "the mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large." Ramsey Theory thus includes parts of many fields of mathematics, including combinatorics, geometry, and number theory. This book addresses famous and exciting problems of Ramsey Theory, along with the history surrounding the discovery of Ramsey Theory. In addition, the author studies the life of Issai Schur, Pierre Joseph Henry Baudet and B.L. van der Waerden. In researching this book over the past 14 years, the author corresponded extensively with B.L. van der Waerden, Paul Erdos, Henry Baudet, and many others. As a result, this book will incorporate never before published correspondence and photographs.
Historians of mathematics will herein find much new information, along with old errors corrected and published here for the first time in book form. And everyone will experience seeing, for the first time, faces one has not seen before in print, on rare and unique photographs of the creators of the mathematics presented herein, from Francis Guthrie to Frank Ramsey, and documents, such as the one where Adolph Hitler commits a "micromanagement" of firing the Jew, Issai Schur from his job as Professor of Mathematics at the University of Berlin.
- Springer New York
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- 6.20(w) x 9.30(h) x 1.30(d)
Table of Contents
Epigraph: To Paint a Bird by Jacques Prévert.- Foreword by Branko Grünbaum.- Foreword by Peter D. Johnson Jr.- Foreword by Cecil Rousseau.- Greetings to the Reader.- Merry-Go-Round.- A Story of Colored Polygons and Arithmetic Progressions.- Colored Plane: Chromatic Number of the Plane.- Chromatic Number of the Plane: The Problem.- Chromatic Number of the Plane: An Historical Essay.- Polychromatic Number of the Plane & Results near the Lower Bound.- De Bruijn-Erdos Reduction to Finite Sets & Results near the Lower Bound.- Polychromatic Number of the Plane & Results near the Upper Bound.- Continuum of 6-Colorings.- Chromatic Number of the Plane in Special Circumstances.- Measurable Chromatic Number of the Plane.- Coloring in Space.- Rational Coloring.- Coloring Graphs.- Chromatic Number of a Graph.- Dimension of a Graph.- Embedding 4-Chromatic Graphs in the Plane.- Embedding World Records.- Edge Chromatic Number of a Graph.- Carsten Thomassen’s 7-Color Theorem.- Coloring Maps.- How The Four Color Conjecture Was Born.- Victorian Comedy of Errors & Colorful Progress.- Kempe-Heawood’s 5-Color Theorem & Tait’s Equivalence.- The 4-Color Theorem.- The Great Debate.- How does one Color Infinite Maps? A Bagatelle.- Chromatic Number of the Plane Meets Map Coloring: Townsend-Woodall’s 5-Color Theorem.- Colored Graphs.- Paul Erdos.- Proof of De Bruijn-Erdos’s Theorem and Its History.- Edge Colored Graphs: Ramsey and Folkman Numbers.- The Ramsey Principle.- From Pigeonhole Principle to Ramsey Principle.- The Happy End Problem.- The Man behind the Theory: Frank Plumpton Ramsey.- Colored Integers: Ramsey Theory before Ramsey & Its AfterMath.- Ramsey Theory before Ramsey: Hilbert’s 1892 Theorem.- Theory before Ramsey: Schur’s Coloring Solution of a Colored Problem & Its Generalizations.- Ramsey Theory before Ramsey: Van der Waerden Tells the Story of Creation.- Whose Conjecture Did Van der Waerden Prove? Two Lives between Two Wars: Issai Schur and Pierre Joseph Henry Baudet.- Monochromatic Arithmetic Progressions: Life after Van der Waerden.- In search of Van der Waerden: The Nazi Leipzig, 1933-1945.- In search of Van der Waerden: The Post War Amsterdam, 1945.- In search of Van der Waerden: The Unsettling Years, 1946-1951.- Colored Polygons: Euclidean Ramsey Theory.- Monochromatic Polygons in a 2-Colored Plane.- 3-Colored Plane, 2-Colored Space and Ramsey Sets.- Gallai’s Theorem.- Colored Integers in Service of Chromtic Number of the Plane: How O’Donnell Unified Ramsey Theory and No One Noticed.- Application of Baudet-Schur-Van der Waerden’s Theorem.- Applications of Bergelson-Leibman’s and Mordell-Faltings’ Theorems.- Solution of an Erdos Problem: O’Donnell’s Theorem.- Predicting the Future.- What if we had no Choice?.- A Glimpse into the Future: Chromatic Number of the Plane, Theorems and Conjectures.- Imagining the Real, Realizing the Imaginary.- Farewell to the Reader.- Two Celebrated Coloring Problems on the Plane.- Bibliography.- Index of Names.- Index of Terms.- Index of Notations.-
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