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 18 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 when firing Issai Schur, from his job as Professor of Mathematics at the University of Berlin.

- Produktdetails
- Verlag: Springer / Springer New York / Springer, Berlin
- Artikelnr. des Verlages: 11019596
- Erscheinungstermin: 11. November 2008
- Englisch
- Abmessung: 241mm x 160mm x 40mm
- Gewicht: 1132g
- ISBN-13: 9780387746401
- ISBN-10: 0387746404
- Artikelnr.: 23899339

Merry-Go-Round.- A Story of Colored Polygons and Arithmetic Progressions.- Colored Plane.- Chromatic Number of the Plane: The Problem.- Chromatic Number of the Plane: An Historical Essay.- Polychromatic Number of the Plane and Results Near the Lower Bound.- De Bruijn-Erd?s Reduction to Finite Sets and Results Near the Lower Bound.- Polychromatic Number of the Plane and Results Near the Upper Bound.- Continuum of 6-Colorings of the Plane.- 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 and Colorful Progress.- Kempe-Heawood's Five-Color Theorem and Tait's Equivalence.- The Four-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 Erd?s.- De Bruijn-Erd?s'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 and Its AfterMath.- Ramsey Theory Before Ramsey: Hilbert's Theorem.- Ramsey Theory Before Ramsey: Schur's Coloring Solution of a Colored Problem and 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 Early Years.- In Search of Van der Waerden: The Nazi Leipzig, 1933-1945.- In Search of Van der Waerden: The Postwar Amsterdam, 1945166.- 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 Chromatic Number of the Plane: How O'Donnell Unified Ramsey Theory and No One Noticed.- Application of Baudet-Schur-Van der Waerden.- Application of Bergelson-Leibman's and Mordell-Faltings' Theorems.- Solution of an Erd?s 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 Problems.

From the reviews:

"It contains a range of combinatorial colouring problems, while those interested in the recent history or the sociology of mathematics will be entertained by lively accounts of the combinatorialists who created and worked on them. ... The book is generally well written and presented, with good diagrams and layout ... . a useful and engaging book." (Robin Wilson, LMS Newsletter, November, 2009)

"This book contains much math of interest and pointers to more math of interest. ... This is a Fantastic Book!. ... The upward closure of the union of the following people: (1) an excellent high school student, (2) a very good college math major, (3) a good grad student in math or math-related field, (4) a fair PhD in combinatories, or (5) a bad math professor. ... Anyone who is interested in math or history of math. This book has plenty of both." (William Gasarch, SIGACT News, Vol. 40 (3), 2010)

"Soifer does a fine job in collating a huge range of sources ... with many interesting nuggets and, where necessary, a real determination to set the historical record straight in terms of the appellation of conjectures and theorems. ... The mathematical colouring book is attractively produced and very readable. ... book is likely to be of primary interest to those seeking a historically aware, up-to-date introductory survey of an engaging, and still emerging, field of combinatorial mathematics." (Nick Lord, The Mathematical Gazette, Vol. 95 (532), March, 2011)

"This very nicely presented book, lovingly prepared by the author over a period of 18 years, studies problems involving colored objects, and the Ramsey theory that such problems are imbedded into. ... recommend this book, both for mathematicians and for those who wish to learn more about mathematicians and their subject." (Arthur T. White, Zentralblatt MATH, Vol. 1221, 2011)

"It contains a range of combinatorial colouring problems, while those interested in the recent history or the sociology of mathematics will be entertained by lively accounts of the combinatorialists who created and worked on them. ... The book is generally well written and presented, with good diagrams and layout ... . a useful and engaging book." (Robin Wilson, LMS Newsletter, November, 2009)

"This book contains much math of interest and pointers to more math of interest. ... This is a Fantastic Book!. ... The upward closure of the union of the following people: (1) an excellent high school student, (2) a very good college math major, (3) a good grad student in math or math-related field, (4) a fair PhD in combinatories, or (5) a bad math professor. ... Anyone who is interested in math or history of math. This book has plenty of both." (William Gasarch, SIGACT News, Vol. 40 (3), 2010)

"Soifer does a fine job in collating a huge range of sources ... with many interesting nuggets and, where necessary, a real determination to set the historical record straight in terms of the appellation of conjectures and theorems. ... The mathematical colouring book is attractively produced and very readable. ... book is likely to be of primary interest to those seeking a historically aware, up-to-date introductory survey of an engaging, and still emerging, field of combinatorial mathematics." (Nick Lord, The Mathematical Gazette, Vol. 95 (532), March, 2011)

"This very nicely presented book, lovingly prepared by the author over a period of 18 years, studies problems involving colored objects, and the Ramsey theory that such problems are imbedded into. ... recommend this book, both for mathematicians and for those who wish to learn more about mathematicians and their subject." (Arthur T. White, Zentralblatt MATH, Vol. 1221, 2011)