Synopses & Reviews
I have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel... I found it hard to stop reading before I finished (in two days) the whole text. Soifer engages the reader's attention not only mathematically, but emotionally and esthetically. May you enjoy the book as much as I did! -Branko Grünbaum University of Washington You are doing great service to the community by taking care of the past, so the things are better understood in the future. -Stanislaw P. Radziszowski, Rochester Institute of Technology They [Van der Waerden's sections] meet the highest standards of historical scholarship. -Charles C. Gillispie, Princeton University You have dug up a great deal of information - my compliments! -Dirk van Dalen, Utrecht University I have just finished reading your (second) article "in search of van der Waerden". It is a masterpiece, I could not stop reading it... Congratulations! -Janos Pach, Courant Institute of Mathematics "Mathematical Coloring Book" will (we can hope) have a great and salutary influence on all writing on mathematics in the future." -Peter D. Johnson Jr., Auburn University Just now a postman came to the door with a copy of the masterpiece of the century. I thank you and the mathematics community should thank you for years to come. You have set a standard for writing about mathematics and mathematicians that will be hard to match. -Harold W. Kuhn, Princeton University The beautiful and unique Mathematical coloring book of Alexander Soifer is another case of ``good mathematics... and presenting mathematics as both a science and an art... It is difficult to explain how much beautiful and good mathematics is included and how much wisdom about life is given. -Peter Mihók, Mathematical Reviews
Review
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)
Review
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)
Synopsis
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.
Synopsis
This is a unique type of book; at least, I have never encountered a book of this kind. The best description of it I can give is that it is a mystery novel, developing on three levels, and imbued with both educational and philosophical/moral issues. If this summary description does not help understanding the particular character and allure of the book, possibly a more detailed explanation will be found useful. One of the primary goals of the author is to interest readers in particular, young mathematiciansorpossiblypre-mathematicians inthefascinatingworldofelegant and easily understandable problems, for which no particular mathematical kno- edge is necessary, but which are very far from being easily solved. In fact, the prototype of such problems is the following: If each point of the plane is to be given a color, how many colors do we need if every two points at unit distance are to receive distinct colors? More than half a century ago it was established that the least number of colors needed for such a coloring is either 4, or 5, or 6 or 7. Well, which is it? Despite efforts by a legion of very bright people many of whom developed whole branches of mathematics and solved problems that seemed much harder not a single advance towards the answer has been made. This mystery, and scores of other similarly simple questions, form one level of mysteries explored. In doing this, the author presents a whole lot of attractive results in an engaging way, and with increasing level of depth."
Synopsis
This book provides an exciting history of the discovery of Ramsey Theory, and contains new research along with rare photographs of the mathematicians who developed this theory, including Paul Erdös, B.L. van der Waerden, and Henry Baudet.
Synopsis
This book covers the Ramsey Theory, from its history to its famous problems. It also offers studies of Issai Schur, Pierre Joseph, Henry Baudet, and B.L. van der Waerden, incorporating photos and correspondence never before published.
About the Author
Alexander Soifer is a Russian born and educated American mathematician, a professor of mathematics at the University of Colorado, an author of some 200 articles on mathematics, history of mathematics, mathematics education, film reviews, etc. He is Senior Vice President of the World Federation of National Mathematics Competitions, which in 2006 awarded him The Paul Erdös Award. 26 years ago Soifer founded has since chaired The Colorado Mathematical Olympiad, and served on both USSR and USA Mathematical Olympiads committees. Soifer's Erdös number is 1. Springer has contracted his 7 books. "The Mathematical Coloring Book" is coming out in October 2008; 4 books will appear in 2009; followed by "Life and Fate: In Search of Van der Waerden", and a joint book with the late Paul Erdos "Problems of p.g.o.m. Erdos." The author's previous books were self-published and received many positive reviews, below are excerpts from reviews of "How Does One Cut A Triangle?: "Why am I urging you to read this? Mainly because it is such a refreshing book. Professor Soifer makes the problems fascinating, the methods of attack even more fascinating, and the whole thing is enlivened by anecdotes about the history of the problems, some of their recent solvers, and the very human reactions of the author to some beautiful mathematics. Most of all, the book has charm, somehow enhanced by his slightly eccentric English, sufficient to carry the reader forward without minding being asked to do rather a lot of work. I am tempted to include several typical quotations but I'll restrain myself to two: From Chapter 8 "Here is an easy problem for your entertainment. Problem 8.1.2. Prove that for any parallelogram P, S(P)=5. Now we have a new problem, therefore we are alive! And the problem is this: what are all possible values of our newly introduced function S(F)? Can the function S(F) help us to classify geometry figures?" And from an introduction by Cecil Rousseau: 'There is a view, held by many, that mathematics books are dull. This view is not without support. It is reinforced by numerous examples at all levels, from elementary texts with page after page of mind-numbing drill to advanced books written in a relentless Theorem-Proof style. "How does one cut a triangle?" is an entirely different matter. It reads like an adventure story. In fact, it is an adventure story, complete with interesting characters, moments of exhilaration, examples of serendipity, and unanswered questions. It conveys the spirit of mathematical discovery and it celebrates the event as have mathematicians throughout history.' And this isn't just publishers going over the top - it's all true!" -- JOHN Baylis in The Mathematical Gazette Soifer's work can rightly be called a "mathematical gem." -- JAMES N. BOYD in Mathematics Teacher This delightful book considers and solves many problems in dividing triangles into n congruent pieces and also into similar pieces, as well as many extremal problems about placing points in convex figures. The book is primarily meant for clever high school students and college students interested in geometry, but even mature mathematicians will find a lot of new material in it. I very warmly recommend the book and hope the readers will have pleasure in thinking about the unsolved problems and will find new ones. -- PAUL ERDÖS It is impossible to convey the spirit of the book by merely listing the problems considered or even a number of solutions. The manner of presentation and the gentle guidance toward a solution and hence to generalizations and new problems takes this elementary treatise out of the prosaic and into the stimulating realm of mathematical creativity. Not only young talented people but dedicated secondary teachers and even a few mathematical sophisticates will find this reading both pleasant and profitable. -- L. M. KELLY in Mathematical Reviews We do not often have possibilities to look into a creative workshop of a mathematician... The beginner, who is interested in the book, not only comprehends a situation in a creative mathematical studio, not only is exposed to good mathematical taste, but also acquires elements of modern mathematical culture. And (not less important) the reader imagines the role and place of intuition and analogy in mathematical investigation; he or she fancies the meaning of generalization in modern mathematics and surprising connections between different parts of this science (that are, as one might think, far from each other) that unite them... This makes the book alive, fresh, and easily readable. Alexander Soifer has produced a good gift for the young lover of mathematics. And not only for youngsters; the book should be interesting even to professional mathematicians. V. G. BOLTYANSKI in SIAM Review
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.-