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Author : Robin Wilson
Publisher : Princeton University Press
ISBN 13 : 0691158223
Total Pages : 218 pages
Book Rating : 4.6/5 (911 download)
Download or read book Four Colors Suffice written by Robin Wilson and published by Princeton University Press. This book was released on 2013-11-10 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published: London: Allen Lane, 2002, under title Four colours suffice.
Author : Rudolf Fritsch
Publisher : Springer Science & Business Media
ISBN 13 : 1461217202
Total Pages : 269 pages
Book Rating : 4.4/5 (612 download)
Download or read book The Four-Color Theorem written by Rudolf Fritsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
Author : Thomas L. Saaty
Publisher :
ISBN 13 : 9780486650920
Total Pages : 217 pages
Book Rating : 4.6/5 (59 download)
Download or read book The Four-color Problem written by Thomas L. Saaty and published by . This book was released on 1986 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robin J. Wilson
Publisher : Princeton University Press
ISBN 13 : 9780691120232
Total Pages : 284 pages
Book Rating : 4.1/5 (22 download)
Download or read book Four Colors Suffice written by Robin J. Wilson and published by Princeton University Press. This book was released on 2002 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.
Author : L.A. Steen
Publisher : Springer Science & Business Media
ISBN 13 : 146139435X
Total Pages : 365 pages
Book Rating : 4.4/5 (613 download)
Download or read book Mathematics Today Twelve Informal Essays written by L.A. Steen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of the present book of essays is to convey to the intelligent nonmathematician something of the nature, development, and use of mathe matical concepts, particularly those that have found application in current scientific research. The idea of assembling such a volume goes back at least to 1974, when it was discussed by the then-newly-formed Joint Projects Committee for Mathematics (JPCM) of the American Mathematical Soci ety, the Mathematical Association of America, and the Society for Indus trial and Applied Mathematics. Currently, the nine members of the JPCM are Saunders Mac Lane (Chairman) of the University of Chicago, Frederick J. Almgren, Jr. of Princeton University, Richard D. Anderson of Louisiana State University, George E. Carrier of Harvard University, Hirsh G. Cohen ofthe International Business Machines Corporation, Richard C. DiPrima of Rensselaer Polytechnic Institute, Robion C. Kirby of the University of California at Berkeley, William H. Kruskal of the University of Chicago, and George D. Mostow of Yale University. The JPCM decided to make production of this volume its first major proj ect and requested the Conference Board of the Mathematical Sciences (CBMS), of which its three sponsoring societies are all member organiza tions, to approach the National Science Foundation on its behalffor support of the undertaking. A proposal submitted by the C BMS in December 1974 and in revised form in July 1975 was granted by the Foundation in May 1976, and work on assembling the volume got under way.
Author : Robert A. Wilson
Publisher : OUP Oxford
ISBN 13 : 019158360X
Total Pages : 153 pages
Book Rating : 4.1/5 (915 download)
Download or read book Graphs, Colourings and the Four-Colour Theorem written by Robert A. Wilson and published by OUP Oxford. This book was released on 2002-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.
Author :
Publisher : Academic Press
ISBN 13 : 9780080873398
Total Pages : 258 pages
Book Rating : 4.8/5 (733 download)
Download or read book The Four-Color Problem written by and published by Academic Press. This book was released on 2011-08-29 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Four-Color Problem
Author : Kenneth I. Appel
Publisher : American Mathematical Soc.
ISBN 13 : 0821851039
Total Pages : 741 pages
Book Rating : 4.8/5 (218 download)
Download or read book Every Planar Map is Four Colorable written by Kenneth I. Appel and published by American Mathematical Soc.. This book was released on 1989 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.
Author : Thomas L. Saaty
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Four-color Problem written by Thomas L. Saaty and published by . This book was released on 1977 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tommy R. Jensen
Publisher : John Wiley & Sons
ISBN 13 : 1118030745
Total Pages : 320 pages
Book Rating : 4.1/5 (18 download)
Download or read book Graph Coloring Problems written by Tommy R. Jensen and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.
Author : Chris McMullen
Publisher :
ISBN 13 : 9781941691090
Total Pages : 426 pages
Book Rating : 4.6/5 (91 download)
Download or read book The Four-Color Theorem and Basic Graph Theory written by Chris McMullen and published by . This book was released on 2020-05-26 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore a variety of fascinating concepts relating to the four-color theorem with an accessible introduction to related concepts from basic graph theory. From a clear explanation of Heawood's disproof of Kempe's argument to novel features like quadrilateral switching, this book by Chris McMullen, Ph.D., is packed with content. It even includes a novel handwaving argument explaining why the four-color theorem is true. What is the four-color theorem? Why is it common to work with graphs instead of maps? What are Kempe chains? What is the problem with Alfred Kempe's attempted proof? How does Euler's formula relate the numbers of faces, edges, and vertices? What are Kuratowski's theorem and Wagner's theorem? What is the motivation behind triangulation? What is quadrilateral switching? What is vertex splitting? What is the three-edges theorem? Is there an algorithm for four-coloring a map or graph? What is a Hamiltonian cycle? What is a separating triangle? How is the four-color theorem like an ill-conditioned logic puzzle? Why is the four-color theorem true? What makes the four-color theorem so difficult to prove by hand?
Author :
Publisher : Academic Press
ISBN 13 : 9780080873398
Total Pages : 258 pages
Book Rating : 4.8/5 (733 download)
Download or read book The Four-Color Problem written by and published by Academic Press. This book was released on 2011-08-29 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Four-Color Problem
Author : G. Ringel
Publisher : Springer Science & Business Media
ISBN 13 : 3642657591
Total Pages : 202 pages
Book Rating : 4.6/5 (426 download)
Download or read book Map Color Theorem written by G. Ringel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1890 P. J. Heawood [35] published a formula which he called the Map Colour Theorem. But he forgot to prove it. Therefore the world of mathematicians called it the Heawood Conjecture. In 1968 the formula was proven and therefore again called the Map Color Theorem. (This book is written in California, thus in American English. ) Beautiful combinatorial methods were developed in order to prove the formula. The proof is divided into twelve cases. In 1966 there were three of them still unsolved. In the academic year 1967/68 J. W. T. Youngs on those three cases at Santa Cruz. Sur invited me to work with him prisingly our joint effort led to the solution of all three cases. It was a year of hard work but great pleasure. Working together was extremely profitable and enjoyable. In spite of the fact that we saw each other every day, Ted wrote a letter to me, which I present here in shortened form: Santa Cruz, March 1, 1968 Dear Gerhard: Last night while I was checking our results on Cases 2, 8 and 11, and thinking of the great pleasure we had in the afternoon with the extra ordinarily elegant new solution for Case 11, it seemed to me appropriate to pause for a few minutes and dictate a historical memorandum. We began working on Case 8 on 10 October 1967, and it was settled on Tuesday night, 14 November 1967.
Author : I.M. James
Publisher : Elsevier
ISBN 13 : 0080534074
Total Pages : 1067 pages
Book Rating : 4.0/5 (85 download)
Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Author : Gary Chartrand
Publisher : CRC Press
ISBN 13 : 0429798288
Total Pages : 503 pages
Book Rating : 4.4/5 (297 download)
Download or read book Chromatic Graph Theory written by Gary Chartrand and published by CRC Press. This book was released on 2019-11-28 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition
Author : Alexander Soifer
Publisher : Springer Science & Business Media
ISBN 13 : 0387746420
Total Pages : 619 pages
Book Rating : 4.3/5 (877 download)
Download or read book The Mathematical Coloring Book written by Alexander Soifer and published by Springer Science & Business Media. This book was released on 2008-10-13 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Nora Hartsfield
Publisher : Courier Corporation
ISBN 13 : 0486315525
Total Pages : 272 pages
Book Rating : 4.4/5 (863 download)
Download or read book Pearls in Graph Theory written by Nora Hartsfield and published by Courier Corporation. This book was released on 2013-04-15 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.
