The Four Color Theorem
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The Four Color Theorem
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Author : Rudolf Fritsch
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
The Four Color Theorem written by Rudolf Fritsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This elegant little book discusses a famous problem that helped to define the field now known as graph theory: what is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries are. Many famous mathematicians have worked on the problem, but the proof eluded formulation until the 1970s, when it was finally cracked with a brute-force approach using a computer. The Four-Color Theorem begins by discussing the history of the problem up to the new approach given in the 1990s (by Neil Robertson, Daniel Sanders, Paul Seymour, and Robin Thomas). The book then goes into the mathematics, with a detailed discussion of how to convert the originally topological problem into a combinatorial one that is both elementary enough that anyone with a basic knowledge of geometry can follow it and also rigorous enough that a mathematician can read it with satisfaction. The authors discuss the mathematics and point to the philosophical debate that ensued when the proof was announced: just what is a mathematical proof, if it takes a computer to provide one - and is such a thing a proof at all?
The Four Color Theorem
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Author : Rudolf Fritsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Four Color Theorem written by Rudolf Fritsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the university reform of the 1970s, the classical Faculty of Science of the venerable Ludwig-Maximilians-Universitat in Munich was divided into five smaller faculties. One was for mathematics, the others for physics, chemistry and pharmaceutics, biology, and the earth sciences. Nevertheless, in order to maintain an exchange of ideas between the various disciplines and so as not to permit the complete undermining of the original notion of "universitas,,,l the Carl-Friedrich-von-Siemens Foundation periodically invites the pro fessors from the former Faculty of Science to a luncheon gathering. These are working luncheons during which recent developments in the various disciplines are presented by means of short talks. The motivation for such talks does not come, in the majority of cases, from the respective subject itself, but from another discipline that is loosely affiliated with it. In this way, the controversy over the modern methods used in the proof of the Four-Color Theorem had also spread to disciplines outside of mathematics. I, as a trained algebraic topologist, was asked to comment on this. Naturally, I was acquainted with the Four-Color 1 A Latin word meaning the whole of something, a collective entirety. Vll viii Preface Problem but, up to that point, had never intensively studied it. As an outsider,2 I dove into the material, not so much to achieve any scientific progress with it but to make this already achieved objective more understandable.
Every Planar Map Is Four Colorable
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Author : Kenneth I. Appel
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Every Planar Map Is Four Colorable written by Kenneth I. Appel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
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.
The Four Color Problem
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Author :
language : en
Publisher: Academic Press
Release Date : 2011-08-29
The Four Color Problem written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Mathematics categories.
The Four-Color Problem
Graphs Colourings And The Four Colour Theorem
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Author : Robert A. Wilson
language : en
Publisher: OUP Oxford
Release Date : 2002-01-24
Graphs Colourings And The Four Colour Theorem written by Robert A. Wilson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-24 with categories.
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.
Four Colours Suffice
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Author : Robin J. Wilson
language : en
Publisher: Allan Lane
Release Date : 2002
Four Colours Suffice written by Robin J. Wilson and has been published by Allan Lane this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
A puzzlers delight for over a century, the four-colour problem was one of the most famous conundrums in mathematics, if not the most famous, and many thousands of puzzlers - amateur problem-solvers and professional mathematicians alike - have struggled to answer it. The problem is simply stated, and involves the colouring of maps: Can every map be coloured with no more than four colours so that neighbouring countries are coloured differently?
The Four Color Problem
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Author : Thomas L. Saaty
language : en
Publisher:
Release Date : 1986
The Four Color Problem written by Thomas L. Saaty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Mathematics Today Twelve Informal Essays
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Author : L.A. Steen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics Today Twelve Informal Essays written by L.A. Steen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
The Mathematical Coloring Book
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Author : Alexander Soifer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-13
The Mathematical Coloring Book written by Alexander Soifer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-13 with Mathematics categories.
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 colorsneeded 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.
Graph Coloring Problems
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Author : Tommy R. Jensen
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-24
Graph Coloring Problems written by Tommy R. Jensen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-24 with Mathematics categories.
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.