Every Planar Map Is Four Colorable

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Every Planar Map is Four Colorable

Author : Kenneth I. Appel
Publisher : American Mathematical Soc.
ISBN 13 : 0821851039
Total Pages : 741 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Every Planar Map is Four Colorable by : Kenneth I. Appel

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.

Every Planar Map is Four Colorable

Author : Kenneth I. Appel
Publisher : American Mathematical Soc.
ISBN 13 : 9780821854310
Total Pages : 762 pages
Book Rating : 4.8/5 (543 download)

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Book Synopsis Every Planar Map is Four Colorable by : Kenneth I. Appel

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 1989-12-31 with total page 762 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.

The Four-Color Theorem

Author : Rudolf Fritsch
Publisher : Springer Science & Business Media
ISBN 13 : 1461217202
Total Pages : 269 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Four-Color Theorem by : Rudolf Fritsch

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.

Four Colors Suffice

Author : Robin J. Wilson
Publisher : Princeton University Press
ISBN 13 : 9780691120232
Total Pages : 284 pages
Book Rating : 4.1/5 (22 download)

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Book Synopsis Four Colors Suffice by : Robin J. Wilson

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.

The Four-color Problem

Author : Thomas L. Saaty
Publisher :
ISBN 13 : 9780486650920
Total Pages : 217 pages
Book Rating : 4.6/5 (59 download)

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Book Synopsis The Four-color Problem by : Thomas L. Saaty

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:

The Four-Color Problem

Author :
Publisher : Academic Press
ISBN 13 : 9780080873398
Total Pages : 258 pages
Book Rating : 4.8/5 (733 download)

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Book Synopsis The Four-Color Problem by :

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

Mathematics Today Twelve Informal Essays

Author : L.A. Steen
Publisher : Springer Science & Business Media
ISBN 13 : 146139435X
Total Pages : 365 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Mathematics Today Twelve Informal Essays by : L.A. Steen

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.

Mathematical Solitaires and Games

Author : Benjamin L Schwartz
Publisher : Routledge
ISBN 13 : 1351843060
Total Pages : 167 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Mathematical Solitaires and Games by : Benjamin L Schwartz

Download or read book Mathematical Solitaires and Games written by Benjamin L Schwartz and published by Routledge. This book was released on 2019-03-19 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of solitaires and games.

Topics in Chromatic Graph Theory

Author : Lowell W. Beineke
Publisher : Cambridge University Press
ISBN 13 : 1316239853
Total Pages : 584 pages
Book Rating : 4.3/5 (162 download)

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Book Synopsis Topics in Chromatic Graph Theory by : Lowell W. Beineke

Download or read book Topics in Chromatic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2015-05-07 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields.

Map Color Theorem

Author : G. Ringel
Publisher : Springer Science & Business Media
ISBN 13 : 3642657591
Total Pages : 202 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Map Color Theorem by : G. Ringel

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.

The Knot Book

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
ISBN 13 : 0821836781
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Knot Book by : Colin Conrad Adams

Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

A Mathematical Introduction to Logic

Author : Herbert B. Enderton
Publisher : Elsevier
ISBN 13 : 0080496466
Total Pages : 330 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis A Mathematical Introduction to Logic by : Herbert B. Enderton

Download or read book A Mathematical Introduction to Logic written by Herbert B. Enderton and published by Elsevier. This book was released on 2001-01-23 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Introduction to Logic

History of Topology

Author : I.M. James
Publisher : Elsevier
ISBN 13 : 0080534074
Total Pages : 1067 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis History of Topology by : I.M. James

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.

Graph Coloring Problems

Author : Tommy R. Jensen
Publisher : John Wiley & Sons
ISBN 13 : 1118030745
Total Pages : 320 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Graph Coloring Problems by : Tommy R. Jensen

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.

Discrete Mathematics

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781724572639
Total Pages : 238 pages
Book Rating : 4.5/5 (726 download)

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Book Synopsis Discrete Mathematics by : Oscar Levin

Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

Automata, Languages and Programming

Author : Andrzej Lingas
Publisher : Springer Science & Business Media
ISBN 13 : 9783540569398
Total Pages : 716 pages
Book Rating : 4.5/5 (693 download)

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Book Synopsis Automata, Languages and Programming by : Andrzej Lingas

Download or read book Automata, Languages and Programming written by Andrzej Lingas and published by Springer Science & Business Media. This book was released on 1993-06-23 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Colloquium on Automata, Languages and Programming (ICALP) is an annual conference series sponsored by the European Association for Theoretical Computer Science (EATCS). It is intended to cover all important areas of theoretical computer science, such as: computability, automata,formal languages, term rewriting, analysis of algorithms, computational geometry, computational complexity, symbolic and algebraic computation, cryptography, data types and data structures, theory of data bases and knowledge bases, semantics of programming languages, program specification, transformation and verification, foundations of logicprogramming, theory of logical design and layout, parallel and distributed computation, theory of concurrency, and theory of robotics. This volume contains the proceedings of ICALP 93, held at LundUniversity, Sweden, in July 1993. It includes five invited papers and 51 contributed papers selected from 151 submissions.

Graph Theory with Algorithms and its Applications

Author : Santanu Saha Ray
Publisher : Springer Science & Business Media
ISBN 13 : 8132207505
Total Pages : 223 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Graph Theory with Algorithms and its Applications by : Santanu Saha Ray

Download or read book Graph Theory with Algorithms and its Applications written by Santanu Saha Ray and published by Springer Science & Business Media. This book was released on 2012-11-02 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book has many important features which make it suitable for both undergraduate and postgraduate students in various branches of engineering and general and applied sciences. The important topics interrelating Mathematics & Computer Science are also covered briefly. The book is useful to readers with a wide range of backgrounds including Mathematics, Computer Science/Computer Applications and Operational Research. While dealing with theorems and algorithms, emphasis is laid on constructions which consist of formal proofs, examples with applications. Uptill, there is scarcity of books in the open literature which cover all the things including most importantly various algorithms and applications with examples.