Every Planar Map is Four Colorable PDF Download
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Author: Kenneth I. Appel
Publisher: American Mathematical Soc.
ISBN: 0821851039
Category : Mathematics
Languages : en
Pages : 760
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Book Description
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: Kenneth I. Appel
Publisher: American Mathematical Soc.
ISBN: 0821851039
Category : Mathematics
Languages : en
Pages : 760
Get Book Here
Book Description
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: Rudolf Fritsch
Publisher: Springer Science & Business Media
ISBN: 1461217202
Category : Mathematics
Languages : en
Pages : 269
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Book Description
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: 9780486650920
Category : Mathematics
Languages : en
Pages : 217
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Book Description
Author: Robin J. Wilson
Publisher:
ISBN:
Category : History
Languages : en
Pages : 292
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Book Description
The four-colour problem was one of the most famous and controversial conundrums ever known, and stumped thousands of puzzlers for over a century. It sounded simple- what is the least number of colours needed to fill in any map, so that neighbouring countries are always coloured differently? However, it would take over a hundred years for amateur problem-solvers and mathematicians alike to answer the question first posed by Francis Guthrie in 1852. And, even when a solution was finally found using computers, debate raged over whether this technology could ever provide the proof that traditional pen-and-paper calculations could. This is the gripping story of the race to solve the riddle - a tale of dedicated puzzlers, mind-boggling maps, human ingenuity and the great rhombicuboctahedron
Author:
Publisher: Academic Press
ISBN: 0080873391
Category : Mathematics
Languages : en
Pages : 277
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Book Description
The Four-Color Problem
Author: Benjamin Schwartz
Publisher: Routledge
ISBN: 1351843079
Category : Games & Activities
Languages : en
Pages : 161
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Book Description
A collection of solitaires and games which include sections on Solitiare Games like Knights Interchanges and The Stacked Playing Cards; Competitive games including SIM as a game of Chance and A winning Opening in Reverse Hex and also Solitaire games with toys like the Tower of Hanoi and Triangular Puzzle Peg.
Author: Lowell W. Beineke
Publisher: Cambridge University Press
ISBN: 1316239853
Category : Mathematics
Languages : en
Pages : 416
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Book Description
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.
Author: Oscar Levin
Publisher: Createspace Independent Publishing Platform
ISBN: 9781534970748
Category :
Languages : en
Pages : 342
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Book Description
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. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. 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.
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
ISBN: 0821836781
Category : Mathematics
Languages : en
Pages : 330
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Book Description
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.
Author: Andrzej Lingas
Publisher: Springer Science & Business Media
ISBN: 9783540569398
Category : Computers
Languages : en
Pages : 716
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Book Description
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.
