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The Four-Color Theorem

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The Four-Color Theorem Cover

 

Synopses & Reviews

Publisher Comments:

This elegant little 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 such that no two adjoining countries have the same color, no matter how convoluted their boundaries. Many famous mathematicians have worked on the problem, but the proof eluded fomulation until the 1950s, when it was finally cracked with a brute-force approach using a computer. The book begins by discussing the history of the problem, and then goes into the mathematics, both pleasantly enough that anyone with an elementary knowledge of geometry can follow it, and still with enough rigor that a mathematician can also read it with pleasure. The authors discuss the mathematics as well as 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?

Synopsis:

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?

Table of Contents

It's History.- Topological maps.- Topological Version of The Four-Color Theorem.- From Topology to Combinatorics.- The Combinatorial Version of The Four-Color Theorem.- Reducibility.- The Quest for Unavoidable Sets.

Product Details

ISBN:
9780387984971
Translator:
Peschke, J.
Author:
Peschke, J.
Author:
Fritsch, Rudolf
Author:
Fritsch, G.
Author:
Fritsch, R.
Publisher:
Springer
Location:
New York :
Subject:
Topology
Subject:
Four-color problem
Subject:
Topology - General
Subject:
MATHEMATICS / Topology
Series:
Universitext
Publication Date:
19980831
Binding:
Hardcover
Language:
English
Illustrations:
Y
Pages:
260
Dimensions:
9.50x6.38x.71 in. 1.22 lbs.

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Related Subjects


Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

The Four-Color Theorem New Hardcover
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Product details 260 pages Springer-Verlag - English 9780387984971 Reviews:
"Synopsis" by , 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?
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