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The Four-Color Theorem: History, Topological Foundations, and Idea of Proof - Tapa dura

Fritsch, Gerda; Fritsch, Rudolf

 
9780387984971: The Four-Color Theorem: History, Topological Foundations, and Idea of Proof
Tapa dura
ISBN 10: 0387984976 ISBN 13: 9780387984971
Editorial: Springer, 1998

Sinopsis

1 History.- 2 (Topological) Maps.- 3 The Four-Color Theorem (Topological Version).- 4 Topology to Combinatorics.- 5 The Four-Color Theorem (Combinatorial Version).- 6 Reducibility.- 7 The Quest for Unavoidable Sets.- Works of Reference.

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De la contraportada

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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Editorial
Springer
Año de publicación
1998
Idioma
Inglés
ISBN 10 
0387984976
ISBN 13 
9780387984971
Encuadernación
Tapa dura
Número de páginas
280
Contacto del fabricante
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