The Four Color Theorem

Author: Rudolf Fritsch
Publisher: Springer Science & Business Media
ISBN: 9781461217206
Release Date: 2012-12-06
Genre: Mathematics

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.

Graphs Colourings and the Four Colour Theorem

Author: Robert A. Wilson
Publisher: OUP Oxford
ISBN: 9780191583605
Release Date: 2002-01-24

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.

Explorations in Topology

Author: David Gay
Publisher: Elsevier
ISBN: 9780124166400
Release Date: 2013-12-04
Genre: Mathematics

Explorations in Topology, Second Edition, provides students a rich experience with low-dimensional topology (map coloring, surfaces, and knots), enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that will help them make sense of future, more formal topology courses. The book's innovative story-line style models the problem-solving process, presents the development of concepts in a natural way, and engages students in meaningful encounters with the material. The updated end-of-chapter investigations provide opportunities to work on many open-ended, non-routine problems and, through a modified "Moore method," to make conjectures from which theorems emerge. The revised end-of-chapter notes provide historical background to the chapter's ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides ideas for continued research. Explorations in Topology, Second Edition, enhances upper division courses and is a valuable reference for all levels of students and researchers working in topology. Students begin to solve substantial problems from the start Ideas unfold through the context of a storyline, and students become actively involved The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material


ISBN: STANFORD:36105022254762
Release Date: 1999
Genre: Academic libraries


ISBN: UOM:39076002412380
Release Date: 2003
Genre: Mathematics

Mathematics A Concise History and Philosophy

Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 0387942807
Release Date: 1994
Genre: Mathematics

This concise introduction explores the key mathematical and philosophical aspects of the history of mathematics. Detailed explanations of mathematical procedures used by famous mathematicians give readers a greater opportunity to learn the history and philosophy through problem solving. 23 illustrations.

Was ist Mathematik

Author: Richard Courant
Publisher: Springer-Verlag
ISBN: 9783642137013
Release Date: 2010-09-02
Genre: Mathematics

"Was ist Mathematik?" lädt jeden ein, das Reich der Mathematik zu betreten, der neugierig genug ist, sich auf ein Abenteuer einzulassen. Das Buch richtet sich an Leser jeden Alters und jeder Vorbildung. Gymnasiallehrer erhalten eine Fülle von Beispielen, Studenten bietet es Orientierung, und Dozenten werden sich an den Feinheiten der Darstellung zweier Meister ihres Faches erfreuen.