Hardcover. 8vo. Published by Springer, New York, 1998. Xvi, 260 pages. Second Printing. Bound in cloth boards with titles present to the spine and front board. Boards have light shelf-wear present to the extremities. No ownership marks present. Text is clean and free of marks. Binding tight and solid. "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?"; 9.5 X 6.4 X 0.7 inches; 260 pages.

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Detalles bibliogr�ficos

T�tulo: The Four-Color Theorem History, Topological Foundations, and Idea of Proof
Editor: Springer, E-072
Fecha de publicaci�n: 1998
Idioma: Ingl�s
ISBN 10: 0387984976
ISBN 13: 9780387984971
Encuadernaci�n: Hardcover
Estado: Very Good

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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.

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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I have been selling books for more than 20 years. I am a specialist in out of print and rare academic titles, art, history, military history and what I like to loosely describe as "Old and Interesting." Here is a helpful list of book terms that I use: Terms for Describing Condition These terms apply to books, dust jackets and magazines. As New is when the book is in the same immaculate condition in which it was published. There are no defects and the dust jacket, if issued with one, is perfect. Fine approaches the condition of "As New," but without being crisp. There may be minor defects, which are noted. Very Good describes a book that does show some small signs of wear but no tears on either binding or paper. Any defects are noted. Good describes the average used and worn book that has all pages or leaves present. All defects are noted. Fair is a well-worn book that has complete text pages but may lack endpapers, half title page, etc. All defects are noted. Poor describes a book that is sufficiently worn so that its only merit is as a reading copy. This book may be soiled, scuffed, stained or spotted and may have loose joints, hinges, pages, etc. All defects are noted. Ex-library books are always noted as such regardless of condition. Book Club Editions (BCE) are always noted as such regardless of condition. Boards are the actual hardcover material of the cover, front and back. Bookplate is usually a square illustrated sticker on which an owner writes his or her name, or on which the author has signed his or her name. Bumped refers to the bent or rounded corners of the boards. Browning or tanning refers to brown or tan looking pages or page edges that appear in some older books. Chip is a tiny piece missing from the edge of the dust jacket. Closed tear is a tiny rip in the dust jacket, but no material is missing (as in a chip). It can be "shut" and protected from further tearing with a Mylar cover. Cocked means the book is no longer square. If laid down, the book appears to be pushed (slanted) forward or backward from the spine. Creasing is where the dust jacket or pages have been bent, and then returned to its original state. Dampstain is a tan or gray stain resulting from water or other liquid damage. End papers or pastedowns are the sheets of paper pasted onto the inner covers, joining the book block to the covers. One side of the sheet is pasted to the inside cover, the other is left free (see FFEP). FFEP stands for front free-endpaper. This is the first page of any book. Though usually blank, it is a common place for an inscription. Foxing is the term used for the rust colored spots which occur on paper. This is the result of oxidation of both organic and iron impurities left behind during the paper making process. Front, top or bottom edge: These are the outside page edges. Loose is what happens to a book which has been read several times. The cover easily flaps open and the pages do not return to a tight condition. Heal or tail is the bottom of the spine. Head is the top of the spine. Mass-Market paperback is the most common paperback book, about four inches wide and seven inches high. Seen most often as "popular" fiction, science fiction and romance books. Mylar cover is the clear film that most fine bookshops use to cover and protect the dust jackets. Spine separation occurs at the head (top) of the spine where the fingers grab and pull the book from the shelf. After repeated pulling, the glue holding the outer spine board to the inner binding separates. Sunned is the fading of paper or binding as a result of sun exposure. Trade paperback is a softcover book which is generally large in size and made of better quality materials than a Mass-Market paperback. Wraps are the outer covers of a softcover (paperback) book or pamphlet.

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