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The Four-Color Problem Paperback – January 1, 1986
- Print length217 pages
- LanguageEnglish
- PublisherDover Pubns
- Publication dateJanuary 1, 1986
- Dimensions5.5 x 0.25 x 8 inches
- ISBN-100486650928
- ISBN-13978-0486650920
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Product details
- Publisher : Dover Pubns (January 1, 1986)
- Language : English
- Paperback : 217 pages
- ISBN-10 : 0486650928
- ISBN-13 : 978-0486650920
- Item Weight : 8 ounces
- Dimensions : 5.5 x 0.25 x 8 inches
- Best Sellers Rank: #5,981,498 in Books (See Top 100 in Books)
- #65,693 in Mathematics (Books)
- Customer Reviews:
About the author
Dr. Thomas L. Saaty is a Distinguished University Professor at the University of Pittsburgh's Joseph M. Katz Graduate School of Business. Dr. Saaty is the creator of the Analytic Hierarchy Process (AHP), a mathematical method that is proven to enhance decision-making outcomes for complex and thorny problems, especially those that involve multiple stakeholders, a scarcity of resources, limited data, and limited time with which to make a decision — in short, all of the factors inherent in the study of economics.
During the past thirty years, Dr. Saaty's pioneering AHP method has been applied, either directly by himself or others, to a broad spectrum of political and economic quandaries. Poland has used the AHP to determine if and when to adopt the euro for its currency. China has used the AHP to decide on the suitability of locations for dams and bridges and whether or not to build them. The National Cancer Institute has used the AHP to prioritize cancer antigens for investment. British Airways has used it to decide on the best entertainment equipment to put in its fleet. Corporations have used it to decide the feasibility of acquiring manufacturing plants in countries overseas. Indeed, the AHP process has virtually limitless applications, and thanks to advanced software and computing power, the process is more scalable than ever.
Dr. Saaty has written more than 35 books and hundreds of academic papers. He earned his PhD in mathematics from Yale University and did post-graduate study at the University of Paris at the Sorbonne. Prior to joining the faculty of the Katz School in 1979, Dr. Saaty was a professor or 10 years at the University of Pennsylvania's Wharton School of Business. Dr. Saaty's global impact has spread through the quality and breadth of his publications. There is now an International Symposium on the AHP, ISAHP, established in 1988, that takes place every two years and also an International Journal of the Analytic Hierarchy Process, IJAHP, devoted to papers about the theory and application of AHP.
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- Reviewed in the United States on October 8, 2016The statement of the mathematical problem known as the Four Colour Conjecture (4CC) until the sensational news of its solution by Appel and Haken in 1976, is easily understood by any schoolboy or schoolgirl. The 4CC was first formulated by Cambridge University student Francis Guthrie in the middle of the nineteenth century and quickly caught the attention of prominent mathematicians in England. Some of the most famous mathematicians of the Victorian age dismissed it a mere puzzle and a few embarrassed themselves with erroneous solutions. Failed attempts to solve the 4CC inspired developments in modern graph theory over the next century but its solution eluded the efforts of everyone who attempted it. Long an attractive topic for amateur mathematicians, the 4CC even featured in Martin Gardner's infamous hoax column in the April 1975 edition of Scientific American. Then, in 1976, Appel and Haken surprised the world with their infeasibly long proof which, controversially, and portending a revolution, involved the use of a computer in an essential way. Yet, as is now universally agreed, their proof was valid; and no traditional proof of the 4CC, which does not involve the assistance of a computer, has been found so far. The use of computers in mathematical proofs has by now become less controversial.
Since the 4CC has always been a popular topic in recreational mathematics there are a number of well-known books written before the proof was published which mention it in the context of graph colouring. Yet there have been few books published since the proof of the 4CC. Some are non-technical and dwell on the colourful history of the men and their mathematics. Most of the actual mathematics of graph colouring is confined to textbooks and inaccessible academic journals.
This is probably the best book for the non-specialist who is interested in the mathematics surrounding the 4CC; and it is certainly the best value being a low priced Dover edition. The book is divided into two parts: Part One deals with the history and proof of the 4CC; Part Two discusses alternative formulations of the 4CC and techniques used in earlier attempts to solve the 4CC. This book should be enjoyed by anyone who is interested in the 4CC, who has a modest background in mathematics and is sufficiently inspired to put in a little effort.