The Pre-Loved edit from Shopbop
To share your reaction on this item, open the Amazon app from the App Store or Google Play on your phone.
Buy used:
$6.74
$3.99 delivery January 30 - 31. Details
Used: Very Good | Details
Sold by HPB-Ruby
Condition: Used: Very Good
Comment: Connecting readers with great books since 1972! Used books may not include companion materials, and may have some shelf wear or limited writing. We ship orders daily and Customer Service is our top priority!
Access codes and supplements are not guaranteed with used items.
Kindle app logo image

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required.

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

QR code to download the Kindle App

Follow the author

Something went wrong. Please try your request again later.

The Four-Color Problem Paperback – January 1, 1986

3.5 3.5 out of 5 stars 2 ratings

off. Enter code INSTAPAY10 at checkout. Discount by Amazon. Terms  off. Promo code INSTAPAY10 is saved to your account. Discount by Amazon. Terms  
Paperback book. Approximately 5.5 x 8 sized book. A total of 217 pages. 1986, Dover Edition, first published in 1986, is an unbridged corrected republication of the work originally published by the McGraw-Hill International Book Company, NY, 1977, USA. The spine is tight, pages are clean and easy to read. Dover Publications, Inc. , NY. The boards show normal shelf wear. Bottom front board has a crease or fine line and bottom corner is worn or rubbed slightly. There is a tiny, very small, light brown stain about midway at the bottom of the book that is barely noticeable on the page edges, however does not bleed into the pages. A couple of minor finger line small creases on the back board where the previous owner held the book and read it. A good price for this book by Thomas L. Saaty and Paul C. Kainen. The following is taken from the prefix of this book: "We believe that mathematicians get more excitement by doing the entire job of proving the existence of solutions and then constructing them by themselves than they do by relying on the computer as a substantial partner in the undertaking. Still, ambitious experts in artificial intelligence are telling us that it will not be long before computers will be doing all that we do, better and faster." It continues: " We hope this book will continue to evoke interest in the four color problem, in its computer aided solution, and perhaps in finding an alternative way to prove it. By the way, a natural follow up would be a four color algorithm." A very interesting book and affordably priced.
The%20Amazon%20Book%20Review
The Amazon Book Review
Book recommendations, author interviews, editors' picks, and more. Read it now

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
  • Customer Reviews:
    3.5 3.5 out of 5 stars 2 ratings

About the author

Follow authors to get new release updates, plus improved recommendations.
Thomas L. Saaty
Brief content visible, double tap to read full content.
Full content visible, double tap to read brief content.

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.

Customer reviews

3.5 out of 5 stars
2 global ratings

Review this product

Share your thoughts with other customers

Top reviews from the United States

  • Reviewed in the United States on October 8, 2016
    The 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.
    One person found this helpful
    Report