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The Fascinating World of Graph Theory, by Arthur Benjamin, Gary Chartrand, Ping Zhang
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The fascinating world of graph theory goes back several centuries and revolves around the study of graphs--mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics--and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently? Requiring readers to have a math background only up to high school algebra, this book explores the questions and puzzles that have been studied, and often solved, through graph theory. In doing so, the book looks at graph theory's development and the vibrant individuals responsible for the field's growth.
Introducing graph theory's fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, the Minimum Spanning Tree Problem, the Königsberg Bridge Problem, the Chinese Postman Problem, a Knight's Tour, and the Road Coloring Problem. They present every type of graph imaginable, such as bipartite graphs, Eulerian graphs, the Petersen graph, and trees. Each chapter contains math exercises and problems for readers to savor.
An eye-opening journey into the world of graphs, this book offers exciting problem-solving possibilities for mathematics and beyond.
- Sales Rank: #459538 in Books
- Published on: 2015-01-18
- Original language: English
- Number of items: 1
- Dimensions: 8.00" h x 5.00" w x 1.00" l, .0 pounds
- Binding: Hardcover
- 344 pages
Review
One of Choice's Outstanding Academic Titles for 2015
"The Fascinating World of Graph Theory is readable and 'student-friendly'--more so than the typical math textbook."--Robert Schaefer, New York Journal of Books
"[The authors] have set out to make graph theory not only accessible to people with a limited mathematics background, but also to make it interesting. They have--by virtue of very clear writing, combined with a greater-than-usual emphasis on the historical and personal side of the subject--succeeded admirably."--Mark Hunacek, MAA Reviews
"The book is written masterfully; the narrative in each chapter flows naturally, engagingly. . . . [I]t's a popular but also comprehensive introduction into graph theory."--Alexander Bogomolny, Cut the Knot blog
"This book is a fun and interesting tour of graph theory, leaving each visitor with a feeling of accomplishment and a satisfying understanding of this unusual mathematical world. . . . This is an entertaining book for those who enjoy solving problems, plus readers will learn about some powerful mathematical ideas along the way!"--Choice
"Here is a book with an enjoyable mix of mathematics and its applications, spiced with liberal amounts of history and anecdote. . . . The value of books like this is that they make mathematics come alive to a broad range of readers who might not look twice at a textbook or monograph."--Norman Biggs, London Mathematical Society Newsletter
"A deftly written and dynamic introduction to graph theory. . . . A superb example of approachable mathematical writing aimed at a broad audience."--Matthew G. Hudelson, SIAM Review
"The authors manage to motivate all topics with interesting applications, historical problems and discussion of concepts from an intuitive point of view."--Radu Trîmbitas, Studia Mathematica
From the Back Cover
"In this attractive introduction to the world of graphs, the authors entice and enthuse readers through a number of fun problems which present various aspects of the subject. Many of these problems are familiar--the four-color problem, the Königsberg Bridge problem, and 'instant insanity'--while others are less well known or of a more serious nature. This book can be used in different ways--as an entertaining book on recreational mathematics or as an accessible textbook on graph theory. I warmly recommend it."--Robin J. Wilson, author of Introduction to Graph Theory
"This is a beautiful introduction to graph theory! It is filled with fun material, clear explanations, and a nice collection of exercises. A great book."--William J. Cook, author of In Pursuit of the Traveling Salesman
"The Fascinating World of Graph Theory is wonderfully written. Entertaining applications appear first and the stories that accompany the examples go well beyond what most other books provide. This book is sure to gain a following."--Jonathan L. Gross, Columbia University
About the Author
Arthur Benjamin is professor of mathematics at Harvey Mudd College. His books include Secrets of Mental Math and Proofs That Really Count. Gary Chartrand is professor emeritus of mathematics at Western Michigan University. Ping Zhang is professor of mathematics at Western Michigan University. Chartrand and Zhang are the coauthors of several books, including A First Course in Graph Theory and Discrete Mathematics.
Most helpful customer reviews
28 of 36 people found the following review helpful.
Fascinating, yes; but also underwhelming
By Herbert L Calhoun
As a retired mathematician, I had not visited graph theory since graduate school, where I learned a great deal about it from the Mathematician Frank Harary's book. So, I was excited to see this title and could not wait to see what was new inside the book.
But ... Well, how shall I put it? After the introduction, I was underwhelmed by this book.
First, the authors tipped-off that they had solved the "Five Princes Problem" introduced in chapter 1 but announced they would not show the solution until chapter 10. Since I could not wait until chapter 10, I naturally flipped to that chapter, but the "Five Princes Problem" was not mentioned there at all? So, then I checked the index, hoping the reference in the intro was simply mistaken, and that it might appear in some other chapter? But the index had only the single entry that appeared in the introduction. (How could you?)
Similarly with the "Konigsberg Bridge Problem," which as it turns out, has a trivial solution depending on where you begin? Well, how could one find seeking out a less elegant but much more complicated solution interesting? I certainly did not!
But also, you did not warn the reader that most of the book would be about proving theorems of use only to Mathematicians who might use graph theory for other more advanced mathematical purposes? After about two dozen of them, those theorems that lead to no where, get to be pretty boring.
Finally, to add insult to injury, my graph theory hero, Frank Harary was mentioned only once throughout the entire book, on pages 252-254 and in a poem in the epilogue. Aggrrr! Two stars
3 of 3 people found the following review helpful.
VERY ENTERTAINING INTRODUCTION TO GRAPH THEORY!!
By COSMIC TRAVELER
Are you a theoretical mathematician? If you are, then this book is for you. Authors Arthur Benjamin, Gary Chartrand and Ping Zhang, have written an outstanding book that introduces you to one of the many remarkable areas of mathematics: Graph Theory.
The authors begin with some curious problems--all of which can be looked at mathematically by means of the main concept of this book: graphs. Next, they discuss theorems from many areas of mathematics that have bee judged among the most beautiful. Then, the authors describe the most fundamental property that a graph can possess, by dealing with the idea that within the graph, travel is possible between every two locations. Also, the authors provide the simplest structure that a connected graph can possess, leading the reader to the class graphs called trees, because they often look like trees. They then doodle with a well-known problem: The Chinese Postman Problem, which deals with minimizing the length of a round trip that a letter carrier might take. Then, the authors discuss a class of graphs named for a famous physicist and mathematician of the nineteenth century: Sir William Rowan Hamilton. In addition, through graph theory, they explain how different types of scheduling are possible. Also, the authors then explain problems of whether a graph can be divided into certain other kinds of graphs, primarily cycles. They then discuss how various voting techniques can result in often surprising outcomes. Next, the authors continue by looking at interesting problems that can be drawn in the plane without any of their edges crossing. Then, they discuss the Four Color Problem: Famous not only for the length of time it took to solve, but for the controversial method that is used to solve it. Finally, the authors conclude with a curious theorem called Road Coloring Theorem, which tells us that in certain traffic systems consisting only of one-way streets in which the same number of roads leave each location, roads can be colored so that directions can be given to arrive at some destination, regardless of the location where the traveler presently resides.
This excellent book introduces you to a subject to which you may have had little or no exposure: The field of graph theory. Among the many things discussed in this great book, is how often a rather curious problem or question can lead not only to a mathematical solution, but to an entire topic in mathematics.
1 of 2 people found the following review helpful.
Good but I keep looking for a book that is ...
By Turkish Rabbi
Good but I keep looking for a book that is less focused on theory (theorems, proofs, etc) and more on application.
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