The Fascinating World of Graph Theory by Arthur Benjamin, Gary Chartrand, Ping Zhang
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The Fascinating World of Graph Theory written by
Arthur T. Benjamin, Harvey Mudd College and
Gary Chartrand, Ping Zhang .
Mathematics rarely has the reputation we feel it deserves. To many, mathematics is an area that is, sadly, too difficult and too boring.
It requires too much effort to learn and to understand. It’s not as much fun as other subjects. In recent years there have been numerous articles written about how many American high-school students have been outperformed in mathematics and science by students from other nations.
There have also been reports of a marked decrease in the number of Americans in colleges earning graduate degrees in mathematics. For whatever reason, not nearly enough talented American students have become sufficiently excited about mathematics. For many students, this is a missed opportunity. For the United States, this is a missed opportunity.
There are many areas within mathematics and we happen to think that they are all exciting. Behind the many interesting theorems in each of these areas is a history of how these came about—a story of how some dedicated mathematicians discovered something of interest and importance. These theorems were often not only attractive to those who discovered them but in many cases unexpected to others. In many instances, these theorems turned out to be extraordinarily useful—both within and outside of mathematics. Our goal in this book is to introduce you to one of the many remarkable areas of mathematics. It is with pleasure that we invite you to enter
The Fascinating World of Graph Theory.
Like every other scholarly field, mathematics is composed of a number of areas, similar in many ways, yet each having their own distinct characteristics. The areas with which you are probably most familiar include algebra, geometry, trigonometry and calculus. Learning and understanding these subjects may very well have required some effort on your part but, hopefully, it has been interesting as well. In fact, learning any subject should be fun. But where did these and all viii Preface
other areas of mathematics come from? The answer to this question is that they came from people—from their curiosity, their imagination, their cleverness. Although many of these people were mathematicians, some were not. Sometimes they were students—like all of us are (or were).
It is our goal here to introduce you to a subject to which you may have had little or no exposure: the field of graph theory. While we wish to show you how interesting this area of mathematics is, we hope to convince you that mathematics itself is not only interesting but can in fact be exciting. So come with us as we take you along on what we believe will be a fascinating journey through the area of graph theory. Not only do we want to introduce you to many of the interesting topics in this area of mathematics, but it is our desire to give you an idea of how these topics may have been discovered and the kinds of problems they can be used to solve.
Among the many things we discuss here is how often a rather curious problem or question can lead not only to a mathematical solution but to an entire topic in mathematics. While it is not our intention to describe some deep or advanced mathematics here, we do want to give an idea of how we can convince ourselves that certain mathematical statements are true.
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.
Title: Teach Your Child Math : Making Math Fun for the Both of You
Author(s): Arthur Benjamin, Gary Chartrand, Ping Zhang
Publisher: Princeton University Press
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The Fascinating World of Graph Theory written by
Arthur Benjamin, Gary Chartrand, Ping Zhang
cover the following topics.
1. Introducing Graphs
2. Classifying Graphs
3. Analyzing Distance
4. Constructing Trees
5. Traversing Graphs
6. Encircling Graphs
7. Factoring Graphs
8. Decomposing Graphs
9. Orienting Graphs
10. Drawing Graphs
11. Coloring Graphs
12. Synchronizing Graphs
Epilogue Graph Theory: A Look Back—The Road Ahead
Index of Names
Index of Mathematical Terms
Open for free download
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