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Fascinating World of Graph Theory [Kietas viršelis]

3.95/5 (115 ratings by Goodreads)
  • Formatas: Hardback, 344 pages, aukštis x plotis: 235x152 mm, weight: 680 g, 300 line illus.
  • Išleidimo metai: 18-Jan-2015
  • Leidėjas: Princeton University Press
  • ISBN-10: 0691163812
  • ISBN-13: 9780691163819
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 344 pages, aukštis x plotis: 235x152 mm, weight: 680 g, 300 line illus.
  • Išleidimo metai: 18-Jan-2015
  • Leidėjas: Princeton University Press
  • ISBN-10: 0691163812
  • ISBN-13: 9780691163819
Kitos knygos pagal šią temą:
An introduction to the mathematical study of graphs draws on a range of disciplines while tracing the theory's development, some of its most famous problems and the achievements of some of its most significant contributors.

Benjamin, Chartrand, and Zhang present this book on graph theory, written in relaxed style but containing end of chapter exercises making it usable as a textbook. In contrast to the typical mathematics approach of building up from the simplest elements, this book begins by introducing some of the most well-known or intriguing problems and theorems in the field, then discussing how to approach them. Topics explored include graph classification, distance and travel, trees, traversing and encircling, factoring and decomposing, orienting, drawing, coloring, and synchronizing graphs. Although proofs are offered which are likely to be inaccessible without mathematical training, the casual reader will still find much of conceptual interest in the text. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

Recenzijos

One of Choice's Outstanding Academic Titles for 2015 "The Fascinating World of Graph Theory shows its pedagogic value. Traditional courseware develops subject matter from the bottom on up, going from basic definitions to the more complex. [ This book] is different, not starting with the simplest structures or algorithms but with interesting problems to be solved, puzzles that use graphs and networks... [ It is] readable and 'student-friendly'--more so than the typical math textbook."--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."--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 "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 "Deftly written and dynamic...The Fascinating World of Graph Theoryis an aptly named book, able to present a wide variety of central topics in graph theory, including the history behind them... in a lively and entertaining manner... A superb example of approachable mathematical writing."--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 Trimbitas, Studia Mathematica "I am not going to try to list the topics that are covered, since there is a great variety. This breadth, along with the superb writing, make the book a must-have for anyone with serious interest in graph theory."--James M. Cargal, UMAP Journal

Daugiau informacijos

Short-listed for Choice Magazine Outstanding Reference/Academic Book Award 2015.
Preface vii
Prologue xiii
1 Introducing Graphs
1(21)
2 Classifying Graphs
22(23)
3 Analyzing Distance
45(22)
4 Constructing Trees
67(24)
5 Traversing Graphs
91(17)
6 Encircling Graphs
108(17)
7 Factoring Graphs
125(18)
8 Decomposing Graphs
143(21)
9 Orienting Graphs
164(19)
10 Drawing Graphs
183(23)
11 Coloring Graphs
206(20)
12 Synchronizing Graphs
226(25)
Epilogue Graph Theory: A Look Back---The Road Ahead 251(4)
Exercises 255(54)
Selected References 309(8)
Index of Names 317(2)
Index of Mathematical Terms 319
Arthur Benjamin is professor of mathematics at Harvey Mudd College. Gary Chartrand is professor emeritus of mathematics at Western Michigan University. Ping Zhang is professor of mathematics at Western Michigan University.