The Fascinating World of Graph Theory (Hardcover)
暫譯: 圖論的迷人世界 (精裝版)
Arthur Benjamin, Gary Chartrand, Ping Zhang
- 出版商: Princeton University
- 出版日期: 2015-01-18
- 售價: $1,270
- 貴賓價: 9.5 折 $1,207
- 語言: 英文
- 頁數: 344
- 裝訂: Hardcover
- ISBN: 0691163812
- ISBN-13: 9780691163819
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商品描述
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.
商品描述(中文翻譯)
圖論的迷人世界可以追溯到幾個世紀前,圍繞著圖的研究——這是一種數學結構,用於顯示物體之間的關係。圖論在生物學、計算機科學、交通科學及其他領域都有應用,涵蓋了一些數學中最美麗的公式以及一些最著名的問題。例如,對於一位旅行推銷員來說,尋找在一次旅行中訪問多個城市的最短路徑是什麼?填充任何地圖所需的最少顏色數量是多少,以確保相鄰區域的顏色始終不同?這本書要求讀者的數學背景僅需到高中代數,探討了通過圖論研究並經常解決的問題和謎題。在此過程中,書中回顧了圖論的發展及為該領域成長做出貢獻的活躍人物。
在介紹圖論的基本概念時,作者探討了多種經典問題,如熄燈謎題、最小生成樹問題、柯尼斯堡橋問題、中國郵差問題、騎士巡遊以及道路著色問題。他們展示了各種各樣的圖類型,例如二部圖、歐拉圖、彼得森圖和樹。每一章都包含數學練習和問題,供讀者品味。
這本書是一場進入圖的世界的啟發性旅程,為數學及其他領域提供了令人興奮的問題解決可能性。