Graph Theory As I Have Known It (Oxford Lecture Series in Mathematics and Its Applications, 11) 1st Edition by W. T. Tutte (PDF)

Description

William Tutte, one of the founders of modern graph theory, provides a unique and personal introduction to the field. Instead of a typical survey, the author looks back at the areas which interested him most, discussing why he pursued certain problems and how he and his colleagues solved them. The book’s extensive references make it a useful starting point for research as well as an important document for anyone interested in the history of graph theory. The author begins with the problems he worked on as an undergraduate at Cambridge and goes on to cover subjects such as combinatorial problems in chess, algebra in graph theory, reconstruction of graphs, symmetry in graphs, and the chromatic eigenvalues. In each case he mixes fascinating historical and biographical information with engaging descriptions of important results.

User’s Reviews

Editorial Reviews: Review “In 1935 Bill Tutte went up to Cambridge University to read for the Natural Sciences Tripos, specialising in chemistry. He also had sufficient interest in mathematical problems to join the Trinity Mathematical Society where he met three mathematics students . . . A problem . . . prompted the four to study the dissection of rectangles into squares and this led them into the realms of graph theory, a subject then researched by comparatively few people. . . . Bill Tutte then turned from chemistry to mathematics and went on to become one of the most distinguished persons in graph theory. . . . [T]he present book . . . is not a comprehensive treatise on graph theory but is restricted to those parts of the subject which Tutte himself researched, telling how he was led to his theorems and their proofs. . . . For those of us who find much research-level mathematical literature heavy going, it is good to have this readable account of how some of the ideas developed.”–Mathematical Reviews”Come, sit down with William T. Tutte, a great mathematician and pleasantly quiet man. He tells you of the friends of his youth and of the problems that filled their lives just before and just after World War II. Reading this book, you will see his early interest in the Hamiltonian cycle problem, his development of algebraic techniques in graph theory, the reconstruction conjecture, graphical enumeration and the Tutte polynomial, and much more. You will come to understand a fine man as well as gain insight into extraordinary mathematics. Tutte’s book presents the deterministic side of graph theory. It describes the mathematical life journey of one of the world’s great mathematicians. To an outsider, the topics he studied may seem unconnected. This book reveals their close connections, however, and they are deep and extensive. It also shows the very great attention to details that is visible in all of Tutte’s work.” — Arthur M. Hobbs, American Mathematical Monthly, April 2001 About the Author W. T. Tutte is a Professor, Department of Combinatorics and Optimization at University of Waterloo.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a unique book. Tutte covers a collection of problems that interested him throughout all his years of studying graph theory, and the detective work that went into finding their solutions. Most start with or relate to the Trinity Four, his group of like-minded fellow undergraduates that conjectured about problems, most of which seem to have to boiled down into graph theory. The tales are fascinating in their recollection of how different ideas came together to form solutions. The solutions are all elegant and ingenious and a pleasure to behold in this explanatory light.Most problems are presented requiring a minimal amount of background knowledge, though a certain degree of mathematical maturity is required (and necessary to fully appreciate things), and having a taken a course on graph theory would ease the digestion of some parts. Owing to the informal discourse, there is no dense theorem-proof-theorem-… division of the material. Rather, it is organized by some sort of problem-(fiddling around)-inspiration-(fiddling around)-eureka! format. But, Tutte keeps everything rigorous and easy to follow. Though, when things would get too tangentially technical, he resorts to illustrative examples. The references are complete, so anyone looking for more detail is taken care of.I believe most aspiring graph theorists would benefit from and relish this book by a master of the subject (and a grandfather to much of it).

⭐It is unquestionably that W. T. Tutte is today one the greatest mathematicians in the world. I read this book with great enthusiasm because the author explains, with the work that made his fame, the most difficult part of the discovery of mathematics: The creativity involved.The students will find in this book a great motivation to thinking in mathematics. For the experimented mathematician this book will make clear the born procces of some classic results in graph theory.This is an excellent book, is just the story of a life of work and fun.

⭐Not found.

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