Combinatorics And Graph Theory - Harris John-M

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Résumé :
This book evolved from several courses in combinatories and graph theory given et Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matching, and Ramsey theory. Chapter 2 studies combinatories, including the principle of inclusion and exclusion, generating functions, recurrence relations, Polya theory, the stable marriage problem, and several important classes of numbers. Chapter 3 presents infinite pigeonhole principles, König's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory. The text is written in an enthusiastic und lively style. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fort that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduates with a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest.

Biographie:
John-M Harris did his undergraduate work et Furman University, and he received his Ph.D. from Emory University. He has thought at Appalachian State University and at Furman. His primary mathematical interest is finite graph theory, focusing mainly on subgraphs, paths, und cycles. Jeffry-L Hirst is a mathematical logician and has published a number of papers analyzing the logical strength of theorems of infinite graph theory end combinatories. He received his BA and MA from the University of Kansas, and his Ph.D. from the Pennsylvania State University. He bas thought at the Ohio State University and Appalachian State University. Michael-J Mossinghoff received his undergraduate degree from Texas A & M University, his MS in computer science from Stanford University, and his Ph.D. in mathematics from the University of Texas at Austin. He has thought at Appalachian State University end UCLA. His research concerns analytic and algorithmic problems in number theory and combinatories.

Sommaire:
["GRAPH THEORY","Introductory concepts","Trees","Planarity","Colorings","Matchings","Ramsey Theory","COMBINATORICS","Three basic problems","Binomial coefficients","The principle of inclusion and exclusion","Generating functions","Polya's theory of counting","More numbers","COMBINATORICS AND GRAPHS","Pigeons and trees","Ramsey revisited","ZFC","The return of König","Ordinals, cardinals and many pigeons","Incompleteness and cardinals","Weakly compact cardinals","Finite combinatorics with infinite consequences","Points of departure","References."]