000			02456nam a2200229 a 4500
020			_a9780387987361
020			_a0387987363
082			_a511.64 _bHAR
100			_aHarris, John M.
245			_aCombinatorics and graph theory
260			_aNew York : _bSpringer, _c©2000.
300			_axiii, 225 pages : _billustrations ;
490			_aUndergraduate texts in mathematics.
500			_aIncludes index
505			_a1. Graph theory -- 1.1 Introductory concepts -- 1.2 Trees -- 1.3 Planarity -- 1.4 Colorings -- 1.5 Matchings -- 1.6 Ramsey theory -- 1.7 References -- 2. Combinatorics -- 2.1 Three basic problems -- 2.2 Binomial coefficients -- 2.3 The principle of inclusion and exclusion -- 2.4 Generating functions -- 2.5 Pólya's theory of counting -- 2.6 More numbers -- 2.7 Stable marriage -- 2.8 References -- 3. Infinite combinatorics and graphs -- 3.1 Pigeons and trees -- 3.2 Ramsey revisited -- 3.3 ZFC -- 3.4 The return of der König -- 3.5 Ordinals, cardinals, and many pigeons -- 3.6 Incompleteness and cardinals -- 3.7 Weakly compact cardinals -- 3.8 Finite combinatorics with infinite consequences -- 3.9 Points of departure -- 3.10 References.
520			_a "This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapter 1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey theory. Chapter 2 studies combinatorics, 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, Konig's lemma, and Ramsey's theorem, and discusses their connections to axiomatic set theory." "The text includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact 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."--Jacket.
650			_aCombinatorial analysis.
650			_aGraph theory.
700			_aHirst, Jeffry L.
700			_aMossinghoff, Michael J.
942			_cREF
999			_c13790 _d13790