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AuthorHarris, John M. author
TitleCombinatorics and Graph Theory [electronic resource] / by John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
ImprintNew York, NY : Springer New York : Imprint: Springer, 2000
Connect tohttp://dx.doi.org/10.1007/978-1-4757-4803-1
Descript XIII, 228 p. online resource

SUMMARY

Three things should be considered: problems, theorems, and applications. - Gottfried Wilhelm Leibniz, Dissertatio de Arte Combinatoria, 1666 This book grew out of several courses in combinatorics and graph theory given at Appalachian State University and UCLA in recent years. A one-semester course for juniors at Appalachian State University focusing on graph theory covered most of Chapter 1 and the first part of Chapter 2. A one-quarter course at UCLA on combinatorics for undergraduates concentrated on the topics in Chapter 2 and included some parts of Chapter I. Another semester course at Appalachian State for advanced undergraduates and beginning graduate students covered most of the topics from all three chapters. There are rather few prerequisites for this text. We assume some familiarity with basic proof techniques, like induction. A few topics in Chapter 1 assume some prior exposure to elementary linear algebra. Chapter 2 assumes some familiarity with sequences and series, especially Maclaurin series, at the level typically covered in a first-year calculus course. The text requires no prior experience with more advanced subjects, such as group theory


CONTENT

Graph Theory: Introductory Concepts -- Trees -- Planarity -- Colorings -- Matchings -- Ramsey Theory -- References; Combinatorics: Three Basic Problems -- Binomial Coefficients -- The Principle of Inclusion and Exclusion -- Generating Functions -- Polya's Theory of Counting -- More Numbers -- Stable Marriage -- References; Infinite Combinatorics and Graph Theory: Pigeons and Trees -- Ramsey Revisited -- ZFC -- The Return of der Koenig -- Ordinals, Cardinals, and Many Pigeons -- Incompleteness and Coardinals -- Weakly Compact Cardinals -- Finite Combinatorics with Infinite Consequences -- Points of Departure -- References


Mathematics Combinatorics Mathematics Combinatorics



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