This book evolved from several courses in combinatorics and graph theory given at Appalachian State University and UCLA. Chapterß1 focuses on finite graph theory, including trees, planarity, coloring, matchings, and Ramsey Theory. Chapterß2 studies combinatorics, including the principle of inclusion and exclusion, generating functions, recurrence relations, P'äoülya Theory, the stable marriage problem, and several important classes of numbers. Chapterß3 presents infinite pigeonhole principles, K"äoünig's Lemma, and Ramsey's Theorem, and discusses their connections to axiomatic set theory.
Rezensionen / Stimmen
From the reviews:
SIAM REVIEW
"The narrative and proofs are well written, and the authors are given to frequent uses of humor. Students should find this book as easy to read as any other good-quality text written with them in mind. Each of the three chapters concludes with several paragraphs describing an excellent selection of more advanced texts or papers to consider for further study"
Reihe
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
1
1 s/w Abbildung
XIII, 228 p. 1 illus.
Dateigröße
ISBN-13
978-1-4757-4803-1 (9781475748031)
DOI
10.1007/978-1-4757-4803-1
Schweitzer Klassifikation
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.
