Combinatorics and Graph Theory
(Sprache: Englisch)
The second edition of this text on combinatorics and graph theory includes new material on an array topics ranging from Eulerian trails to combinatorial geometry to the pigeonhole principle. There are also numerous new exercises throughout the book.
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Produktinformationen zu „Combinatorics and Graph Theory “
The second edition of this text on combinatorics and graph theory includes new material on an array topics ranging from Eulerian trails to combinatorial geometry to the pigeonhole principle. There are also numerous new exercises throughout the book.
Klappentext zu „Combinatorics and Graph Theory “
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, Pólya 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 and 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 fact that mathematics is a living discipline. The text is primarily directed toward upper-division undergraduate students, but lower-division undergraduateswith a penchant for proof and graduate students seeking an introduction to these subjects will also find much of interest.
Inhaltsverzeichnis zu „Combinatorics and Graph Theory “
- 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
Bibliographische Angaben
- Autoren: John Harris , Jeffry L. Hirst , Michael Mossinghoff
- 2008, 2nd ed., 381 Seiten, Maße: 16,3 x 23,9 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387797106
- ISBN-13: 9780387797106
Sprache:
Englisch
Rezension zu „Combinatorics and Graph Theory “
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"From the reviews of the second edition: "Any undergraduate work in combinatorics or graph theory, whether a course or independent study, would likely be well served by this textbook ... . The authors offer a wide selection of topics, often in more depth than other undergraduate texts, in an engaging and clear style. ... Each chapter concludes with extensive notes on further reading." (Brian Hopkins, Mathematical Reviews, Issue 2010 b) "Combinatorics and Graph Theory is a popular pair of topics to choose for an undergraduate course. ... The book is written in a reader-friendly style and there are enough exercises. ... It is certainly good that someone took the effort to write ... in a form that is appropriate for undergraduates. ... the book will most often be used for a reading class by a student who already has a background in combinatorics and who wants to learn about the set theoretical aspect of it." (Miklós Bóna, SIGACT News, Vol. 40 (3), 2009)"This undergraduate textbook contains three chapters: Graph Theory, Combinatorics and Infinite Combinatorics and Graphs. ... There is a short section on References in each chapter introducing briefly other books dealing with the topics covered in the respective chapter. A full list of 293 references, about 550 exercises and an index with 13 pages are also provided." (Dalibor Froncek, Zentralblatt MATH, Vol. 1170, 2009)
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