Douglas B. WestCambridge University Press, 7/16/2020EAN 9781107058583, ISBN10: 1107058589Hardcover, 988 pages, 25.1 x 19.8 x 5.6 cmLanguage: EnglishThis long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics. The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments. Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science. Optional more advanced material also makes it valuable as a research reference. Suitable for a one-year course or a one-semester introduction, this textbook prepares students to move on to more advanced material. It is organized to emphasize connections among the topics, and facilitate instruction, self-study, and research, with more than 2200 exercises (many accompanied by hints) at various levels of difficulty. Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language. The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.IntroductionPart I. Enumeration1. Combinatorial arguments2. Recurrence relations3. Generating functions4. Further topicsPart II. Graphs5. First concepts for graphs6. Matchings7. Connectivity and cycles8. Coloring9. Planar graphsPart III. Sets10. Ramsey theory11. Extremal problems12. Partially ordered sets13. Combinatorial designsPart IV. Methods14. The probabilistic method15. Linear algebra16. Geometry and topologyAppendix. Hints to selected exercisesReferencesAuthor indexNotation indexSubject index.
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