An invitation to combinatorics
著者
書誌事項
An invitation to combinatorics
（Cambridge mathematical textbooks）
Cambridge University Press, 2022
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注記
Includes bibliographical references (p. 602-608) and index
内容説明・目次
内容説明
Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author - an award-winning teacher - writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.
目次
- Preface
- Introduction
- 1. Induction and Recurrence Relations
- 2. The Pigeonhole Principle and Ramsey Theory
- 3. Counting, Probability, Balls and Boxes
- 4. Permutations and Combinations
- 5. Binomial and Multinomial Coefficients
- 6. Stirling Numbers
- 7. Integer Partitions
- 8. The Inclusion-Exclusion Principle
- 9. Generating Functions
- 10. Graph Theory
- 11. Posets, Matchings, and Boolean Lattices
- Appendices
- Bibliography
- Index.
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