Combinatorial Mathematics This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods. Douglas B. West (Author) 9781107058583, Cambridge University Press Hardback, published 16 July 2020 988 pages, 2200 exercises25.2 x 19.8 x 5.7 cm, 2 kg '… this is a great, well-written book, covering the main topics of combinatorics; it is a great option to support several types of courses in combinatorics, perfect as a textbook for graduate students, and very useful for researchers. Highly recommended.' Juan José Montellano Ballesteros, zbMATH This 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. Introduction Part I. Enumeration: 1. Combinatorial arguments 2. Recurrence relations 3. Generating functions 4. Further topics Part II. Graphs: 5. First concepts for graphs 6. Matchings 7. Connectivity and cycles 8. Coloring 9. Planar graphs Part III. Sets: 10. Ramsey theory 11. Extremal problems 12. Partially ordered sets 13. Combinatorial designs Part IV. Methods: 14. The probabilistic method 15. Linear algebra 16. Geometry and topology Appendix. Hints to selected exercises References Author index Notation index Subject index. Subject Areas: Combinatorics & graph theory [PBV], Discrete mathematics [PBD]
