Combinatorial Mathematics

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.

Douglas B. West is Professor of Mathematics at Zhejiang Normal University and Professor Emeritus at the University of Illinois, where he won a campus-wide teaching award in 2002. Professor West has written more than 250 research articles on diverse topics in combinatorics and has advised 38 doctoral students. His earlier books include Introduction to Graph Theory (2001), a popular textbook adopted around the world for courses. He is Editor-in-Chief of Discrete Mathematics (since 2007) and Associate Editor of the American Mathematical Monthly (editing solutions for the Problems section since 1986). He also maintains web pages at https://faculty.math.illinois.edu/~west/ giving links to conferences in discrete mathematics and advice on writing mathematics.