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COMBINATORIAL MATHEMATICS 2020 (H)
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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.
> Can be used as a text for a one-year sequence, or as a one-semester introduction leading to an advanced course, with a complete solutions manual available online for instructors > Contains more than 2200 exercises at various levels. Especially instructive, interesting, or valuable exercises are marked with a diamond symbol > Includes several thousand references (with pointers to pages where cited) and many exercises, theorems, and proofs that have not previously appeared in textbooks
Table of Contents
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. |
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Springer 國外現貨




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