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west d combinatorial mathematics 2020

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Textbook in PDF format 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. From the Preface: Combinatorics is now a mature discipline. Although some see it as a maelstrom of isolated problems, it has central themes, techniques, and results that make it a surprisingly coherent subject. Meanwhile, it still rewards its students with endless discovery and delight. This book introduces the reader to a substantial portion of combinatorics. It is not exhaustive in topics, results, or bibliography. However, it is thorough enough to equip the reader with the tools needed to read or do research in combinatorics or to apply combinatorics in other areas of mathematics and computer science. It assumes the maturity and sophistication of graduate students without assuming prior exposure to combinatorics. It assumes basic undergraduate mathematics, such as elementary set theory, induction, equivalence relations, limits, elementary calculus, and some linear algebra. More advanced or specialized material is planned to appear in The Art of Combinatorics, a four-volume series of texts intended for researchers and for advanced graduate courses in combinatorics. Nevertheless, there is enough here to reward substantial study and investigation. Preface. Introduction. Enumeration Combinatorial Arguments. Recurrence Relations. Generating Functions. Further Topics. Graphs First Concepts for Graphs. Matchings. Connectivity and Cycles. Coloring. Planar Graphs. Sets Ramsey Theory. Extremal Problems. Partially Ordered Sets. Combinatorial Designs. Methods The Probabilistic Method. Linear Algebra. Geometry and Topology. Hints to Selected Exercises References Author Index Glossary of Notation Subject Index

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west d combinatorial mathematics 2020

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