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Combinatorial Mathematics

All titles
Combinatorial Mathematics

Combinatorial Mathematics

Douglas B. West, University of Illinois, Urbana-Champaign
July 2020
Hardback
9781107058583

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    Description

    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

    Reviews & endorsements

    'This is a great book by a great writer. It covers the main topics of combinatorics, is well written and presents many beautiful ideas and techniques. It is very helpful to students, teachers and researchers. I would like to have this book on my desk.' Alexandr Kostochka, University of Illinois

    'This is a real gem, capturing the spirit, breadth and depth of combinatorics. Doug West is a master of exposition, his thorough treatment of the subject will be useful for students and researchers in mathematics and computer science.' Noga Alon, Princeton University, New Jersey

    'A comprehensive and comprehensible treatment of combinatorial mathematics - what the author intended, and more - a valuable resource on the subject. It may well stimulate the addition to the university curriculum of courses in this area. Borrowing advice from the past, my recommendation for anyone wanting a definitive book on combinatorics is 'Go West, my friend, go West!'' Lowell Beineke, Purdue University Fort Wayne

    'I have taught out of this book for many years. It is the ideal textbook for graduate students or advanced undergraduates. The book is filled with lots of great problems that are well suited for homework assignments and potential research projects. Highly recommended.' Arthur Benjamin, Harvey Mudd College, California

    'This book is impressive both for its breadth and its hundreds of exercises. Serious study of it will richly reward the reader.' Daniel Cranston, Virginia Commonwealth University

    '… 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

    See more reviews

    Product details

    July 2020
    Hardback
    9781107058583
    988 pages
    252 × 198 × 57 mm
    2kg
    2200 exercises
    Available

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    Contents

    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.
      • Show more

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