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Combinatorics : an upper-level introductory course in enumeration, graph theory, and design theory

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    Author: Morris, Joy
    Contributor: BC Open Textbook Project; BCcampus
    Date:
    Created
    2017
    Summary:

    Combinatorics provides an introduction to enumeration, graph theory, and design theory. It is aimed at upper-level undergraduate students and the exercises expect some mathematical sophistication, including a reasonable ability to construct proofs. The text is designed to be used in an undergraduate course, but could be suitable for independent study by a student with some mathematical background and understanding of proofs. It does not assume any background knowledge of combinatorics.

    Contents:
    • What is Combinatorics?
    • Part I. Enumeration. Basic Counting Techniques
    • Permutations, Combinations, and the Binomial Theorem
    • Bijections and Combinatorial Proofs
    • Counting with Repetitions
    • Induction and Recursion
    • Generating Functions
    • Generating Functions and Recursion
    • Some Important Recursively-Defined Sequences
    • Other Basic Counting Techniques
    • Part II. Graph Theory. Basics of Graph Theory
    • Moving through graphs
    • Euler and Hamilton
    • Graph Colouring
    • Planar graphs
    • Part III. Design Theory. Latin squares
    • Designs
    • More designs
    • Designs and Codes
    • Appendix A. Solutions to selected exercises.
    Genre:
    Instructional and educational works, Math and science
    Subject(s): Combinatorial analysis | Textbooks
    Original Publisher: [Place of publication not identified], Joy Morris
    Language(s): English
    Collection(s)/Series: BC Open Textbooks