Applied combinatorics

書誌事項

Applied combinatorics

Alan Tucker

Wiley, c2002

4th ed

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

This book is designed for use by students with a wide range of ability and maturity. The stronger the students, the harder the exercises that can be assigned. The book can be used for one--quarter, two--quarter, or one--semester course depending on how much material is used. Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This book teaches students in the mathematical sciences how to reason and model combinatorically. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problem solving. The three principle aspects of combinatorical reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem (e.g. finding manageable subpieces or first solving the problem with three objects instead of n), and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.

目次

GRAPH THEORY. Elements of Graph Theory. Covering Circuits and Graph Coloring. Trees and Searching. Network Algorithms. ENUMERATION. General Counting Methods for Arrangements and Selections. Generating Functions. Recurrence Relations. Inclusion- Exclusion. ADDITIONAL TOPICS. Polya's Enumeration Formula. Games with Graphs. Appendix 1: Set Theory. Appendix 2: Mathematical Induction. Appendix 3: A Little Probability. Appendix 4: The Pigeonhole Principle. Glossary of Counting and Graph Theory Terms. Bibliography. Solutions to Odd-Numbered Problems. Index

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詳細情報

  • NII書誌ID(NCID)
    BA54650885
  • ISBN
    • 047143809X
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    New York
  • ページ数/冊数
    ix, 446 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
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