Combinatorics (Google eBook)

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John Wiley & Sons, Sep 24, 2003 - Mathematics - 576 pages
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A mathematical gem–freshly cleaned and polished

This book is intended to be used as the text for a first course in combinatorics. the text has been shaped by two goals, namely, to make complex mathematics accessible to students with a wide range of abilities, interests, and motivations; and to create a pedagogical tool, useful to the broad spectrum of instructors who bring a variety of perspectives and expectations to such a course.

Features retained from the first edition:

  • Lively and engaging writing style
  • Timely and appropriate examples
  • Numerous well-chosen exercises
  • Flexible modular format
  • Optional sections and appendices

Highlights of Second Edition enhancements:

  • Smoothed and polished exposition, with a sharpened focus on key ideas
  • Expanded discussion of linear codes
  • New optional section on algorithms
  • Greatly expanded hints and answers section
  • Many new exercises and examples
  

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Contents

Chapter 1 The Mathematics of Choice
1
Chapter 2 The Combinatorics of Finite Functions
117
Chapter 3 Pólyas Theory of Enumeration
175
Chapter 4 Generating Functions
253
Chapter 5 Enumeration in Graphs
337
Chapter 6 Codes and Designs
421
Appendix A1 Symmetric Polynomials
477
Appendix A2 Sorting Algorithms
485
Appendix A3 Matrix Theory
495
Bibliography
501
Hints and Answers to Selected OddNumbered Exercises
503
Index of Notation
541
Index
547
Copyright

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Popular passages

Page xii - It seems that mathematical ideas are arranged somehow in strata, the ideas in each stratum being linked by a complex of relations both among themselves and with those above and below. The lower the stratum, the deeper (and in general the more difficult) the idea. Thus the idea of an "irrational" is deeper than that of an integer; and Pythagoras's theorem is, for that reason, deeper than Euclid's.
Page 20 - It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge. . . . The most important questions of life are, for the most part, really only problems of probability.

References to this book

Multilinear Algebra
Russell Merris
Limited preview - 1997

About the author (2003)

RUSSELL MERRIS, PhD, is Professor of Mathematics and Computer Science at California State University, Hayward. Among his other books is Graph Theory, also published by Wiley.

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