Russell Merris

Combinatorics

• Gebundenes Buch

Produktbeschreibung

Updating and expanding upon the successful First Edition of Combinatorics, this new edition provides the foundation for mastering combinatorics. Blending an engaging style with mathematical rigor, Professor Merris provides a uniquely flexible tool for a wide variety of approaches to combinatorics. After covering the basics in the first two chapters, the structure of the book allows instructors to customize courses by selecting chapters and topics according to their own course needs.

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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

Produktdetails

• Wiley-Interscience Series in Discrete Mathematics and Optimization
• Verlag: Wiley & Sons
• 2. Aufl.
• Seitenzahl: 576
• Erscheinungstermin: 15. August 2003
• Englisch
• Abmessung: 240mm x 161mm x 35mm
• Gewicht: 930g
• ISBN-13: 9780471262961
• ISBN-10: 047126296X
• Artikelnr.: 11763924

Autorenporträt

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.

Inhaltsangabe

Preface. Chapter 1: The Mathematics of Choice. 1.1. The Fundamental
Counting Principle. 1.2. Pascal's Triangle. *1.3. Elementary Probability.
*1.4. Error-Correcting Codes. 1.5. Combinatorial Identities. 1.6. Four Ways
to Choose. 1.7. The Binomial and Multinomial Theorems. 1.8. Partitions.
1.9. Elementary Symmetric Functions. *1.10. Combinatorial Algorithms.
Chapter 2: The Combinatorics of Finite Functions. 2.1. Stirling Numbers of
the Second Kind. 2.2. Bells, Balls, and Urns. 2.3. The Principle of
Inclusion and Exclusion. 2.4. Disjoint Cycles. 2.5. Stirling Numbers of the
First Kind. Chapter 3: Pólya's Theory of Enumeration. 3.1. Function
Composition. 3.2. Permutation Groups. 3.3. Burnside's Lemma. 3.4. Symmetry
Groups. 3.5. Color Patterns. 3.6. Pólya's Theorem. 3.7. The Cycle Index
Polynomial. Chapter 4: Generating Functions. 4.1. Difference Sequences.
4.2. Ordinary Generating Functions. 4.3. Applications of Generating
Functions. 4.4. Exponential Generating Functions. 4.5. Recursive
Techniques. Chapter 5: Enumeration in Graphs. 5.1. The Pigeonhole
Principle. *5.2. Edge Colorings and Ramsey Theory. 5.3. Chromatic
Polynomials. *5.4. Planar Graphs. 5.5. Matching Polynomials. 5.6. Oriented
Graphs. 5.7. Graphic Partitions. Chapter 6: Codes and Designs. 6.1. Linear
Codes. 6.2. Decoding Algorithms. 6.3. Latin Squares. 6.4. Balanced
Incomplete Block Designs. Appendix A1: Symmetric Polynomials. Appendix A2:
Sorting Algorithms. Appendix A3: Matrix Theory. Bibliography. Hints and
Answers to Selected Odd-Numbered Exercises. Index of Notation. Index. Note:
Asterisks indicate optional sections that can be omitted without loss of
continuity.

Rezensionen

"...broad and interesting..." ( Zentralblatt Math , Vol.1035, No.10, 2004)
"...engagingly written...a robust learning tool..." ( American Mathematical Monthly , March 2004)