Combinatorial Methods with Computer Applications / Edition 1

by Jonathan L. Gross

Overview

Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course.

After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces.

Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.

Product Details

ISBN-13:	9781584887430
Publisher:	Taylor & Francis
Publication date:	11/16/2007
Series:	Discrete Mathematics and Its Applications
Edition description:	New Edition
Pages:	726
Product dimensions:	7.00(w) x 10.00(h) x (d)

Table of Contents

Preface. Introduction to Combinatorics. Sequences. Solving Recurrences. Evaluating Sums. Subsets and Binomials. Partitions and Permutations. Integer Operators. Graph Fundamentals. Graph Theory Topics. Graph Enumeration. Designs. Appendix. Bibliography. Solutions and Hints. Indices.

What People are Saying About This

From the Publisher

… The book is very carefully written and might be a good starting point for undergraduate students. …
—Zentralblatt MATH 1168

I recently got [this] book on combinatorics and applications to computer science, and I like it so much that I am trying to re-shape some of the discrete maths courses I teach so that I could use it. I liked particularly [the] section on asymptotics, which is much more accessible for my undergrads than Graham, Knuth, and Patashnik.
—Josef Lauri, University of Malta

Editorial Reviews

… The book is very carefully written and might be a good starting point for undergraduate students. …
—Zentralblatt MATH 1168

I recently got [this] book on combinatorics and applications to computer science, and I like it so much that I am trying to re-shape some of the discrete maths courses I teach so that I could use it. I liked particularly [the] section on asymptotics, which is much more accessible for my undergrads than Graham, Knuth, and Patashnik.
—Josef Lauri, University of Malta

From the Publisher