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Combinatorial Methods with Computer Applications (Discrete Mathematics and Its Applications), by Jonathan L. Gross
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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.
- Sales Rank: #4303635 in Books
- Brand: Brand: Chapman and Hall/CRC
- Published on: 2007-11-16
- Original language: English
- Number of items: 1
- Dimensions: 10.31" h x 1.53" w x 7.26" l, 2.88 pounds
- Binding: Hardcover
- 664 pages
- Used Book in Good Condition
Review
… 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
About the Author
Jonathan L. Gross is Professor of Computer Science at Columbia University. His mathematical work in topology and graph theory have earned him an Alfred P. Sloan Fellowship, an IBM Postdoctoral Fellowship, and numerous research grants. With Thomas Tucker, he wrote Topological Graph Theory and several fundamental pioneering papers on voltage graphs and on enumerative methods. He has written and edited eight books on graph theory and combinatorics, seven books on computer programming topics, and one book on cultural sociometry.
Most helpful customer reviews
1 of 1 people found the following review helpful.
generally good book on discrete mathematics
By Chee Lim Cheung
This is, on the whole, a generally good book on discrete mathematics- strong on graphs (the author's specialty) and networks, not so comprehensive on combinatorics. The eclectic mix of topics covered - permutations, recurrences, generating functions, graphs, networks, finite geometries, etc - tend to make the book disjointed and unfocused at times. The reader will be better served by studying the topics individually in greater depth. A possible reading list would be: Combinatorial Problems and Exercises by Lovasz, generatingfunctionology by Wilf and, yes, Gross's very own Graph Theory and Its Applications.
1 of 1 people found the following review helpful.
Combinatorics
By Dragos Velicanu
Good book overall. Easy to read and informative. Good at teaching you how to solve problems. Example problems are sometimes only the easiest problems, and extending the method to harder problems is not always trivially apparent. Also sometimes skips somewhat important steps in solving example problems.
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