Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica

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Cambridge University Press, 2003 - Mathematics - 480 pages
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Combinatorica, an extension to the popular computer algebra system MathematicaTM, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

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About the author (2003)

Steven S. Skiena is Distinguished Teaching Professor of Computer Science at Stony Brook University. He is the author of four well-regarded books: The Algorithm Design Manual (2008), Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win (2001), Programming Challenges (with Miguel Revilla, 2003) and Computational Discrete Mathematics (with Sriram Pemmaraju, 2003). Skiena heads the Lydia news/blog analysis project at Stony Brook, using large-scale text analysis to chart the frequency, sentiment and relationships among millions of people, places, and things. This technology forms the foundation of General Sentiment (http: //www.generalsentiment.com), where he serves as co-founder and Chief Scientist. Lydia news analysis has been applied to several social science research projects, including financial forecasting and presidential election analysis. The rankings underlying Who's Bigger? derive from this analysis.

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