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Veteran Mathematica User Steven Skiena Is Showing the Fun of Discrete Mathematics

Published April 28, 2003

Steven Skiena began using Mathematica before there was a Mathematica. Skiena met Stephen Wolfram, the creator of Mathematica, at the University of Illinois while Wolfram was working on an early version of the program. Skiena became interested in Wolfram’s project and soon began developing Combinatorica, a bundled Mathematica package that provides functions specific to discrete mathematics and graph theory.

As one of the first Mathematica users, Skiena is quick to explain why he likes it, saying, “The original version of Combinatorica is 15 years old, and yet it still runs reliably on the current version of Mathematica.” Skiena notes that virtually no other platform has this kind of longevity. “Even the standard versions of C have changed since I wrote Combinatorica,” he adds.

Combinatorica was one of the first packages to be bundled with Mathematica. The package, which currently extends Mathematica by over 450 functions for combinatorics and graph theory, is perhaps one of the most widely used software tools for teaching and research in discrete mathematics.

The release of Mathematica 4.2 brought with it a new version of Combinatorica. This latest version was redesigned and rewritten by Skiena and Sriram Pemmaraju, a fellow computer scientist. Benefits of the new package include faster processing, the ability to manipulate much larger graphs, more powerful drawing and visualization capabilities, nearly twice as many functions, and updates to most of the old functions.

According to Skiena, a package this big and powerful required a book to showcase all of its features. He provided this with Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, the first book about Combinatorica. He and Pemmaraju are now working on a new version of the book entitled Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, which will document all updates to the package. Additional resources are available on the Combinatorica website.

Skiena calls the upcoming book “the definitive guide to Combinatorica.” It will contain enough discussion and expository matter for beginners to understand and appreciate all of the algorithms and theorems that it covers. The book will also provide examples of all Combinatorica functions for users who need in-depth information. Additionally, Computational Discrete Mathematics is versatile enough to serve as a combinatorics and graph theory textbook to teach or supplement semester-long courses. Experimenting with Combinatorica provides an exciting new way to learn combinatorics and graph theory. Says Skiena, “We want to show the fun of discrete mathematics.”

Along with his work as a developer of Combinatorica, Skiena is a computer science professor at State University of New York at Stony Brook and also an author of several math-related books. One of his books, Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win, describes how to use computer simulations and computer modeling techniques to increase winnings when betting on jai alai matches. Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, will be published in June 2003 by Cambridge University Press.