Veteran Mathematica User Steven Skiena Is Showing the Fun of Discrete
Mathematics
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
indepth information. Additionally,
Computational Discrete Mathematics is versatile enough to serve as a combinatorics
and graph theory textbook to
teach or supplement semesterlong 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 mathrelated 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.
