The excitement of discrete mathematics comes from discovery, the act of uncovering beautiful and important properties of graphs, partitions, permutations, and other combinatorial objects. The appeal of discrete mathematics is its concreteness, that you can draw these objects on a blackboard and get a feel for them in a way quite different from more abstract areas of mathematics.

Unfortunately, only very small structures can be built on a blackboard; computers are needed to experiment with larger ones. The goal of Combinatorica is to advance the study of combinatorics and graph theory by making a wide variety of functions available for active experimentation. Together, this book and Combinatorica provide a unique resource for discovering discrete mathematics.

▪About Combinatorica

Combinatorica has been perhaps the most widely used software for teaching and research in discrete mathematics since its initial release in 1990. Combinatorica is an extension to Mathematica, which has been used by researchers in mathematics, physics, computer science, economics, and anthropology. Combinatorica received a 1991 EDUCOM Higher Education Software Award for Distinguished Mathematics Software and has been employed in teaching from grade school to graduate school.

But times change, in this case for the good. Desktop computers (and Mathematica) are now more than 100 times faster than when Combinatorica was originally developed. Computational problems unimaginable on research machines then can now be done at home by high school students. Mathematica itself has gone through several versions, resulting in a significantly improved user interface, more functionality, better performance, and improved typesetting facilities.