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pemmaraju s computational discrete mathematics 2003

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Textbook in PDF format 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. This book presents the second-generation version of Combinatorica, which is a dramatic improvement over the original. Enhancements since the previous version include: Improved Performance - We have made incredible strides in efficiency since the original Combinatorica. All examples in the original edition of Implementing Discrete Mathematics involved graphs of fewer than 100 vertices, because larger examples were either impossible or hopelessly slow. Now we can work on interesting graphs with tens of thousands of vertices and hundreds of thousands of edges. Indeed, all the examples in this book run comfortably on a two-year-old laptop computer that has seen better days! Improved Graph Representation and Visualization - The Combinatorica graph structure has been completely revamped, enabling us to efficiently represent very large graphs, with edge/vertex weights, labels, and graphics. These improvements make Combinatorica a viable platform for developing significant graph applications in Mathematica. Color graphics displays and printers are now ubiquitous, although they were prohibitively expensive back in 1990. In response, we have brought a new degree of color and style to Combinatorica graphics. Graphs can now be drawn with a variety of edge and vertex presentations and give complete freedom to highlight and position graph elements. We provide the power to animate interesting structures and algorithms on graphs, and to transform these videos to animated GIF files for Web pages. New Functionality - Combinatorica now adds more than 450 functions for combinatorics and graph theory to Mathematica - twice as many as the previous version. Existing functions have been made more sophisticated, with new options and better algorithms. The new Combinatorica pro vides extensive support for Polya's theory of counting and algebraic combinatorics, as well as new combinatorial objects such as set partitions and restricted growth functions. These changes reflect demands from our users, recent developments in combinatorics and graph theory, and the additional functionality of new releases of Mathematica. Combinatorica is included with every copy of Mathematica as DiscreteMath'Combinatorica'. The Combinatorica described in this book appears in Mathematica Version 4.2 and beyond, but our package is backwards compatible with earlier versions of Mathematica. The latest release of Combinatorica is available from our Web site http://www.combinatorica.com, where we maintain software, data, and other materials of interest to the Combinatorica community. Register at www.combinatorica.com to hear about updates to the package. Combinatorica: An Explorer's Guide. Permutations and Combinations. Algebraic Combinatorics. Partitions, Compositions, and Young Tableaux. Graph Representation. Generating Graphs. Properties of Graphs. Algorithmic Graph Theory

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pemmaraju s computational discrete mathematics 2003

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