Foundations of Combinatorics with Applications

Author(s) : Edward A. Bender and S. Gill Williamson
Publication Date : 2005
Publisher : Dover Publications

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Book Excerpts:

Combinatorics, the mathematics of the discrete, has blossomed in this generation. On the theoretical side, a variety of tools, concepts and insights have been developed that allow us to solve previously intractable problems, formulate new problems and connect previously unrelated topics. On the applied side, scientists from physicists to biologists have found combinatorics essential in their research. In all of this, the interaction between computer science and mathematics stands out as a major impetus for theoretical developments and for applications of combinatorics. This text provides an introduction to the mathematical foundations of this interaction and to some of its results.

Combinatorics is too big a subject to be done justice in a single text. The selection of material in this text is based on the need to provide a solid introductory course for students in pure mathematics and in mathematical computer science. Naturally, the material is also heavily influenced by author's own interests.

Intended Audience:

This book does not assume any previous knowledge of combinatorics or discrete mathematics. Except for a few items which can easily be skipped over and some of the material on 'generating functions' in Part IV, calculus is not required. What is required is a certain level of ability or 'sophistication' in dealing with mathematical concepts. The level of mathematical sophistication that is needed is about the same as that required in a solid beginning calculus course.

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