Foundations of Combinatorics with Applications

Intended as an introduction to the mathematical foundations of the interaction between computer science and mathematics as a major impetus for theoretical developments and applications of combinatorics.

**Tag(s):**
Discrete Mathematics

**Publication date**: 31 Dec 2005

**ISBN-10**:
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**ISBN-13**:
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**Paperback**:
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**Views**: 18,424

Foundations of Combinatorics with Applications

Intended as an introduction to the mathematical foundations of the interaction between computer science and mathematics as a major impetus for theoretical developments and applications of combinatorics.

Terms and Conditions:

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.

Edward A. Bender wrote:This is copyrighted but may be downloaded at no charge for personal and course use. Please email us if you are a professor using it in a course.

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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About The Author(s)

Edward A. Bender is a Professor Emeritus of Mathematics in the Department of Mathematics at the UC San Diego. He received his Ph.D. in Mathematics at California Institute of Technology in 1966.

S. Gill Williamson is Professor Emeritus in the Department of Computer Science and Engineering at the University of California San Diego. His main research area is Algorithmic Combinatorics.

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