Synopses & Reviews
While the mathematics of classical engineering and science is primarily "continuous, " the mathematics of computer science is primarily "discrete" or "combinatorial." This volume provides a useful guide to combinatorial mathematics for computer scientists and applied mathematicians. Based on a beginning graduate-level course taught by the author, it covers the two major subdivisions of combinatorics, enumeration and graph theory, with emphasis on the conceptual needs of computer science. Each part is divided into a "basic concepts" chapter that emphasizes the intuitive ideas of the subject, followed by four "topics" chapters that explore these ideas in depth. Given the rapid and continued growth of computer science today, this accessible, well-written volume will be an invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics.
Synopsis
Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.
Synopsis
Useful guide covers two major subdivisions of combinatorics enumeration and graph theory with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Includes 219 figures.
Table of Contents
Preface
Acknowledgments
Suggestions on How to Use This Book
Study Guide for Part I: Linear Order
Study Guide for Part II: Graphs, Trees, and Recursion
Part I. Linear Order
1. Basic concepts of Linear Order
2. Topic I: Sorting
3. Topic II: Basic Combinatorial Lists
4. Topic III: Symmetry--Orbit Enumeration and Orderly Algorithms
5. Topic IV: Some Classic Combinatorics
A. Generating Functions
B. The Principle of Inclusion-Exclusion
C. Möbius Inversion
D. Network Flows
References for Linear Order
Part II. Graphs, Trees, and Recursion
6. Basic Concepts of Graphs, Trees, and Recursion
7. Topic I: Depth First Search and Planarity
8. Topic II: Depth First Search and Nonplanarity
9. Topic III: Triconnectivity
10. Topic IV: Matroids
References for Graphs, Trees, and Recursions
Index