Descrite Math Home   Discrete Mathematics               Kenneth H. Rosen
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Sample Chapters from Applications of Discrete Mathematics

Chapter 5 Coding Theory

Chapter 7 Catalan Numbers

The book Applications of Discrete Mathematics, edited by John G. Michaels and Kenneth H. Rosen (McGraw-Hill, 1991), is a companion book to Rosen’s textbook Discrete Mathematics and Its Applications, Fourth Edition. This applications book contains 24 chapters, each devoted to a detailed explanation of an application of discrete mathematics not usually covered in an introductory discrete mathematics textbook. Also included in each chapter is a set of exercises (with solutions), a set of computer projects, and a list of suggested readings.

The topics covered in Applications of Discrete Mathematics are grouped into three overlapping categories: discrete structures and computing, combinatorics, and graph theory. The applications are drawn from the areas of computer science, social sciences, physical sciences, and mathematics. Chapter topics include:

    1. The Apportionment Problem
    2. Finite Markov Chains
    3. Rational Election Procedures
    4. Godel’s Undecidability Theorem
    5. Coding Theory
    6. Stirling Numbers
    7. Catalan Numbers
    8. Ramsey Numbers
    9. Arrangements with Forbidden Positions
    10. Block Designs and Latin Squares
    11. Scheduling Problems and Bin Packing
    12. Burnside-Polya Counting Methods
    13. Food Webs
    14. Applications of Subgraph Enumeration
    15. Traveling Salesman Problem
    16. The Tantalizing Four Cubes
    17. The Assignment Problem
    18. Shortest Path Problems
    19. Network Survivability
    20. The Chinese Postman Problem
    21. Graph Layouts
    22. Graph Multicolorings
    23. Network Flows
    24. Petri News

The following two chapters are representative of the many applications covered in this applications book:

Chapter 5: Coding Theory. This chapter extends the concept of coding that is briefly touched upon in Chapter 2 of Discrete Mathematics and Its Applications 4/E.

Chapter 7: Catalan Numbers. This chapter discusses material drawn from the area of combinatorics and deals with a sequence of integers that models many phenomena.

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