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Pearls of Discrete Mathematics 1st Edition by Martin Erickson ISBN 978-1439816165 1439816166

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Pearls of Discrete Mathematics 1st Edition Martin Erickson Digital Instant Download

Author(s): Martin Erickson
ISBN(s): 9781439816165, 1439816166
Edition: 1
File Details: PDF, 1.44 MB
Year: 2009
Language: english
SKU: EB-2542204 Category: Tag:

Pearls of Discrete Mathematics 1st Edition by Martin Erickson – Ebook PDF Instant Download/Delivery: 978-1439816165, 1439816166
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Product details: 

ISBN 10:  1439816166

ISBN 13: 978-1439816165

Author:  Martin Erickson

Methods Used to Solve Discrete Math Problems
Interesting examples highlight the interdisciplinary nature of this area

Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics.

Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix.

With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.

Table of contents: 

  1. Counting: Basic

  2. Subsets of a Set

  3. Pascal’s Triangle

  4. Binomial Coefficient Identities

  5. Counting: Intermediate

  6. Finding a Polynomial

  7. The Upward-Extended Pascal’s Triangle

  8. Recurrence Relations and Fibonacci Numbers

  9. Counting: Advanced

  10. Generating Functions and Making Change

  11. Integer Triangles

  12. Rook Paths and Queen Paths

  13. Discrete Probability

  14. Probability Spaces and Distributions

  15. Markov Chains

  16. Random Tournaments

  17. Number Theory

  18. Divisibility of Factorials and Binomial Coefficients

  19. Covering Systems

  20. Partitions of an Integer

  21. Information Theory

  22. What Is Surprise?

  23. A Coin-Tossing Game

  24. Shannon’s Theorems

  25. Games

  26. A Little Graph Theory Background

  27. The Ramsey Game

  28. Tic-Tac-Toe and Animal Games

  29. Algorithms

  30. Counters

  31. Listing Permutations and Combinations

  32. Sudoku Solving and Polycube Packing

 
 

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