Erickson Pearls of Discrete Mathematics

1. Auflage 2010
ISBN: 978-1-4398-1617-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 280 Seiten

Reihe: Discrete Mathematics and Its Applications

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.

Zielgruppe

Undergraduate, graduate, and advanced high school students in mathematics; mathematicians and computer scientists.

Autoren/Hrsg.

Erickson, Martin

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

Counting: Basic
Subsets of a Set
Pascal’s Triangle
Binomial Coefficient Identities
Counting: Intermediate
Finding a Polynomial
The Upward-Extended Pascal’s Triangle
Recurrence Relations and Fibonacci Numbers
Counting: Advanced
Generating Functions and Making Change
Integer Triangles
Rook Paths and Queen Paths
Discrete Probability
Probability Spaces and Distributions
Markov Chains
Random Tournaments
Number Theory
Divisibility of Factorials and Binomial Coefficients
Covering Systems
Partitions of an Integer
Information Theory
What Is Surprise?
A Coin-Tossing Game
Shannon’s Theorems
Games
A Little Graph Theory Background
The Ramsey Game
Tic-Tac-Toe and Animal Games
Algorithms
Counters
Listing Permutations and Combinations
Sudoku Solving and Polycube Packing
Appendix A: Hints and Solutions to Exercises
Appendix B: Notation
Bibliography
Index

Über Autor(innen)

Martin Erickson is a professor of mathematics at Truman State University.