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
Biography
Martin Erickson is a professor of mathematics at Truman State University.
…this book will remind you why you think mathematics is fun. … the real strengths of this text would be self-study for the motivated student or a source of interesting examples for a more traditional course in various areas of discrete mathematics. … The motivated student will learn much new mathematics if they work through this book carefully. For a student curious about exactly which topics make up the field of discrete mathematics, a more cursory trip through this book will do a good job of answering the question. For the library with a collection in recreational mathematics, this book will serve as a nice bridge to the ‘more serious’ associated areas of mathematics. And finally, for the professional mathematician, using this book as bedtime reading just might remind you of why you found math fun in the first place.
—Robert A. Beezer, University of Puget Sound, SIAM Review, Vol. 52, Issue 3, 2010The book will be beneficial to many undergraduates in mathematics. In fact, many sections are within reach of some advanced high school students who would like to explore interesting topics in mathematics. … Summing Up: Recommended.
—CHOICE, April 2010, Vol. 47, No. 08The book under review is a friendly volume in discrete mathematics, which covers various classical topics, such as counting, probability and number theory, and more recent topics, such as information theory, game theory and algorithms. As far as I know, this book is one of only a few at this level that covers such recent topics. Because it covers algorithms, … the book may be interesting for students interested in computer programming. … This is essentially a textbook for undergraduates, and perhaps it can be useful for high school students as well. … because of the variety of topics, teachers will have many choices of what to cover for students in applied fields. …
—Mehdi Hassani, MAA Reviews, December 2009
