W.D. Wallis is Professor Emeritus of Southern Illiniois University. John C George is Asscoiate Professor at Gordon State College.

Introduction

Some Combinatorial Examples

Sets, Relations and Proof Techniques

Two Principles of Enumeration

Graphs

Systems of Distinct Representatives

Fundamentals of Enumeration

Permutations and Combinations

Applications of P(n, k) and (n k)

Permutations and Combinations of Multisets

Applications and Subtle Errors

Algorithms

Probability

Introduction

Some Definitions and Easy Examples

Events and Probabilities

Three Interesting Examples

Probability Models

Bernoulli Trials

The Probabilities in Poker

The Wild Card Poker Paradox

The Pigeonhole Principle and Ramsey's Theorem

The Pigeonhole Principle

Applications of the Pigeonhole Principle

Ramsey's Theorem - the Graphical Case

Ramsey Multiplicity

Sum-Free Sets

Bounds on Ramsey Numbers

The General Form of Ramsey's Theorem

The Principle of Inclusion and Exclusion

Unions of Events

The Principle

Combinations with Limited Repetitions

Derangements

Generating Functions and Recurrence Relations

Generating Functions

Recurrence Relations

From Generating Function to Recurrence

Exponential Generating Functions

Catalan, Bell and Stirling Numbers

Introduction

Catalan Numbers

Stirling Numbers of the Second Kind

Bell Numbers

Stirling Numbers of the First Kind

Computer Algebra and Other Electronic Systems

Symmetries and the P¿olya-Redfield Method

Introduction

Basics of Groups

Permutations and Colorings

An Important Counting Theorem

P¿olya and Redfield's Theorem

Partially-Ordered Sets

Introduction

Examples and Definitions

Bounds and lattices

Isomorphism and Cartesian products

Extremal set theory: Sperner's and Dilworth's theorems

Introduction to Graph Theory

Degrees

Paths and Cycles in Graphs

Maps and Graph Coloring

Further Graph Theory

Euler Walks and Circuits

Application of Euler Circuits to Mazes

Hamilton Cycles

Trees

Spanning Trees

Coding Theory

Errors; Noise

The Venn Diagram Code

Binary Codes; Weight; Distance

Linear Codes

Hamming Codes

Codes and the Hat Problem

Variable-Length Codes and Data Compression

Latin Squares

Introduction

Orthogonality

Idempotent Latin Squares

Partial Latin Squares and Subsquares

Applications

Balanced Incomplete Block Designs

Design Parameters

Fisher's Inequality

Symmetric Balanced Incomplete Block Designs

New Designs from Old

Difference Methods

Linear Alge