Interactive Mathematics Miscellany and Puzzles . At an introductory level, combinatorics is usually considered as a branch of discrete mathematics in which the main problem is that of counting the number of ways of arranging or choosing objects from a finite set according to some simple specified rules. Thus the crux of the problem, at the beginning stage at least, is mainly that of enumeration. In some cases these arrangements also have to meet certain optimality criteria, in which case we seek an optimal solution of the problem. Thus in a wider sense, combinatorics deals with the enumeration, existence, analysis, and optimization of discrete structures.
Combinatorial mathematics has a variety of applications.
It is utilized in several physical and social sciences, for example, chemistry, computer science, operations research, and statistics. Consequently, there has recently been a rapid growth in the depth and breadth of the field of combinatorics. The subject is becoming an increasingly important component of the curriculum both at the graduate and undergraduate levels at universities and colleges in the United States and abroad. In this book I have attempted to present the important concepts of contemporary combinatorics in a sequence of four chapters. I hope that students will find this book useful for a course in combinatorics or discrete mathematics either as the main text or as a supplementary text.