The growth in digital devices, which require discrete formulation of problems, has revitalized the role of combinatorics, making it indispensable to computer science. Furthermore, the challenges of new technologies have led to its use in industrial processes, communications systems, electrical networks, organic chemical identification, coding theory, economics, and more. With a unique approach, Introduction to Combinatorics builds a foundation for problem-solving in any of these fields. Although combinatorics deals with finite collections of discrete objects, and as such differs from continuous mathematics, the two areas do interact. The author, therefore, does not hesitate to use methods drawn from continuous mathematics, and in fact shows readers the relevance of abstract, pure mathematics to real-world problems. The author has structured his chapters around concrete problems, and as he illustrates the solutions, the underlying theory emerges. His focus is on counting problems, beginning with the very straightforward and ending with the complicated problem of counting the number of different graphs with a given number of vertices. Its clear, accessible style and detailed solutions to many of the exercises, from routine to challenging, provided at the end of the book make Introduction to Combinatorics ideal for self-study as well as for structured coursework. By concentrating on counting problems, Introduction to Combinatorics conveys basic ideas of its subject. Topics include combinations, permutations, the inclusion-exclusion principles, partitions, Stirling's Formula, generating functions, recurrence relations, groups, group actions, and graphs. The final two chapters discuss the application of group theory to counting patterns, via Burnside's Theorem and Polya's Theorem. Slomson's approach is to begin with concrete problems, and to use them as a lead-in to general theory. Numerous exercises-most of which are provided with detailed answers-are included for the advanced student. Among the applications considered are approaches to probability problems, especially in card games. Introduces basic ideas of combinatorics by concentrating on counting problems. The topics covered include combinations, permutations, the inclusion-exclusion principle, partitions, Stirling's formula, generating functions, recurrence relations, group actions and graphs. Exercises are provided. The main aim of this chapter is to introduce you to the idea of combinatorial thinking.
