Introduction to Combinatorics

This book 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, groups, group actions and graphs. The final chapters discuss the application of group theory to counting patterns, via Burnside's theorem and Polya's theorem. The book uses concrete problems to lead to the general theory. Exercises for the student are provided, as well as the answers to them. Among the applications considered are those to probability problems, especially in card games.