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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.
Table of ContentsIntroduction Permutations and Combinations The Inclusion-Exclusion Principle Partitions Stirling's Approximation Partitions and Generating Functions Generating Functions and Recurrence Relations Permutations and Groups Group Actions Graphs Counting Patterns Polya's Theorem Solutions to the Exercises Suggestions for Further Reading List of Symbols Index