
How to Count
An Introduction to Combinatorics, Second Edition
- 444 pages
- English
- PDF
- Available on iOS & Android
About this book
Emphasizes a Problem Solving Approach
A first course in combinatorics
Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics.
New to the Second Edition
This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet's pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises.
Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Polya's counting theorem.
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Information
Table of contents
- Front cover
- Table of Contents
- Preface to the Second Edition
- Acknowledgments
- Authors
- Chapter 1. Whatâs It All About?
- Chapter 2. Permutations and Combinations
- Chapter 3. Occupancy Problems
- Chapter 4. The InclusionâExclusion Principle
- Chapter 5. Stirling and Catalan Numbers
- Chapter 6. Partitions and Dot Diagrams
- Chapter 7. Generating Functions and Recurrence Relations
- Chapter 8. Partitions and Generating Functions
- Chapter 9. Introduction to Graphs
- Chapter 10. Trees
- Chapter 11. Groups of Permutations
- Chapter 12. Group Actions
- Chapter 13. Counting Patterns
- Chapter 14. PĂłlya Counting
- Chapter 15. Dirichletâs PigeonholePrinciple
- Chapter 16. Ramsey Theory
- Chapter 17. Rook Polynomials and Matchings
- Solutions to the A Exercises
- Books for Further Reading
- Index of Notation
- Back cover