Mitchel T. Keller and William T. Trotter

Digital versions PDF and HTML (online)
Source available     Yes
Exercises Yes
Answers No
Solution Manual Chapters 2, 3, 5-9 available to instructors
License Creative Commons Attribution Share Alike
  • 362 pages (PDF) and 16 chapters for a one semester course
  • Print version for about $15 from Amazon and other sellers
  • Source files written in Mathbook XML available on GitHub
  • Course adoption list
  • HTML version makes some use of live Sage cells
  • For more information and to download PDF or to access HTML

This book was designed for the junior level combinatorics course at Georgia Tech for students in computer science and in applied mathematics. The authors began writing the book in 2004 and has benefited from extensive classroom use. The source is now in MathBook XML, which serves as the common source for all three versions: HTML, PDF, and print, and so they are virtually identical. The HTML version does have the advantage of live Sage cells that the reader can evaluate and modify.


  1. An Introduction to Combinatorics
  2. Strings, Sets, and Binomial Coefficients
  3. Induction
  4. Combinatorial Basics
  5. Graph Theory
  6. Partially Ordered Sets
  7. Inclusion-Exclusion
  8. Generating Functions
  9. Recurrence Equations
  10. Probability
  11. Applying Probability to Combinatorics
  12. Graph Algorithms
  13. Network Flows
  14. Combinatorial Applications of Network Flows
  15. Pólya’s Enumeration Theorem
  16. The Many Faces of Combinatorics