Combinatorics - Version 2.1

• Part I. Enumeration
  • Chapter 1. What is Combinatorics?
  • Chapter 2. Basic Counting Techniques
  • Chapter 3. Permutations, Combinations, and the Binomial Theorem
  • Chapter 4. Bijections and Combinatorial Proofs
  • Chapter 5. Counting with Repetitions
  • Chapter 6. Induction and Recursion
  • Chapter 7. Generating Functions
  • Chapter 8. Generating Functions and Recursion
  • Chapter 9. Some Important Recursively-Defined Sequences
  • Chapter 10. Other Basic Counting Techniques
• Part II. Graph Theory
  • Chapter 11. Basics of Graph Theory
  • Chapter 12. Moving through graphs
  • Chapter 13. Euler and Hamilton
  • Chapter 14. Graph Colouring
  • Chapter 15. Planar graphs
• Part III. Design Theory
• • Chapter 16. Latin squares
  • Chapter 17. Designs
  • Chapter 18. More designs
  • Chapter 19. Designs and Codes
• Appendix A. Complex Numbers
• Appendix B. Biographical Briefs
• Appendix C. Solutions to Selected Exercises
• Appendix D. List of Notation
• Index

Combinatorics is an upper-level introductory course in enumeration, graph theory, and design theory.