Material Detail

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

Table of Contents: 

• Chapter 1. What is Combinatorics? 

Part I. Enumeration

• 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

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