The textbook is "Combinatorics and Graph Theory", by John M. Harris, Jeffry L. Hirst and Michael J. Massinghoff, Springer (2000)

Here is the plan of the course:

1. 9/6                   Basic definitions - Section 1.1
   
2. 9/11                 Trees, definitions and first properties - Section 1.2
   
3. 9/13                 Spanning trees and matrix tree theorem - Section 1.2
   
4. 9/18                 Planar graphs, Euler's formula, regular polyhedra - Section 1.3
   
5. 9/20                 Kuratowski's theorem - Section 1.3
   
6. 9/25                 Colorings, chromatic numbers, Brooks's theorem - Section 1.4
   
7. 9/27                 The 4-color problem, chromatic polynomials - Section 1.4
   
8. 10/2-4              Matchings - Section 1.5
   
9. 10/9-11            Ramsey theory - Section 1.6
   
10. 10/16               Midterm
    
11. 10/18               Binomial coefficients - Section 2.2
    
12. 10/23               The principle of inclusion and exclusion - Section 2.3
    
13. 10/25-11/2       Generating functions - Section 2.4
    
14. 11/6                 Groups - Section 2.4.1
    
15. 11/8                 Burnside's lemma - Section 2.4.2
    
16. 11/13               Cycle index and Polya's enumeration formula - Sections 2.5.3-2.5.4
    
17. 11/15,11/27     Stirling, Bell and Euler numbers - Section 2.6
    
18. 11/29               Stable matchings - Section 2.7
    
19. 12/4-6              Review