A Course in Combinatorics

1. Graphs; 2. Trees; 3. Colourings of graphs and Ramsey's theorem; 4. Turán's theorem; 5. Systems of distinct representatives; 6. Dilworth's theorem and extremal set theory; 7. Flows in networks; 8. De Bruijn sequences; 9. The addressing problem for graphs; 10. The principle of inclusion and exclusion: inversion formulae; 11. Permanents; 12. The van der Waerden conjecture; 13. Elementary counting: Stirling numbers; 14. Recursions and generated functions; 15. Partitions; 16. (0,1) matrices; 17. Latin squares; 18. Hadamard matrices, Reed-Muller codes; 19. Designs; 20. Codes and designs; 21. Strongly regular graphs and partial geometries; 22. Orthogonal Latin squares; 23. Projective and combinatorial geometries; 24. Gaussian numbers and q-analogues; 25. Lattices and Möbius inversion; 26. Combinatorial designs and projective geometry; 27. Difference sets and automorphisms; 28. Difference sets and the group ring; 29. Codes and symmetric designs; 30. Association schemes; 31. Algebraic graphs: eigenvalue techniques; 32. Graphs: planarity and duality; 33. Graphs: colourings and embeddings; 34. Trees, electrical networks and squared rectangles; 35. Pólya theory of counting; 36. Baranyai's theorem; Appendices.