CMPSCI 575/MATH 513: Combinatorics and Graph Theory

David Mix Barrington

Fall, 2016

Lecture Notes

Lectures were prepared in Apple Keynote (.key files) and are given here as .pdf files. The schedule may be adjusted due to weather cancellations or other changes in the syllabus.

  1. Combinatorics Overview (7 Sept) (.pdf)
  2. Graph Theory Overview (9 Sept) (.pdf)
  3. Isomorphism and Edge Counting (12 Sept) (.pdf)
  4. Graph Planarity (14 Sept) (.pdf)
  5. Euler and Hamilton Paths (16 Sept) (.pdf)
  6. Graph Coloring (19 Sept) (.pdf)
  7. Graph Coloring Theorems (21 Sept) (.pdf)
  8. Trees (23 Sept) (.pdf)
  9. The Traveling Salesperson Problem (26 Sept) (.pdf)
  10. Sorting and Decision Trees (28 Sept) (.pdf)
  11. Shortest Paths (30 Sept) (.pdf)
  12. Minimum Spanning Trees (3 Oct) (.pdf)
  13. Network Flow (5 Oct) (.pdf)
  14. (Lecture 14 canceled) (.pdf)
  15. Basic Counting Principles (17 Oct) (.pdf)
  16. Arrangements With Repetition (19 Oct) (.pdf)
  17. Distributions (21 Oct) (.pdf)
  18. Binomial Coefficient Identities (24 Oct) (.pdf)
  19. Generating Function Models (26 Oct) (.pdf)
  20. Calculating Coefficients of GF's (28 Oct) (.pdf)
  21. Partitions (31 Oct) (.pdf)
  22. Exponential Generating Functions (2 Nov) (.pdf)
  23. Recurrence Relations (4 Nov) (.pdf)
  24. Recurrences: D&C and Linear (7 Nov) (.pdf)
  25. Recurrences and Generating Functions (9 Nov) (.pdf)
  26. The Inclusion/Exclusion Formula (14 Nov) (.pdf)
  27. Rook Polynomials (16 Nov) (.pdf)
  28. Equivalence and Symmetry (18 Nov) (.pdf)
  29. Burnside's Theorem (28 Nov) (.pdf)
  30. The Cycle Index (30 Nov) (.pdf)
  31. Polya's Formula (2 Dec) (.pdf)
  32. Combinatorial Game Theory (5 Dec) (.pdf)
  33. Nim and the Grundy Function (7 Dec) (.pdf)
  34. Partisan Games (9 Dec) (.pdf)
  35. Conway's Number Systems (12 Dec) (.pdf)
  36. Course Review (14 Dec) (.pdf)

Last modified 27 November 2016