MATH 413 - Introduction to Combinatorics

Schedule

  1. Jan 14 Class organization, What is combinatorics? Chapter 1.1 - Perfect convers of chessboard
  2. Jan 16 Magic squares,4 color theorem, 36 officers (Latin squares). Chapter 1.X
  3. Jan 18 Basic counting principles. Addition, multiplication, substraction and division principles. Chapter 2.1
  4. Jan 21 M. L. King day
  5. Jan 23 Permutations, P(n,r) and combinations C(n,k). Chapter 2.2
  6. Jan 25 Identities with binomial coefficient - counting argument and paths in square gird.
  7. Jan 28 combinations and permutations with repetitions.
  8. Jan 30 Discrete probability and pigeonhole principle HW1 deadline
  9. Feb 1 Stronger for of pigeonhole principle
  10. Feb 4 Erdos-Szekeres for sequences and Ramsey theorem
  11. Feb 6 Generalizations of Ramsey theorem and Chinese remainder theorem. Starting Pascal triangle from chapter 5 HW2 deadline
  12. Feb 8 Binomial theorem
  13. Feb 11 Binomial identities
  14. Feb 13 Sperners theorem and Multinomial coefficient HW3 deadline
  15. Feb 14 6pm MIDTERM
  16. Feb 15 Solution to midterm
  17. Feb 18 Coeficients in expansion of polynoms. Generalization of Binomial theorem.
  18. Feb 20 Principle of Inclusion and exclusion
  19. Feb 22 Derangements HW4 deadline
  20. Feb 25 Permitations with forbidden patterns
  21. Feb 27 HW5 deadline
  22. Mar 1
  23. Mar 4 Generating functions
  24. Mar 6 Generating functins HW6 deadline
  25. Mar 8 Exponential generating functions
  26. Mar 11 Exponential generating functions and recurrence sequences
  27. Mar 13 recurrence sequences HW7 deadline
  28. Mar 15 review session
  29. Mar 18 vacation
  30. Mar 20 vacation
  31. Mar 22 vacation
  32. Mar 25 Snow holliday!
  33. Mar 27 no class - for Midterm 1
  34. Mar 28 6pm MIDTERM
  35. Mar 29 Solutions to midterm
  36. Apr 1 recurrence relations and writing as generating series and vice versa
  37. Apr 3 recurrences where characteristic polynomial has repeated root, introduction to nonhomogeneous recurrence relations
  38. Apr 5 nonhomogeneous recurrence relations
  39. Apr 8 more nonhomogeneous and number of tirangulations of a polygon
  40. Apr 10 Catalan numbers and first try for difference sequences HW8 deadline
  41. Apr 12 no class - for Midterm 2
  42. Apr 15 no class - for Midterm 3
  43. Apr 17 Difference sequences HW9 deadline
  44. Apr 19 Stirling numbers of the second kind
  45. Apr 22 Stirling numbers of the first kind
  46. Apr 24 review for midterm HW 10 deadlne
  47. Apr 25 6pm MIDTERM
  48. Apr 26 Partition numbers
  49. Apr 29 Partition numbers, some solutions to the midterm
  50. Apr 29 6pm-8pm Review for the final exam AH 143 (instead of May 1 class)
  51. May 1 no class - class was on Apr 29
  52. May 3 extra HW11 deadline
  53. May 4 HW11 solutions posted online
  54. May 8 FINAL EXAM!