Office: Armstrong Hall 408H

Office Hours: MWF 2:30pm-3:30pm, and by appointment

Class Meetings: MWF 1:30pm-2:20pm in Armstrong Hall 415

No. | Date | Class Summary | Section(s) | Quiz | Quiz Soln | Comments |

1 | Jan 14 | Introduction; Elementary Principles | 1.1 | - | - | HW1 assigned. |

2 | Jan 16 | Words; Binomial Coefficients and Theorem | 1.1 | - | - | - |

3 | Jan 18 | Stars and Bars Model; Lattice Path Model | 1.1,1.2 | - | - | - |

4 | Jan 23 | Elementary Identities; Extended Binomial Theorem | 1.2 | - | - | - |

5 | Jan 25 | Sums of Polynomials; Delannoy Numbers | 1.2 | - | - | - |

6 | Jan 28 | Delannoy Numbers and Taxi Balls | 1.2 | - | - | HW1 due; HW2 assigned. |

7 | Jan 30 | Aztec Diamond; Cayley's Formula | 1.3 | - | - | - |

8 | Feb 1 | Cayley's Formula; Multinomial Coefficients | 1.3 | - | - | - |

9 | Feb 4 | Ballot Problem; Catalan Numbers | 1.3 | - | - | - |

10 | Feb 6 | Catalan Numbers | 1.3 | - | - | - |

11 | Feb 8 | Recurrence Relations: Fibonacci Numbers, Derangements | 2.1 | - | - | - |

12 | Feb 11 | Catalan Recurrence; Multiparameter Recurrences; Systems of Recurrences | 2.1 | - | - | HW2 due; HW3 assigned. |

13 | Feb 13 | Recurrences on Graphs; Characteristic Equation Method | 2.1,2.2 | - | - | - |

14 | Feb 15 | Recurrences: Generating Function Method I | 2.2 | - | - | - |

15 | Feb 18 | Recurrences: Generating Function Method II | 2.2 | - | - | - |

16 | Feb 20 | Recurrences: Substitution and Asymptotics | 2.3 | - | - | - |

17 | Feb 22 | Recurrences: Sterling's Formula | 2.3 | - | - | - |

18 | Feb 25 | Ordinary Generating Functions | 3.1 | - | - | HW3 due. |

19 | Feb 27 | OGFs: Permutation Statistics | 3.1 | - | - | - |

20 | Mar 1 | Midterm Exam: Ch. 1 and 2 | - | - | - | - |

21 | Mar 4 | OGFs: Permutations by number of cycles | 3.1 | - | - | HW4 assigned. |

22 | Mar 6 | OGFs; Eulerian Numbers: Permutations by number of runs | 3.1 | - | - | - |

23 | Mar 8 | Inclusion/Exclusion: Basics | 4.1 | - | - | - |

24 | Mar 11 | Combinatorial Proofs via Inclusion/Exclusion | 4.1 | - | - | - |

25 | Mar 13 | Inclusion/Exclusion: Eulerian numbers and the chromatic polynomial | 4.1 | - | - | - |

26 | Mar 15 | Pigeonhole Principle Applications I | 10.1 | - | - | - |

27 | Mar 15 | Pigeonhole Principle Applications II (Makeup Class) | 10.1 | - | - | - |

- | Mar 18 | No Class; Makeup on Fri, Mar 15 | - | - | - | - |

28 | Mar 20 | Pigeonhole Principle Applications III | 10.1 | - | - | - |

29 | Mar 22 | Erdős--Szekeres Theorem | 10.1 | - | - | HW4 due. |

30 | Apr 1 | Ramsey Theory: Introduction | 10.2 | - | - | HW5 assigned. |

31 | Apr 3 | Ramsey Theory for Graphs | 10.2 | - | - | - |

32 | Apr 5 | Ramsey's Theorem I | 10.2 | - | - | - |

33 | Apr 8 | Ramsey's Theorem II | 10.2 | - | - | - |

34 | Apr 10 | Ramsey's Theorem: Applications | 10.2 | - | - | - |

35 | Apr 12 | Graph Ramsey Theory | 10.2 | - | - | - |

36 | Apr 15 | Turán's Theorem; Erdős--Stone | 11.1 | - | - | HW5 due. |

37 | Apr 17 | Kruskal--Katona I | 11.2 | - | - | - |

38 | Apr 19 | Kruskal--Katona II | 11.2 | - | - | HW6 assigned. |

39 | Apr 22 | Sperner's Theorem; Erdős's extension | 11.2 | - | - | - |

40 | Apr 24 | Intersecting Families; Erdős--Ko--Rado | 11.2, 12.1 | - | - | - |

41 | Apr 26 | Posets | 12.1 | - | - | - |

42 | Apr 29 | Dilworth's Theorem | 12.1 | - | - | HW6 due. |

43 | May 1 | Ranked and Graded Posets; Symmetric Chain Decompositions | 12.2 | - | - | - |

44 | May 3 | Strong Sperner Property; Inductive Sym. Chain Decomp. of Boolean Lattice | 12.2 | - | - | - |

- | May 10 | Final Exam | - | - | - | - |

milans@math.wvu.edu