Most of the readings are assigned from the required textbook Bona, Miklos. *A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory*. World Scientific Publishing Company, 2011. ISBN: 9789814335232. [Preview with Google Books]

SES # | TOPICS | READINGS |
---|---|---|

1 | Pigeonhole Principle | Chapter 1 |

2 | Induction, Elementary Counting | Chapter 2 and start Chapter 3. |

3 | Elementary Counting (concluded) | Chapter 3 (continued) |

4 | Binomial Theorem, Compositions | Chapter 4 |

5 | Compositions (concluded), Integer Partitions | Chapter 5 |

6 | Integer Partitions (concluded) | |

7 | Set Partitions | |

8 | Permutations, Cycle Type | Chapter 6 |

9 | Permutations (cont.), Stirling Numbers of the First Kind | |

10 | Permutations (concluded) | |

11 | The Sieve | Chapter 7 |

12 | The Sieve (cont.), Generating Functions | |

13 | Generating Functions (continued) | Chapter 8 |

14 | Generating Functions (concluded) | |

15 | Catalan Numbers | |

16 | Midterm One-Hour Exam 1 (Chapters 1–7, omitting pp. 123–24) | |

17 | Partitions | Chapter 8 (continued) |

18 | Exponential Generating Functions | |

19 | Exponential Generating Functions (concluded) | |

20 | Vertex Degree, Eulerian Walks | Chapter 9 |

21 | Isomorphism, Hamiltonian Cycles | |

22 | Tournaments, Trees | Chapter 10 |

23 | Counting Trees | |

24 | Minimum Weight Spanning Trees | Matrix-Tree Theorem (PDF) More on Matrix-Tree Theorem (PDF) |

25 | Matrix-Tree Theorem | Chapter 10 (continued) |

26 | Matrix-Tree Theorem (concluded), Bipartite Graphs | Finish Chapter 10 and start Chapter 11. |

27 | Bipartite Graphs (concluded) | Chapter 11 |

28 | Matchings in Bipartite Graphs | Chapter 11 (continued) |

29 | Midterm One-Hour Exam 2 (Chapters 8–10.2) | |

30 | Latin Rectangles, Konig-Egervary Theorem | Chapter 11 (continued) |

31 | Matchings in Bipartite Graphs (concluded) | |

32 | Chromatic Polynomials | |

33 | Planar Graphs | Chapter 12 |

34 | Polyhedra | |

35 | Polyhedra (concluded) | |

36 | Coloring Maps | |

37 | Ramsey Theory | Chapter 13 |

38 | A Probabilistic Proof | |

39 | Discussion of Final Exam, Answering Questions | |

40 | Final Exam (Chapters 1–12) |