General Information | HW Assignments | Student Presentations | Syllabus |

**Announcements:**

- The student presentations are scheduled as follows: March 4 (Nick, Mike B., Henry), March 6 (Patricia and Shawn), March 8 (Madi and Mike L.). Feel free to ask me about references or how much material is reasonable to present in the time you have.

Date | Covered in class | Written homework assignment | Due date | Problems to discuss in next class (not to be turned in) |
---|---|---|---|---|

1/7 | Introduction, basic counting | Problem 4 | 1/16 | Problem 5 (to be discussed in class on 1/16) |

1/9 | Fibonnaci numbers, tilings (taught by Natasha Komarov) | Prove using a direct combinatorial argument: a) _{1}+f_{3}+...+f_{2n-1}=f_{2n}-1_{n}^{2}+f_{n+1}^{2}=f_{2n+2} |
1/16 | |

1/11 | More Fibonnaci identities, Lucas numbers (taught by Natasha Komarov) | Prove using a direct combinatorial argument: c) L_{n}=f_{n-1}+2f_{n-2}. |
1/16 | |

1/15 (x-hour) | Compositions, subsets | Problem 5 | 1/23 | Problem 10 |

1/16 | Binomial coefficients | Problems 8,12 | 1/23 | Problem 13 |

1/18 | Binomial coefficient identities | Problem d) | 1/23 | Problem 20 |

1/22 (x-hour) | Lattice paths, sequences | Problem e) | 1/30 | Problem 21 |

1/23 | Divisibility, multisets | Problem 26 | 1/30 | Problem 31 |

1/25 | Fibonnaci numbers revisited | Problems 32, 33 | 1/30 | Problems 34, 35 |

1/28 | Permutations, basics | Problem 41 | 2/6 | Problem 47 |

1/30 | Fixed points and inversions in permutations | Problem 46 | 2/6 | |

2/1 | Derangements, the Principle of Inclusion-Exclusion | Problem 48 | 2/6 | Problem 50 |

2/4 | More derangements, cycle decomposition | Problem 55 | 2/13 | Problem 53 |

2/5 (x-hour) | Involutions, cycles | Problem 56 | ||

2/6 | Stirling numbers of the first kind | Problems f) and g) | 2/13 | Problem 61 |

2/11 | Records, Foata's fundamental transformation | Problem 63 | 2/20 | Problem 72 |

2/13 | Alternating permutations, Integer partitions | Problems 87 | 2/20 | Problems 94, 98 |

2/15 | Partition bijections | Problems 89, 93 | 2/20 | Problems 96, 98, 103 |

2/18 | More partition bijections | Problem h) | 2/27 | |

2/20 | Harmonic number indentities (taught by Natasha Komarov) | |||

2/22 | Stirling number indentities (taught by Natasha Komarov) | Problems i) and j) | 2/27 | |

2/25 | Euler's pentagonal number formula | Problem 119 | ||

2/27 | Parking functions | Problems k) and l) | 3/6 | Problem 164 |

3/1 | Catalan numbers | Problem 161 | 3/6 | |

3/4 | Student presentation 1. Mike B., Henry and Nick: Domino tilings of Aztec diamonds. | |||

3/6 | Student presentation 2. Patricia and Shawn. Derangements and the sum of the largest fixed points. | |||

3/8 | Student presentation 3. Madi and Mike L.: The inversion number and the major index of permutations. |

Last updated June 27, 2016 13:25:43 EDT