The calendar below provides information on the course's lecture (L) and quiz (E) sessions.

SES # | TOPICS | KEY DATES |
---|---|---|

L1 | Introduction to course, walks on graphs, rational generating functions and Fibonacci numbers | |

L2 | Walks on graphs II: walks on complete graphs and cubes | |

L3 | Walks on graphs III: the Radon transform | |

L4 | Random walks, the Perron-Frobenius theorem | Homework 1 due |

L5 | Introduction to partially ordered sets and the Boolean poset | |

L6 | Partially ordered sets II: Dilworth's and Sperner's theorem | |

L7 | Partially ordered sets III: the Mobius function | Homework 2 due |

L8 | Group actions on Boolean algebras | |

L9 | Group actions on Boolean algebras II: proof of the Sperner property | |

L10 | Introduction to partitions and two proofs of Euler's theorem | Homework 3 due |

L11 | Partitions II: Euler Pentagonal theorem and other identities | |

L12 | Partitions in a box, q-binomial coefficients, and introduction to Young tableaux | |

L13 | Standard Young tableaux and the Hook length formula | Homework 4 due |

L14 | The Hook length formula II, and introduction to the RSK algorithm | |

L15 | Proof of Schensted's theorem | |

L16 | Catalan numbers | Homework 5 due |

E1 | In-class quiz 1 | |

L17 | Counting Hasse walks in Young's lattice | |

L18 | An introduction to symmetric functions | |

L19 | Symmetric functions II | Homework 6 due |

L20 | Polya theory I | |

L21 | Polya theory II | Homework 7 due |

L22 | Polya theory III, intro to exponential generating functions | |

L23 | Exponential generating functions and tree enumeration | |

L24 | Tree enumeration II | Homework 8 due |

L25 | Matrix tree theorem | |

L26 | Matrix tree theorem II and Eulerian tours | |

L27 | Eulerian tours II | Homework 9 due |

E2 | In-class quiz 2 | |

L28 | Binary de Brujin sequences | |

L29 | Chip firing games I | |

L30 | Chip firing games II: the critical group | |

L31 | Chip firing games III: proof of uniqueness | |

L32 | Perfect matchings and Domino tilings | Homework 10 due |

L33 | Perfect matchings and Domino tilings II | |

L34 | Pfaffians and matching enumeration | |

L35 | Aztec diamonds | |

L36 | Aztec diamonds II; Lattice path enumeration | |

L37 | Lattice path enumeration II |