Office Hours: 2:00-3:00pm Thursdays

Alex Scheffelin, alexs98@uw.edu

Office Hours: 3:30-4:30pm Fridays

The Category Theory lecture notes can be found here.

Week | Subject | Sections from Aluffi | Problem Set | Lecturer(s) |
---|---|---|---|---|

Winter Break | Set Theory and Category Theory | Chapter 1 | Problem Set | Andreas (guest lecturer) |

Week 1 | The definition of a group and examples | Sections 2.1 and 2.2 | Problem Set | Daniel R. |

Week 2 | Group homomorphisms and the category of groups | Sections 2.3 and 2.4 | Problem Set | Peter & Yunkyu |

Week 3 | Subgroups, normality, and quotient groups | Sections 2.6 and 2.7 | Problem Set | Max |

Week 4 | Cannonical decomposition and Lagrange's theorem, presentations and free groups | Sections 2.5 and 2.8 | Problem Set | Jason |

Week 5 | Group actions, the conjugation action, and the class formula | Sections 2.9 and 4.1 | Problem Set | Chen |

Week 6 | The Sylow theorems | Section 4.2 | Problem Set | Omar |

Week 7 | Composition series and solvability | Section 4.3 | Problem Set | Bashir |

Week 8 | The symmetric group | Section 4.4 | Problem Set | Zack |

Week 9 | More products of groups, exact sequences of groups, the extension problem | Section 4.5 | Problem Set | |

Week 10 | The classification of finite abelian groups | Section 4.6 |

Week | Subject | Sections from Dummit & Foote | Problem Set |
---|---|---|---|

Week 0 | The definition of a ring and examples | Sections 7.1 and 7.2 | Problem Set |

Week 1 | Ring homomorphisms, quotient rings, and ideals | Section 7.3 and 7.4 | Problem Set |

Week 2 | Euclidean domains, P.I.D.s, and U.F.D.s | Sections 8.1, 8.2, and 8.3 | Problem Set |

Week 3 | Polynomial rings | Sections 9.1, 9.2, and 9.3 | Problem Set |

Week 4 | More polynomial rings | Sections 9.4 and 9.5 | |

Week 5 | Field extensions and geometry | Sections 13.1, 13.2, and 13.3 | |

Week 6 | More field theory | Sections 13.4, 13.5, and 13.6 | |

Week 7 | The fundamental theorem of Galois theory | Sections 14.1 and 14.2 | |

Week 8 | Field extensions and geometry | Sections 14.4 and 14.5 | |

Week 9 | Galois groups of polynomials | Section 14.6 | |

Week 10 | The Abel-Ruffini theorem | Section 14.7 |