# Course Schedule and Problem Sets

This is a tentative schedule for the course, and might change later in the semester. Remember to watch the videos before the meetings to be prepared to do the problem sets. You can see the videos by using the links below or by going to the Videos and lecture notes page

All videos were produced by Øyvind Solberg and obtained from the 2020 course page, while the layout and the (preliminary) schedule was taken from the 2021 course page.

Week | Tuesday Topic | Tuesday Videos | Tuesday Problem Set | Thursday Topic | Thursday Videos | Thursday Problem Set | |
---|---|---|---|---|---|---|---|

09.1-13.1 | Introduction | Motivation and overview | None | Quivers and path algebras | 1a, 1b, 1c, 1d, 1e | Exercise Sheet 1 Hints | |

16.1-20.1 | Representations of quivers | 2a, 2b, 2c, 2d | Exercise Sheet 2 Hints | Representations of quivers | 2e, 2f, 2g, 2h, 2i | Exercise Sheet 3 Hints | |

23.1-27.1 | Quivers with relations | 3a, 3b | Exercise Sheet 4 Hints | Length, filtrations, and short exact sequences | 4a, 4b, 4c | Exercise Sheet 5 Hints | |

30.1-3.2 | Composition series and exact sequences | 4d, 4e, 4f | Exercise Sheet 6 Hints | The Jordan-Holder Theorem | 4g, 4h | No new exercises | |

6.2-10.2 | Morphisms and extensions of finite length modules | 4i, 4j, 4k | Exercise Sheet 7 Hints | Artinian and Noetherian modules | 4l, 4m, 4n | Exercise Sheet 8 Hints | |

13.2-17.2 | The radical of a ring | 5a, 5b, 5c, 5d | Exercise Sheet 9 Hints | Radical of (left) artinian rings | 5e, 5f, 5g | No new exercises | |

20.2-24.2 | Radical of (left) artinian rings and radical of modules | 5h, 5i, 5j, 5k | Exercise Sheet 10 Hints | Radical of modules/representations. | 5l, 5m, 5n | No new exercises | |

27.2-3.3 | Tops and essential epimorphisms | 5o, 5p, 5q, 5r | Exercise Sheet 11 Hints | Projective modules and projective covers | 6a, 6b, 6c, 6d, 6e | Exercise Sheet 12 Hints | |

6.3-10.3 | Projective modules and projective covers | 6f, 6g, 6h, 6i | Exercise Sheet 13 Hints | The Krull-Remak-Schmidt Theorem (projectives) | 6j, 6k, 6l | No new exercises | |

13.3-17.3 | The Krull-Remak-Schmidt Theorem (general) | 7a,7b, 7c | Exercise Sheet 14 Hints | Artin algebras | 8a, 8b | No new exercises | |

20.3-24.3 | Categories and functors | 9a, 9b, 9c | Exercise Sheet 15 Hints | Categories and Functors | 9d, 9e, 9f, 9g | No new exercises | |

27.3-31.3 | Categories and functors | none | No new exercises | Categories and functors | none | No new exercises | |

3.4-7.4 | NO LECTURE (easter break) | none | NO LECTURE (easter break) | ||||

10.4-14.4 | Projectivization | 10a, 10b, 10c, 10d | Exercise Sheet 16 Hints | Basic algebras | 11a, 11b | Exercise Sheet 17 Hints | |

17.4-21.4 | Basic algebras | 11c, 11d, 11e | No new exercises | Duality | 12a, 12b, 12c, 12d, 12e | Exercise Sheet 18 Hints | |

24.4-28.4 | Injective modules | 13a, 13b, 13c, 13d, 13e | Exercise Sheet 19 Hints | Injective modules | No new exercises | ||

1.5-5.5 | none | none |