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