Math 817: Groups and Rings, Fall 2023

The course syllabus is here.

Instructor

Dr. Katrina Honigs, khonigs@sfu.ca, Office SC K 10506
Office hours: Mondays 1:30-2:20

Lectures

12:30-2:20 pm TTh, AQ 5014

Final Exam

12-3 pm Tues Dec 12, AQ 5005

Textbooks

  • Aluffi, Algebra: Chapter 0
  • Serre, Linear Repepresentations of Finite Groups

    • Problem sets

  • Problem set 1, Part 1 and Part 2, Due Sept 19
  • Problem set 2, Part 1 and Part 2 , Due Oct 3 Oct 5
  • Problem set 3, Due Oct 17
  • Problem set 4 Part 1 and Part 2, Due Oct 31
  • Problem set 5 Part 1 and Part 2, Due Nov 14
  • Problem set 6 Part 1 and Part 2, Due Nov 28 Nov 30

    • Lecture schedule:

    Date Problem Sets Lecture Topic Text references Dark Souls III Location
    Sept 7 HW 1, Part 1 becomes available Syllabus,
    Categories and Universal Properties    		 Aluffi: Ch. I, §3-5 Cemetary of Ash
    Sept 12 HW 1, Part 2 becomes available More universal properties,
    Introduction to groups     		Aluffi: Ch. I §5, Ch. II §1-4 Firelink shrine
    Sept 14 Free groups, subgroups Aluffi: Ch. II §5-6 Start of High Wall of Lothric
    Sept 19 HW 1 due at start of class
    HW 2, Part 1 becomes available     		Quotients, First Isomorphism theorem, Aluffi: Ch. II §7-8 High Wall of Lothric
    Sept 21 Second and Third Isomorphism Theorem,
    Lagrange's Theorem, Group actions    		 Aluffi: Ch. II §8-9 Undead Settlement
    Sept 26 HW 2, Part 2 available Proof of Orbit-Stabilizer, Conjugation action Ch. II §9, Ch. IV §1 Road of Sacrifices
    Sept 28 Finish of conjugation action
    Sylow Theorem I    		 Ch. IV §1,2 End of Road of Sacrifices
    Cathedral of the Deep
    Oct 3
    Oct 5 HW 2 due at start of class
    HW 3 becomes available     		Sylow Theorems II, III
    Applications of Sylow Theorems     		Ch. IV §2 Cathedral of the Deep
    Cathedral of the Deep boss fight
    Oct 10 No lecture, Monday schedule today
    Oct 12 Composition Series and Solvability Ch. IV §3 Farron Keep
    Oct 17 HW 3 due at start of class
    HW4 Part 1 becomes available    		 Finishing solvability and derived series
    Conjugacy classes of Sn, Definition of An    		 Ch. IV §3,4 Catacombs of Carthus
    Oct 19 Conjugacy classes of An, A5 is simple Ch. IV §4 Meet Siegward of Catarina
    Oct 24 HW 4 Part 2 becomes available Semidirect products Ch. IV §5 Smouldering Lake
    Oct 26 Finish semidirect products,
    applications, start of rings    		 Ch. IV §5, Briefly: Ch. IV §6, Ch. III Smouldering Lake,
    Old Demon King boss fight
    Oct 31 HW 4 due at start of class
    HW 5 Part 1 becomes available     		Intro to: Rings, modules, PID's
    Free resolutions     		Ch. III, Ch. VI: §4,5 Irithyll of the Boreal Valley
    Nov 2 Classification of f.g. modules over PID
    Linear transformations as modules over PID     		Ch. VI: § 5,6,7 Irithyll Dungeon
    Nov 7 HW 5 Part 2 becomes available Reminder on matrix invariants
    Start of Cayley--Hamilton proof     		Ch. VI: §6,7 Irithyll Dungeon
    Nov 9 Cayley--Hamilton, Jordan canonical form
    		 Ch. VI: §7 Irithyll Dungeon
    Nov 14 HW 5 due at start of class
    HW 6 Part 1 becomes available     		Tensor products, symmetric and exterior products, hom Ch. VIII: §2.1-2.3,§3-5 Profaned Capitol
    Nov 16 Dual vector space
    Start of representation theory    		 Ch. VIII: §5, Serre, Part 1 Ch. 1 Enter Anor Londo
    Nov 21 HW 6 Part 2 becomes available Decomposing representations,
    Representations of abelian groups     		Serre, Part 1 Ch. 1-2 Anor Londo
    Nov 23 HW 6 Part 2 becomes available Decomposing regular representations,
    Start of characters     		Serre, Part 1 Ch. 2 Anor Londo, Lothric Castle
    Nov 28 Properties of characters Serre, Part 1 Ch. 2 Lothric Castle
    Nov 30 HW 6 due Characters and conjugacy classes Serre, Part 1 Ch. 2 Lothric Castle
    Dec 5 Group rings, Sn, induced representations, Dn Serre, Part 1 Ch. 5, Part 2 Ch. 6, 7 Consumed King's Garden,
    Archdragon Peak