Logbook

This page, which will be updated as the course progresses, is a simple log of the material covered in each lecture to help you review in case you miss a lecture.

2023-03-21 Lecture 01 - G-sets and group actions, Chapter 1. 

2023-03-24 Lecture 02 - Structure theory of G-sets, Chapter 2 (Sections 2.1-2.3).

2023-03-28 Lecture 03 - Structure theory of G-sets, Chapter 2 (Sections 2.14-2.5).

2023-03-31 Lecture 04 - Structure theory of G-sets, Chapter 2 (Sections 2.6-2.9).

2023-04-01 Lecture 05 - Counting with group actions, Chapter 3.

2023-04-01 Seminar - MATP33-2023-04-04-Seminar.pdf Download MATP33-2023-04-04-Seminar.pdf 

2023-04-11 Lecture 06 - The Sylow Theorems, Chapter 4 (see also self-study section therein).

2023-04-11 Seminar - MATP33-2023-04-11-Seminar.pdf Download MATP33-2023-04-11-Seminar.pdf

2023-04-14 Lecture 07 - Interlude: The language of categories, Chapter 5.

2023-04-18 Lecture 08 - Modules over a ring, Chapter 6 (Sections 6.1-6.3).

2023-04-18 Seminar - MATP33-2023-04-18-Seminar.pdf Download MATP33-2023-04-18-Seminar.pdf

2023-04-21 Cancelled

2023-04-25 Lecture 09 - Modules over a ring, Chapter 6 (Sections 6.4-6.6).

2023-04-25 Seminar - MATP33-2023-04-25-Seminar.pdf Download MATP33-2023-04-25-Seminar.pdf

 2023-04-28 Lecture 10 - Modules over a ring, Chapter 6 (Sections 6.7-6.8).

2023-05-02 Lecture 11 - Properties of modules, Chapter 7 (Sections 7.1-7.2)

2023-05-03 Seminar - MATP33-2023-05-02-Seminar.pdf Download MATP33-2023-05-02-Seminar.pdf

2023-05-05 Lecture 12 - Properties of modules, Chapter 7 (Sections 7.3-7.4, 7.5 is extra material)

2023-05-09 Lecture 13 - The Artin-Wedderburn Theorem, Chapter 8 (Sections 8.1-8.3, 8.4 is extra material)

2023-05-09 Seminar - MATP33-2023-05-09-Seminar.pdf Download MATP33-2023-05-09-Seminar.pdf

2023-05-10 Lecture 14 Replacement lecture - Finiteness properties of rings and modules, Chapter 9 (Sections 9.1)

2023-05-12 Lecture 15 - Modules over principal ideal domains, Chapter 10 (Section 10.1 is self-study, Sections 10.2-10.3)

2023-05-16 Lecture 16 - Modules over principal ideal domains, Chapter 10 (Sections 10.4-10.5)

2023-05-19 Lecture 17 - Tensor products, Chapter 11

2023-05-23 Lecture 18 - Solutions to mock (take-home) exam: MATP33-Mock exam.pdf Download MATP33-Mock exam.pdf MATP33-Mock exam-solutions.pdf Download MATP33-Mock exam-solutions.pdf

In the upcoming lectures we plan (!) to cover the following topics:

• (Finitely-generated) modules over a PID
• Tensor products

Lecture notes will be uploaded the day of each lecture.