| Date | Themes | Reference |
| Log of what we have covered |
| 20.08 (Tuesday) | Introduction, definitions, various examples of rings (polynomial rings, ring of group endomorphisms, Boolean rings), and basic properties of rings. | Chap 9.1, 9.2, 9.3 |
| 21.08 (Wednesday) | Subrings, characteristic of a ring, idempotent and nilpotent elements, (left, right, and 2-sided) ideals, homomorphisms, intersections of ideals | Chap 9.4, 9.5, 10.1 |
| 27.08 (Tuesday) | Present problem set 1 during first half of class. Fundamental theorem of ring homomorphisms, ideal correspondence theorem, sum and direct sum of ideals | Chap 10.2, 10.3 |
| 28.08 (Wednesday) | Maximal and prime ideals, nilpotent and nil ideals. | Chap 10.4, 10.5 |
| 03.09 (Tuesday) | Present problem set 2 during first half of class. Zorn's lemma and existence of maximal ideals. Unique factorization domains. | Chap 10.6, 11.1 |
| 04.09 (Wednesday) | Unique factorization domains, principal ideal domains, and Euclidean domains | 11.2, 11.3 |
| 10.09 (Tuesday) | Problem set 3 during first half. Start modules and vector spaces. | Chap 14.1 |
| 11.09 (Wednesday) | Submodules, direct sums of submodules, R-homomorphisms and quotient modules | Chap 14.2, 14.3 |
| 17.09 (Tuesday) | Present problem set 4 in class. | Chap 14.1-14.3 |
| 18.09 (Wednesday) | Simple (or irreducible) modules, semisimple (or completely reducible) modules, free modules | Chap 14.4, 14.5 |
| 24.09 (Tuesday) | Q is not a free Z-module example, More about free modules, Additional examples from chapter 14 | 14.1-14.5 |
| 25.09 (Wednesday) | Start noetherian and artinian modules | Chap 19.1, 19.2 |
| 01.10 (Tuesday) | Present problem set 5 in class. Noetherian and artinian modules, continued. | 19.2 |
| 02.10 (Wednesday) | Noetherian and artinian modules, continued. | 19.2 |
| 08.10 (Tuesday) | Discuss nil and nilpotent ideals in relation to noetherian/artinian properties, discuss ring/module structure | Chap 19.2 |
| 09.10 (Wednesday) | Proof of Hilbert Basis Theorem | 19.2 |
| 15.10 (Tuesday) | Present problem sets 6 and 7 in class. | 19.1-19.2 |
| 16.10 (Wednesday) | Start proving the Wedderburn-Artin Theorem. | 19.3 |
| 22.10 (Tuesday) | Finish proving the Wedderburn-Artin Theorem. Start studying finitely generated modules over PIDs. | ch.20-21 / Dummit&Foote ch.12 |
| 23.10 (Wednesday) | Submodules of free modules over PIDs | ch.20-21 / Dummit&Foote ch.12 |
| 29.10 (Tuesday) | Decomposition of finitely generated modules over PIDs, invariant factor form, elementary divisor form | ch.20-21 / Dummit&Foote ch.12 |
| 30.10 (Wednesday) | Primary decomposition theorem, Decomposition of finitely generated modules over PIDs: uniqueness | ch.20-21 / Dummit&Foote ch.12 |
| 05.11 (Tuesday) | Discuss problem set 8 in class. Begin Smith normal form, Rational canonical form | ch.20-21 / Dummit&Foote ch.12 |
| 06.11 (Wednesday) | Rational canonical form | ch.20-21 / Dummit&Foote ch.12 |
| 12.11 (Tuesday) | Jordan canonical form | ch.20-21 / Dummit&Foote ch.12 |
| 13.11 (Wednesday) | Jordan canonical form | ch.20-21 / Dummit&Foote ch.12 |
| Future plans |
| 19.11 (Tuesday) | Review course material and what will be covered on the final exam. Go over solutions to questions from PID problem sheet. |
| 20.11 (Wednesday) | Additional review problems, go over questions from following old exams: 2012(#1,24), 2014(all), 2015(#1,3), 2018(all) |
| 26.11 (Tuesday) | EXAM from 15:00-19:00 |