| Date | Themes | Reference |
| Log of what we have covered |
| 23.08 (Thursday) | 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 |
| 24.08 (Friday) | Subrings, characteristic of a ring, idempotent and nilpotent elements, ideals | Chap 9.4, 9.5, 10.1 |
| 30.08 (Thursday) | Problem set 1 during second half. More ideals and homomorphisms, left ideals, right ideals, ideals in the full matrix algebra, Intersections of ideals | Chap 10.1, 10.2 |
| 31.08 (Friday) | Sums and direct sum of ideals, minimal, maximal and prime ideals, the real numbers as the rings of Cauchy-sequences modulo the ideal of sequences converging to zero | Chap 10.3, 10.4 |
| 06.09 (Thursday) | Problem set 2 during second half. The Chinese remainder theorem, Maximal ideals are prime, the maximal ideals of Z, C[x] and R[X], description of prime ideals for commutative rings. | Chap 10.4, 10.5 |
| 07.09 (Friday) | Nilpotent and nil ideals, Zorns's lemma and the existence of maximal ideals. | Chap 10.5, 10.6 |
| 13.09 (Thursday) | Problem set 3 during second half. Start modules and vector spaces. | Chap 14.1, 14.2, 14.3 |
| 14.09 (Friday) | Submodules, direct sums of submodules, R-homomorphisms and quotient modules | Chap 14.3, 14.4 |
| 20.09 (Thursday) | Simple modules, completely reducible modules, exercises to do in class | Chap 14.4 |
| 21.09 (Friday) | Free modules, additional Examples from chapter 14 | Chap 14.5, and examples 14.1-14.5 |
| 27.09 (Thursday) | Present problem set 4 in class. Discuss Hom(R,R). | 14.1-14.5 |
| 28.09 (Friday) | Discuss Hom(M,M) where M is a direct sum of modules; Start noetherian and artinian modules | Chap 19.1, 19.2 |
| 04.10 (Thursday) | Present problem set 5 in class. Also discuss exact sequences and commutative diagrams. | Ch. 14 |
| 05.10 (Friday) | Noetherian and artinian modules, continued. | 19.2 |
| 11.10 (Thursday) | Finish more of 19.2 including results on nil and nilpotent ideals | Chap 19.2 |
| 12.10 (Friday) | Start discussing Problem set 6, Wedderburn-Artin + examples | 19.2, 19.3 |
| 18.10 (Thursday) | More examples illustrating Wedderburn-Artin's theorem and modules of finite length. | 19.2, 19.3 |
| 19.10 (Friday) | Smith normal form | 20.1-20.3 |
| 25.10 (Thursday) | Present problem sets 6 and 7 in class. | |
| 26.10 (Friday) | NO CLASS – complete Problem set 8 out of class. I would suggest finding a quiet place during class time and seeing how far you can get on these 5 exam problems during 2 hours. | |
| 01.11 (Thursday) | Decomposition of finitely generated modules over PID | 21.1-20.2 |
| 02.11 (Friday) | Decomposition and applications to finitely generated abelian groups | 20.2-20.3 |
| 08.11 (Thursday) | Applications to finitely generated abelian groups; Rational canonical form | 20.3, 21.3, 21.4 |
| 09.11 (Friday) | Rational canonical form, generalized Jordan form | 21.1-21.5 |
| 15.11 (Thursday) | Do problem set 10 (out of class - NO CLASS this day) |
| 16.11 (Friday) | Present problem set 9 in class. |
| Future plans |
| 22.11 (Thursday) | Review course material and what will be covered on the final exam, cover problems from 2015 exam |
| 23.11 (Friday) | Additional review problems, go over questions from any old exams or problem sets |