The table below indicates which topics we will cover in each class. Before each class, you should read the lecture notes up to and including the place indicated below. You should then try all the exercises up to and including the one indicated in the table.
| Date | Reading | Exercises | Topics |
|---|---|---|---|
| Sep 9 | §1.1 (up to Ex. 1.1.10) | 1.1.4 | Rings: definition and examples |
| Sep 14 | §1.1 | 1.1.21 | Properties of rings, isomorphic rings. |
| Sep 16 | §1.2 | 1.2.16 | Integral domains and fields, field of fractions |
| Sep 21 | §1.3 | 1.3.24 | Ideals and quotient rings |
| Sep 23 | §1.4 (up to Ex. 1.4.12) | 1.4.8 | Ring homomorphisms |
| Sep 28 | §1.4 | 1.4.29 | First Isomorphism Theorem, Chinese Remainder Theorem |
| Sep 30 | §2.1 (up to Ex. 2.1.11) | 2.1.6 | Polynomial rings |
| Oct 5 | §2.1 | 2.1.29 | The division algorithm, evaluation and roots of polynomials |
| Oct 7 | §2.2 (up to Ex. 2.2.19) | 2.2.16 | Irreducible polynomials, factoring polynomials over the real and complex numbers, Gauss' Lemma, Modular Irreducibility Test |
| Oct 14 | §2.2 | 2.2.26 | Eisenstein Criterion, gcd of polynomials, euclidean algorithm, unique factorization of polynomials |
| Oct 19 | §2.3 | 2.3.20 | Quotient rings of polynomials over a field |
| Oct 21 | §2.4 | 2.4.3 | Finite fields |
| Oct 26–30 | Reading week | ||
| Nov 2 | §3.1 (up to Prop. 3.1.21) | 3.1.13 | Unique factorization domains |
| Nov 4 | §1.1–2.4 | Midterm test | |
| Nov 9 | §3.1 | 3.1.18 | Unique factorization domains |
| Nov 11 | §3.2 | 3.2.12 | Principal ideal domains |
| Nov 16 | §3.3 | 3.3.7 | Euclidean domains |
| Nov 18 | §4.1 | 4.1.6 | Modules |
| Nov 23 | §4.2 | 4.2.7 | Submodules |
| Nov 25 | §4.3–4.5 | 4.5.5 | Quotient modules, free modules, direct sum |
| Nov 30 | §4.6 | 4.6.8 | Module homomorphisms |
| Dec 2 | §4.7, 4.8 | 4.8.4 | Isomorphism theorems, modules over commutative rings |
| Dec 7 | §4.9 | 4.9.3 | Modules over principal ideal domains |
| Dec 9 | Review | ||