Rings and Fields (lectures)
| Date | Topic | Read | Links |
|---|---|---|---|
| 2025.01.06 | Induction | ||
| 2025.01.08 | Peano arithmetic | §1.1 | notes01 |
| 2025.01.09 | Well-ordering principle | §1.1 | problems01 |
| 2025.01.13 | Equivalence relations | §2.1 | solutions01 |
| 2025.01.15 | Negative integers | §1.2 | notes02 |
| 2025.01.16 | Division with remainder | §1.3 | problems02 |
| 2025.01.20 | Euclidean algorithm | §1.4 | solutions02 |
| 2025.01.22 | Congruence | §2.2 | notes03 |
| 2025.01.23 | Modular arithmetic | §2.3–2.4 | problems03 |
| 2025.01.27 | Fermat's Little Theorem | §2.5 | solutions03 |
| 2025.01.29 | Rings | §3.1–3.2 | notes04 |
| 2025.01.30 | Subrings | §4.2 | problems04 |
| 2025.02.03 | Domains and Fields | §3.3 | solutions04 |
| 2025.02.05 | Polynomials | §7.1 | notes05 |
| 2025.02.06 | Roots | §7.2 | problems05 |
| 2025.02.10 | Ring homomorphisms | §4.3 | solutions05 |
| 2025.02.12 | Ideals | §5.1–5.2 | notes06 |
| 2025.02.13 | Quotient Rings | §5.3–5.4 | problems06 |
| 2025.02.13 | Midterm | ||
| Winter break | |||
| 2025.02.24 | Isomorphisms | §4.4 | solutions06 |
| 2025.02.26 | First isomorphism theorem | §5.5 | notes07 |
| 2025.02.27 | Ideals in a quotient | §5.7 | problems07 |
| 2025.03.03 | Direct decomposition of a ring | §5.6 | solutions07 |
| 2025.03.05 | Rings of fractions | §6.5 | notes08 |
| 2025.03.06 | Recognizing fields | §13.1 | problems08 |
| 2025.03.10 | Prime ideals | §6.1 | solutions08 |
| 2025.03.12 | Euclidean domains | §6.3 | notes09 |
| 2025.03.13 | Extended Euclidean algorithm | problems09 | |
| 2025.03.17 | Principal ideal domains | §6.2 | solutions09 |
| 2025.03.19 | Unique factorization domains | §6.4 | notes10 |
| 2025.03.20 | Non-Euclidean principal ideal domains | problems10 | |
| 2025.03.24 | Factoring polynomials | §7.3 | solutions10 |
| 2025.03.26 | Irreducibility Criteria | §7.4 | notes11 |
| 2025.03.27 | Counting irreducibles | §7.5 | problems11 |
| 2025.03.31 | Gaussian primes | §10.4 | solutions11 |
| 2025.04.02 | Sums of two squares | §10.4 | notes12 |
| 2025.04.03 | Review | problems12 | |
| 2025.04.?? | Extra tutorial | TBA | solutions12 |
| 2025.04.?? | Exam | TBA |