MAT 4233 — Weekly Schedule
Fall 2026
Texts
Primary text
- LiZh — Li & Zhao, Introduction to Abstract Algebra, Les Ulis: EDP Sciences, 2022. ISBN 978-2-7598-2915-6. DOI: 10.1051/978-2-7598-2916-3
Supplementary reading
- Childs — Childs, A Concrete Introduction to Higher Algebra, 3rd ed., Springer, 2009. ISBN 978-0-387-74527-5. DOI: 10.1007/978-0-387-74725-5
- Rosebrock — Rosebrock, Visual Group Theory, Springer, 2024. ISBN 978-3-662-69364-3. DOI: 10.1007/978-3-662-69365-0
- Beardon — Beardon, Algebra and Geometry, Cambridge University Press, 2005. ISBN 978-0-521-81362-4. DOI: 10.1017/CBO9780511800436
Handouts & papers
- Conrad — Conrad, The Gaussian Integers
Schedule
| Date | Topic | Reading |
|---|---|---|
| Thu 20 Aug | Lecture — Course launch. The integers: division algorithm, gcd, Bezout | Childs Ch. 3 |
| Tue 25 Aug | Lecture — Congruence and the ring Zn | Childs Ch. 5 & 6 |
| Thu 27 Aug | Lecture — Binary operations; Cayley tables; isomorphic binary structures | LiZh §1.1-1.2 |
| Tue 1 Sep | Lecture — Plane isometries and finite symmetry groups: cyclic and dihedral | Rosebrock Ch. 1; Beardon §3.1-3.4; E-handout: Complex geometry (passphrase in Canvas) |
| Thu 3 Sep | Lecture — Groups: axioms and first properties | LiZh §1.3 |
| Tue 8 Sep | Q&A (Due: Set 1) | Problem Set 1 (PDF); Activity: Symmetry Groups and Cayley Graphs (Colab, ungraded) |
| Thu 10 Sep | Lecture — Subgroups; examples | LiZh §1.4 |
| Tue 15 Sep | Lecture — Cyclic groups; the order of an element; generators | LiZh §1.5 |
| Thu 17 Sep | Lecture — Generating sets | LiZh §1.6 |
| Tue 22 Sep | Lecture — Permutation groups; cycle notation; Cayley’s theorem | LiZh §2.1 |
| Thu 24 Sep | Lecture — Alternating groups; the sign of a permutation; A4 and the tetrahedron | LiZh §2.2 |
| Tue 29 Sep | Q&A (Due: Set 2) | Problem Set 2 (PDF) |
| Thu 1 Oct | Exam — Midterm Exam 1 — Sets 1 and 2 | |
| Tue 6 Oct | Lecture — Cosets; Lagrange’s theorem; index | LiZh §3.1 |
| Thu 8 Oct | Lecture — Homomorphisms: kernel, image, and first properties | LiZh §3.3 |
| Thu 15 Oct | Lecture — Normal subgroups; quotient groups | LiZh §3.4 |
| Tue 20 Oct | Lecture — The fundamental homomorphism theorem; groups of small order | LiZh §3.4 |
| Thu 22 Oct | Lecture — Rings and subrings; units and zero divisors | LiZh §4.1 |
| Tue 27 Oct | Q&A (Due: Set 3) | |
| Thu 29 Oct | Lecture — Integral domains and fields; Euler’s and Fermat’s theorems | LiZh §4.2; LiZh §4.6 |
| Tue 3 Nov | Lecture — Ring homomorphisms, ideals and quotient rings; fundamental homomorphism theorem | LiZh §4.5 |
| Thu 5 Nov | Lecture — Ideal theory: principal, prime and maximal ideals | LiZh §4.7 |
| Tue 10 Nov | Lecture — Irreducibles and primes; unique factorization domains; principal ideal domains | LiZh §5.1-5.2 |
| Thu 12 Nov | Lecture — Euclidean domains; the Euclidean algorithm in Z and in k[x] | LiZh §5.3 |
| Tue 17 Nov | Lecture — Multiplicative norms; the Gaussian integers Z[i]; Fermat’s Two Squares theorem | LiZh §5.5; Conrad (statements and examples; proofs optional) |
| Thu 19 Nov | Q&A (Due: Set 4) | |
| Tue 24 Nov | Lecture — Sums of three and four squares; Z[sqrt(-5)] and the failure of unique factorization | Instructor notes |
| Tue 1 Dec | Review — Review — the exam pool | |
| Thu 3 Dec | Exam — Midterm Exam 2 — Sets 3 and 4 |