MAT 5173 — Weekly Schedule
Fall 2026
Texts
Primary text
- Ash — Ash, Abstract Algebra: The Basic Graduate Year, 2002
Secondary reading
- 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
- CLO — Cox, Little & O’Shea, Ideals, Varieties, and Algorithms, 5th ed., Springer, 2025. ISBN 978-3-031-91840-7. DOI: 10.1007/978-3-031-91841-4
Supplementary reading
- Shafarevich — Shafarevich, Basic Algebraic Geometry 1, 3rd ed., Springer, 2013. ISBN 978-3-642-37955-0. DOI: 10.1007/978-3-642-37956-7
- 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
- Smith — Smith, Kahanpaa, Kekalainen & Traves, An Invitation to Algebraic Geometry, Springer, 2000. ISBN 978-0-387-98980-8. DOI: 10.1007/978-1-4757-4497-2
Schedule
| Date | Topic | Reading |
|---|---|---|
| Wed 19 Aug | Lecture — Course launch; groups and subgroups | Ash §1.1; LiZh §1.3-1.4 |
| Mon 24 Aug | Lecture — Permutation groups; cyclic groups; the order of an element | Ash §1.2; LiZh §1.5, §2.1; Rosebrock Ch. 2; E-handout: Complex geometry (passphrase in Canvas) |
| Wed 26 Aug | Lecture — Cosets, normal subgroups and homomorphisms | Ash §1.3; LiZh §3.1, §3.3 |
| Mon 31 Aug | Lecture — The isomorphism theorems | Ash §1.4; LiZh §3.4 |
| Wed 2 Sep | Lecture — Direct products | Ash §1.5; Beardon Ch. 12 |
| Wed 9 Sep | Lecture — Quotient groups and the isomorphism theorems; direct products | Ash §1.3-1.4; LiZh §3.3, §3.4 |
| Mon 14 Sep | Lecture — Quotient groups and the isomorphism theorems; direct products (continued) | Ash §1.3-1.4; LiZh §3.3, §3.4 |
| Wed 16 Sep | Q&A (Due: Set 1) | Problem Set 1 (PDF); Activity: Quotients and Homomorphic Images (Colab, ungraded) |
| Mon 21 Sep | Lecture — Rings: basic definitions and properties; ideals, homomorphisms and quotient rings | Ash §2.1-2.2; LiZh §4.1, §4.5 |
| Wed 23 Sep | Lecture — The isomorphism theorems for rings; maximal and prime ideals | Ash §2.3-2.4; LiZh §4.5, §4.7 |
| Mon 28 Sep | Lecture — Polynomial rings; unique factorization | Ash §2.5-2.6; LiZh §5.1 |
| Wed 30 Sep | Lecture — Polynomial rings and unique factorization (continued) | Ash §2.5-2.6; LiZh §5.1 |
| Mon 5 Oct | Q&A (Due: Set 2) | Problem Set 2 (PDF); Activity: Polynomial Factorization (Colab, ungraded) |
| Wed 7 Oct | Exam — Midterm Exam 1 — Sets 1 and 2 | |
| Wed 14 Oct | Lecture — Principal ideal domains and Euclidean domains; rings of fractions; irreducible polynomials | Ash §2.7-2.9; LiZh §5.2-5.3 |
| Mon 19 Oct | Lecture — Field extensions; degree; simple extensions | Ash §3.1; LiZh §6.1-6.2 |
| Wed 21 Oct | Lecture — Splitting fields; algebraic closures | Ash §3.2-3.3; LiZh §6.3 |
| Mon 26 Oct | Lecture — Separability; normal extensions; finite fields | Ash §3.4-3.5; Ash §6.4; LiZh §6.4 |
| Wed 28 Oct | Lecture — Separability, normal extensions and finite fields, continued | Ash §3.4-3.5; Ash §6.4 |
| Mon 2 Nov | Q&A (Due: Set 3) | Problem Set 3 (PDF); Activity: Finite Fields and Polynomials (Colab, ungraded) |
| Wed 4 Nov | Lecture — Affine varieties; V(I) and I(V); the Nullstellensatz and the Hilbert basis theorem (stated, not proved) | CLO §1.1-1.4; Ash §8.1-8.3; Smith Ch. 1 (handout) |
| Mon 9 Nov | Lecture — Fixed fields and Galois groups | Ash §6.1 |
| Wed 11 Nov | Lecture — The fundamental theorem of Galois theory | Ash §6.2 |
| Mon 16 Nov | Lecture — The fundamental theorem, continued; computing Galois groups | Ash §6.3; Ash §6.4 |
| Wed 18 Nov | Q&A (Due: Set 4) | |
| Mon 23 Nov | Lecture — Survey: the unsolvability of the quintic | Ash §6.8 |
| Mon 30 Nov | Review — Review — the exam pool | |
| Wed 2 Dec | Exam — Midterm Exam 2 — Sets 3 and 4 |