Syllabus
The following is a tentative syllabus for the course. This page will be updated irregularly.
| Week | Date | Sections in DF | Description |
|---|---|---|---|
| 1 | Mon 9/16 | History and motivation for abstract algebra | |
| Wed 9/18 | 1.1 | Basic Axioms and Examples | |
| Thur 9/19 (x) | 0.1 | Logic, Set Theory, Functions | |
| Fri 9/20 | 1.2 | Dihedral Groups | |
| 2 | Mon 9/23 | 1.3 | Symmetric Groups |
| Wed 9/25 | 0.2-0.3 | Properties of the Integers; Z/nZ | |
| Thur 9/26 (x) | Proof writing; Mathematical induction | Fri 9/27 | 1.4-1.6, 4.4 | Matrix Groups; The Quaternion Group; Homomorphisms, Isomorphisms, and Automorphisms |
| 3 | Mon 9/30 | 1.7 | Group Actions |
| Wed 10/2 | 2.1-2.2 | (Subgroups) Definition and Examples; Centralizers and Normalizers, Stabilizers and Kernels | Thur 10/3 (x) | Proof writing; Midterm review |
| Fri 10/4 | 2.3 | Cyclic Groups and Cyclic Subgroups | |
| 4 | Mon 10/7 | 2.4-2.5 | Subgroups Generated by Subsets of a Group; The Lattice of Subgroups of a Group |
| Wed 10/9 | 3.1 | (Quotient Groups and Homomorphisms) Definitions and Examples | Fri 10/11 | 3.1 | More on Quotient Groups and Homomorphisms |
| 5 | Mon 10/14 | 3.2 | More on Cosets and Lagrange's Theorem |
| Wed 10/16 | 3.3, 3.5 | The Isomorphism Theorems; Transpositions and the Alternating Group | |
| Fri 10/18 | 4.1-4.3 | Group Actions; Cayley's Theorem; The Class Equation | |
| 6 | Mon 10/21 | 4.5 | The Sylow Theorems |
| Wed 10/23 | 4.5 | The Sylow Theorems (cont.) | |
| Thur 10/24 (x) | Midterm review | ||
| Fri 10/25 | 5.1-5.2 | Direct Products; Fundamental Theorem of Finite Abelian Groups | |
| 7 | Mon 10/28 | 7.1 | (Rings) Basic Definitions and Examples |
| Wed 10/30 | 7.2 | Examples: Polynomial Rings, Matrix Rings, and Group Rings | |
| Fri 11/1 | 7.3 | Catch-up and Ring Homomorphisms | |
| 8 | Mon 11/4 | 7.3 | Quotient Rings |
| Wed 11/6 | 7.4 | Properties of Ideals | |
| Thurs 11/7 (x) | 3.4 | (Optional lecture) Composition Series and the Hoelder Program | |
| Fri 11/8 | 8.1 | Euclidean Domains | |
| 9 | Mon 11/11 | 8.2 | Principal Ideal Domains (PIDs) |
| Wed 11/13 | 8.3 | Unique Factorization Domains (UFDs) | |
| Fri 11/15 | 9.1-9.2 | (Polynomial Rings) Definitions and Basic Properties; Polynomial Rings over Fields I | |
| 10 | Mon 11/18 | 9.4-9.5 | Polynomial Rings over Fields II and irreducibility criteria |