This is the introductory course in algebra, intended for honours students. Students who wish to buy a single abstract algebra book should buy the book [1], which will serve you for both 322 and 323 this year, and also covers the material of 422 and 423. The gentler and less-terse alternative is the book [2]. If you want a group-theory specific textbook, the best book in my opinion is Rotman's (reference [3] below). You can download a copy by following the link while on the UBC network. That said, any book titled "Group Theory" (topic-specific) or "algebra" or "abstract algebra" (wide-coverage) is fine.
During the course, we will study three classical theorems by Sylow. They are, of course, discussed in detail in the textbooks. Sylow's original paper from 1872 (written in French) is available online from the Göttingen University Library.
Readings are generally from Dummit and Foote (sections marked "N" are in the lecture notes). Those reading Rotman can find the material there
| Week | Date | Material | Reading | Notes |
|---|---|---|---|---|
| 1 | Th 10/9 | Introduction The Integers |
§0.2 |
Putnam Sessions |
| T 15/9 | Modular arithmetic | §§0.3,0.1 | Relations | |
| Th 17/9 | (continued) | PS1 due | ||
| 2 | T 22/9 | Permutations | §1.3 | |
| Th 24/9 | (continued) | PS2 due | ||
| 3 | T 29/9 | Groups and subgroups | §§1.1,1.2,1.5,2.1 | Concepts to review |
| Th 1/10 | Homomorphisms, Cyclic groups | PS3 due | ||
| 4 | T 6/10 | Cosets and Lagrange's Theorem Normal Subgroups |
§3.2 | |
| Th 8/10 | Quotient groups | §3.3 | PS4 due | |
| 5 | T 13/10 |
Isomorphism Theorems Simplicity of A_n |
§3.3 §4.6 |
Feedback form |
| 6 | Th 15/10 | Group actions | §1.7, §§4.1-4.2 | PS5 due |
| T 20/10 | Midterm Exam | Midterm | Midterm | |
| 7 | Th 22/10 | Conjugation | §4.3 | Zagier's Trick |
| T 27/10 | Orbits, stabilizers | Examples PS6 due |
||
| 8 | Th 29/10 | p-groups | N4.1 | Groups of order p^3 |
| T 3/11 | pq-groups | N4.2 | ||
| 9 | Th 5/11 | (continued) | N4.2 | PS7 due |
| T 10/11 | Sylow's Theorems | §4.5 | ||
| 10 | Th 12/11 | Applications | PS8 due | |
| T 17/11 | Groups of medium order | §6.2 | ||
| Th 19/11 | Finite Abelian groups | §6.1 | PS9 due | |
| 11 | T 24/11 | Finitely generated abelian groups | §5.2 | |
| Th 26/11 | Nilpotent groups | §6.1 | PS10 due | |
| 12 | T 1/12 | Solvable groups | §6.1 | |
| Th 3/12 | Last lecture | §6.1 | ||
| M 7/12 | Review: 10:00-12:00 at MATH 225 | |||
| T 8/12 | Final exam: 15:30-18:00 at IBLC 182 |
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