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 (an alternative is book [2], which is gentler and less terse). If you want a grouptheory 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" (topicspecific) or "algebra" or "abstract algebra" (widecoverage) 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 GĂ¶ttingen 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 4/9  Introduction The Integers 
§0.2 

T 9/9  Modular arithmetic  §§0.3,0.1  
Th 11/9  (continued)  PS1 due  
2  T 16/9  Permutations  §1.3  
Th 18/9  (continued)  PS2 due  
3  T 23/9  Groups and subgroups  §§1.1,1.2,1.5,2.1  Concepts to review 
Th 25/9  Homomorphisms, Cyclic groups  PS3 due  
4  T 30/9  Cosets and Lagrange's Theorem Normal Subgroups 
§3.2  
Th 2/10  Quotient Groups  §3.3  PS4 due  
5  T 7/10  Isomorphism Theorems Simplicity of A_n 
§3.3 §4.6 
Feedback form 
6  Th 9/10  Group actions  §1.7, §§4.14.3  PS5 due 
T 14/10  Midterm Exam  Midterm  Midterm  
7  Th 16/10  (continued)  Zagier's Trick  
T 21/10  Examples: orbits, stabilizers  
8  Th 23/10  pgroups  PS6 due  
T 28/10  pqgroups  
9  Th 30/10  (continued) Sylow's Theorems 
§4.5 
PS7 due 
T 4/11  (continued)  §4.5  
10  Th 6/11  Groups of medium order  §6.2  
Th 13/11  (continued)  
11  T 18/11  Finite Abelian groups  §6.1  
Th 20/11  Finitely generated abelian groups  §5.2  
12  T 25/11  Solvable groups  §6.1  
Th 27/11  Solvable groups  §6.1  
M 15/12  Final exam 
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Last modified Friday March 06, 2015