370 Honours Algebra 2007
Course Page
 
Office hours before the exam:  Dec 5, 17:00-19:00,
Dec 6, 12:20-14:00

Course Outline


Assignment 1, Due Oct 2, (from the Artin Book)

2.4.20; 2.4.21: 2.8.9; 2.8.11; 2.10.10



Schedule:

Sept. 5-12 : Ch.2, group, subgroup, isomorphisms, homomorphisms, kernel, image.

Sept.12-19 Cosets, Products of groups

Sept. 21: Quotient groups

Sept. 24,  26: The group of Motions of the plane

Sept. 26: Finite groups of Motions.

Assignment 2: Chapter 5
2.14; 3.3; 4.10; 4.20; 5.7; 8.8
 due Oct 15  (three randomly choosen problems will be marked)

Solutions to Assignment 1

Oct. 1- Oct. 10 Discrete groups of motions. Frieze groups. group operations.
The operation on cosets, the Counting formula, Permutation representation.
The operation of a group on itself.

Oct. 12.  Review for the midterm (solving problems).

Solutions to Assignment 2

Assignment 3 (Due Nov 7)

Chapter 6:  1.8 c,f;   1.10 d;  2.12;  3.13;  4.17.

Solutions to the midterm


Oct 14-26 The Sylow Theorems, The groups of Order 12, Simplicity of $A_n$, n>4..

Oct 30 Computation in the Symmetric group.

Nov 1-Nov 7. The structure of finitely generated abelian groups. (Ch 12, Section 6)

Nov. 9 The free group, Generators and relations
Nov. 12, 14, 16  Subgroups of a free group. The graph-theoretic tools for free groups. The Todd- Coxeter algorithm.
Nov. 19.   The Classical linear groups.  Chapter 8, Sections 1-3.
Solutions to Assignment 3

Assignment 4, Due Nov. 30
Chapter 6,
Section 6, # 16,17;
Section 7, # 2
Section 8, # 4,10
Section 9, # 3a, 11a

Solutions to assignment 4, part 1.

<>Chapter 12,
Section 6, # 3 (b), (c), # 4.

Solutions to assignment 4, part 2