__370 Honours Algebra 2007__

__Course Page__

Office hours before the
exam: Dec 5, 17:00-19:00,

Dec 6, 12:20-14:00

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)

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).

Assignment 3 (Due Nov 7)

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

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

<>Chapter 12,

Section 6, # 3 (b), (c), # 4.

Solutions to assignment 4, part 2