__370 Honours Algebra 2009__

__Course Page__

Midterm, Wed, Oct 14, 17:00-19:00, Burn
920

Office hours: MW 14:00-15:00

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

__2.4.20; 2.4.21: 2.8.9; 2.8.11; 2.10.10
__

Assignment
2: Artin's Chapter 5

2.14; 3.3; 4.10; 4.20; 5.7; 8.8

due Oct 12 (three randomly choosen
problems will be marked)

1.8 c,f; 1.10 d; 3.13; 3.14; 4.17; 5.3; 6.20

Due Nov 4.

Solutions to Assignment 3, part 1

Solutions to assignment 3, part 2

Assignment 4, Artin's Chapter 6

7.2; 8.4; 8.10; 9.3a; 9.11a

Due Nov 13.

Solutions to assignment 4 page1, page 2, page 3

Assignment 5, Due Dec 1.

Section 2, #2,

Prove Proposition 3.20

Chapter 12,

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

Solutions to assignment
5,
part 1

Solutions to assignment 4, part 2

Wallpaper groups program by R. Adams

Schedule:

__Sep. 2-9: Groups, subgroups, homomorphisms,
normal subgroups, examples.
__

__Sep. 11: Symmetric and alternating
groups. The center and the derived subgroup. Cosets and
Lagrange's theorem
__

__Sep.
14: Quotients and the three isomorphism theorems.
__

__Sep. 16: Correspondence between subgroups of $G$
containing ker f and the quotient group $G/ker f$ __

Oct. 26, 28, 30: Subgroups of a free group. The graph-theoretic tools for free groups (notes
of A.Tomberg)

Nov 2: The Todd- Coxeter algorithm.

Nov 4-16 Artin, Chapter 8, Sections 1-3. The
classical linear groups, SU_2 as S^3, latitures, longitudes. The
orthogonal representation of SU_2.

Nov 18 - Dec 1. Modules and abelian groups (Chapter 12)