370 Honours Algebra 2009
Course Page

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

Course Outline

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

Solutions to Assignment 1

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)

<>Assignment 3, Artin's Chapter 6
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.

<>Chapter 8,
Section 2, #2,
Prove Proposition 3.20

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

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)