## Math 31, Winter 2005

# Topics in Algebra

## Handouts used in the class

**Introduction:** Basic information
about the course.

**Chapter 1. Dihedral groups:**
full page and
pocket size for
symmetries of a square and
multiplication table handouts.

**Chapter 2. Groups:**
examples.

**Chapter 4. Cyclic Groups:** Major facts.

**Chapter 5. Permutation Groups:** Major
facts.

**Chapter 6. Isomorphisms:** Major
facts.

**Chapter 7. Cosets and Lagrange's Theorem:** Major
facts about cosets.

**Chapter 8. External Direct Products:** Major
properties.

**Chapter 8. RSA algorithm:**
Example.

**Chapter 9. Normal Subgroups and Factor Groups:** Major
fact.

**Chapter 9. Normal Subgroups and Factor Groups:**
Example.

**Chapter 10. Group Homomorphisms:** Major
facts.

**Chapter 12. Rings:** Major
facts.

**Chapter 15. Ring Homomorphisms:** Major
facts.

**Chapter 16. Polynomial Rings:** Major
facts.

**Chapter 17. Factorization of Polynomials:** (Ir)Reducibility
tests and
proof of the fact the reducibility of an
integer polynomial over **Q** implies reducibility over **Z**.