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.