# Topics in Algebra

 General Information Syllabus Homework Assignments Exam Related Class Material

## 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.