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# Group theory: course

### From Mathematics Is A Science

## 1 Description

This is a one-semester course in modern algebra and groups.

## 2 Prerequisites

## 3 Outline

- Review
- Modular arithmetic
- Permutations
- Definition of group
- Homomorphisms of groups
- Subgroups
- Products of groups
- Quotients of groups
- Classification of abelian groups
- Rings and fields
- Transformation groups

## 4 Notes

Text:

- Contemporary Abstract Algebra by Gallian
- A First Course in Abstract Algebra Fraleigh. Chapters: 1. Groups and subgroups, 2. More groups and cosets, 3. Homomorphisms and factorgroups, 5. Introduction to rings and fields.