An Introduction to Groups (UMAP)

A unit that involves applications of abstract algebra. By the end of this module students will be able to: 1) understand what groups are and why they are important; 2) identify certain groups, subgroups, cyclic groups, and isomorphic groups; and 3) construct groups.

Table of Contents:

1. WHY STUDY GROUPS?
1.1 The Power of Generalization
1.2 What is a Group?
1.3 Examples of Groups

2. SYMMETRY GROUPS
2.1 The Symmetry Group of a Plane Figure
2.2 The Symmetry Group of a Regular Polygon

3. THE STRUCTURE OF GROUPS
3.1 Subgroups
3.2 The Division Property
3.3 Cyclic and Dihedral Groups
3.4 Isomorphisms

4. SAMPLE EXAM

5. ANSWERS TO EXERCISES

6. ANSWERS TO SAMPLE EXAM