## Course curriculum

1. Welcome to Group Theory

2. Support Socratica

1. Group Definition

2. Example 1: The Integers

3. Example 2: Vectors

4. Example 3: Nonzero Real Numbers

5. Subgroups - Definition & Examples

6. Group Multiplication Tables (Cayley Tables)

7. Cosets and Lagrange's Theorem

1. Cyclic Groups

2. Symmetries of a Triangle

3. Dihedral Group

4. Group Example - S1

5. Symmetric Groups

6. Cycle Notation for Permutations

7. Matrix Groups

1. Group Homomorphisms

2. The Kernel of a Homomorphism

3. Normal Subgroups and Factor Groups

4. Isomorphisms - Example 1

5. Automorphisms

1. Direct Products of Groups

1. Simple Groups

• Free
• 25 lessons
• 2 hours of video content

## Group Theory Topics

We focus on the main topics to help you see the forest for the trees

• Learn the motivation and definition of the central concept in abstract algebra - the group

• See many examples of groups including symmetric groups, dihedral groups, matrix groups, and more

• Explore the concept of "homomorphism", a technique for comparing two groups to see how similar - or dissimilar - they are from each other

## Évariste Galois

Learn about the young mathematician who was instrumental in developing the concept of a group and developing what has become known as Galois Theory.

## Release Notes

Version 1.02

2024-02-09: Group example - nonzero real numbers
2024-01-23: Example of how vectors for an abelian group