Learn Group Theory

Description

In this course, you will learn :

• What transforms a set into a group?
• Explore group axioms using cube symmetries.
• Explore some real-world applications to learn more about groups.
• Discover the structure of groups within groups.
• Use groups to help you understand this perplexing toy.
• By categorising a group's elements, you can learn a lot about it.
• Investigate the interaction between a group and the set on which it acts.
• Discover a useful method for constructing larger groups from smaller ones.
• Investigate the structure of finite groups to discover fascinating new relationships.

Syllabus :

1. Introduction

• Symmetry
• Combining Symmetries
• Group Axioms
• Cube Symmetries

 

2. Fundamentals

• Axioms and Basic Examples
• More Group Examples
• Subgroups
• Abelian Groups

 

3. Applications

• Number Theory
• Puzzle Games
• Rubik's Cubes

 

4. Advanced Topics

• Normal Subgroups
• Isomorphism Theorems
• Conjugacy Classes
• The Symmetric Group

 

5. Group Actions

• Group Actions
• Burnside's Lemma
• Semidirect Products
• Sylow Theorems

Show more