The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.

Additional study materials

Group Example - A Complex Circle

Learn about an interesting group: the set of all complex numbers of magnitude 1. This is both a circle and a group.

The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to continue your study of abstract algebra be learning about rings, fields, modules and vector spaces.

Group Example - A Complex Circle

Group Example - A Complex Circle

Learn about an interesting group: the set of all complex numbers of magnitude 1. This is both a circle and a group.

BUYTo unlock bonus features,

sign in or create a free Socratica account.

Group Example - A Complex Circle

Learn about an interesting group: the set of all complex numbers of magnitude 1. This is both a circle and a group.

Course Page

Course Description

Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.