Abstract Algebra

Lessons

What is Abstract Algebra?
Group Definition
Group Definition (Quick)
Cosets and Lagrange's Theorem
Cayley Tables
Groups - Motivation for Definition
Normal Subgroups and Factor Groups
Subgroups
Cyclic Groups
Group or Not Group? (Integer Edition)
Group Homomorphisms
Group Homomorphisms (Quick)
Isomorphisms for Groups
Kernel of Group Homomorphisms
Order of an Element
Cycle Notation for Permutations
Symmetric Groups
Dihedral Groups
Direct Products of Groups
Matrix Groups
Simple Groups
Symmetry Groups of Triangles
Ring Definition
Ring Definition (Quick)
Ring Examples
Units in a Ring
Field Definition
Field Definition (Quick)
Field Examples: Infinite Fields
Ideals in Rings
Integral Domains
Modules
Vector Spaces

Course Overview

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.

It may be confusing that there are two math courses called ALGEBRA. If you’re looking for the algebra class you take in high school, where you “solve for x” — visit our Socratica High algebra course. We’ll take good care of you over there! 

But if you’re looking for the kind of algebra that math majors study in college, you’re in the right place. This is ABSTRACT ALGEBRA, and this is where to start if you want to learn about the fundamental abstract structures of math. 

In this class, you’ll learn about 
▪ Groups
▪ Rings
▪ Fields
▪ Modules
▪ Vector Spaces
... and much more

This is a video-based class that allows you to learn at your own pace. Find the complete list of videos below. For select lessons, there will be additional handouts and activities. We encourage you to sign up for the Abstract Algebra mailing list to receive free updates to the course.

Resources

Abstract Algebra Textbook
Abstract Algebra Textbook
Abstract Algebra by Dummit & Foote is a standard textbook used by colleges and universities. It is extremely well written with lots of examples and exercises. It covers all the topics for a solid first course in Abstract Algebra. We use this on occasion as a reference for inspiration or reference. Highly recommended!
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