Abstract Algebra


Groups - Motivation for Definition

The definition of a group is very abstract. We motivate this definition with a simple, concrete example from basic algebra.

Why did we need to define a group in the first place? What motivated the creation of this abstract idea, and hence, launch an entire field of mathematics (Abstract Algebra)?

Hint: what can you accomplish if a group has these characteristics?
▪ Set of elements
▪ Has an operation *
▪ Closed under that operation *
▪ Has an identity e
▪ Has inverses
▪ Associative

If you’d like to review this definition in more detail, visit The Definition of a Group. In this shorter video, we’ll provide the surprisingly simple motivation for why a group was defined in this way. More lessons and resources below.

Course Page


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!