Course:

Abstract AlgebraThe 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.

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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.