What is Abstract Algebra?

Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in the sciences, too.

Abstract Algebra is also known as “modern algebra.” Compared to most other math subjects, it truly is a modern invention! While a lot of math got its start in ancient days, Abstract Algebra was invented in the 1800s by a teenager named Évariste Galois.

At this point, mathematicians had worked out ways to solve linear equations, quadratic equations, cubic equations, and even quartic equations. But Galois was on the hunt to solve equations of higher degree. To do this, he invented a new kind of abstraction: a mathematical tool called the “group.”

Abstract Algebra includes powerful tools of mathematical abstraction including groups, rings, fields, vector spaces, modules, and more.

Other abstract structures followed, including rings, fields, vector spaces, modules, and more. Applications of these concepts continue to be developed in a variety of fields, including physics, chemistry, and computer science.

Before you get started learning Abstract Algebra, watch this enticing video that will give you a hint of its power and reach. More lessons and resources listed below.