Abstract Algebra Teaching and Learning

Definition

As a mathematical discipline, Abstract Algebra, also called modern algebra or structural algebra, denotes, by opposition to classical algebra which focuses on formal manipulation of abstract symbols in relation to solving equations, the new image of algebra that emerged at the turn of the twentieth century. It was first presented in history in the textbook Moderne Algebra (Waerden 1930) which “inverted the conceptual hierarchy of classical algebra” (Corry 2016) by putting algebraic structures to the fore and seeing properties of numbers, polynomials, etc., as consequences of what is known on general structures rather than the other way round.

In an educational context, Abstract Algebra usually designates an upper division undergraduate course typically required for mathematics majors and centered on the structures of groups, rings, and fields. In general, it is encountered by students upon completion of courses in Linear Algebra. Abstract Algebra courses are thus taught at...