Abstract Algebra: A First Course

When a student of mathematics studies abstract algebra, he or she inevitably faces questions in the vein of, "What is abstract algebra" or "What makes it abstract?"

Algebra, in its broadest sense, describes a way of thinking about classes of sets equipped with binary operations. In high school algebra, a student explores properties of operations (+, −, ×, and ÷) on real numbers.

Abstract algebra studies properties of operations without specifying what types of number or object we work with....