Algebra, created in the medieval era in the Arab world, is the study of operations (such as addition and multiplication) on objects (such as numbers, polynomials, and matrices). Abstract algebra, developed in the 19th century, studies common features and properties of such operations on algebraic systems. Algebra is a fundamental and universal language upon which most other branches of mathematics are built. In recent decades, algebra has become an increasingly important field of study due to its numerous contemporary applications in physics, chemistry, computer science, data communication and security.

We start with properties of integers and modular arithmetic, and then move on to the theory of groups, rings and fields. Groups are motivated by the study of symmetry and are important in crystallography, quantum physics and cryptography. Rings and fields are abstractions of standard notions of addition and multiplication, with applications to error-correcting codes.

Abstract algebra is a contemporary subject as its concepts and methodologies are used by working mathematicians, computer scientists, physicists and chemists. Faculty from other departments will be invited to give guest lectures on applications of algebraic structures. This course will therefore serve as a bridge course to further studies in many departments, and it will expose students to potential junior paper or senior thesis projects through dialogues with guest lecturers from other departments.