Aims: To introduce the students to various algebraic structures that are essential for studies in higher algebra.
At the end of the course the students will be conversant with algebraic structures relating to groups, rings and modules. Moreover students will achieve a solid ground for further studies in algebra. In particular the student will be prepared for studies in MA40188, MA40037, MA40038 and MA40054.
Introduction to group theory: subgroups and Lagrange's Theorem, normal subgroups, quotient groups and the isomorphism theorems. Abelian groups. Rings. Integral domains. Fields. Field of quotients of an integral domain. Ideals and quotient rings. Polynomial rings. Factorization in integral domains. Principal ideal domains. Modules over principal ideal domains.