MAT 427E - Algebra II

Course Objectives

1. To provide an introduction to the study of structures and classifications of groups.
2. To teach basics of fields and field extensions
3. To demonstrate some applications of group theory and field theory.
4. To prepare students to graduate-level courses in number theory and algebra.

Course Description

Group actions, Sylow theorems, solvable groups, nilpotent groups, polynomials and factorization, extension fields, simple extension theorem, finite fields, separable extensions, normal extensions, the main theorem of Galois theory, solvability by radicals, geometric constructions by a straightedge and a compass