Algebra I

3 units

An introductory graduate level course on the basic structures and methods of algebra. Detailed survey of group theory including the Sylow theorems and the structure of finitely generated Abelian groups, followed by a study of basic ring theory and the Galois theory of fields. Math 5031 and Math 5032 form the basis for the Ph.D. qualifying exam in algebra. Prerequisite: Math 430 or the equivalent, or permission of the instructor.