A survey course in three parts. I: the theorems of Burnside, Sylow, and Jordan-Holder, toward the classification of finite simple groups. II: (noncommutative) rings and modules over PIDs, including applications to classification problems. III: additional topic chosen by instructor, e.g., category theory, homological algebra, division rings, and representation theory.
Prerequisites: Graduate Student status.
Outcomes: Students will demonstrate facility with standard proof techniques in abstract algebra, and the ability to work with algebraic structures (including actions, morphisms, and quotients; concretely and abstractly); Students will recognize the common theme of classification uniting the course topics.
Prerequisites: Graduate Student status.
Outcomes: Students will demonstrate facility with standard proof techniques in abstract algebra, and the ability to work with algebraic structures (including actions, morphisms, and quotients; concretely and abstractly); Students will recognize the common theme of classification uniting the course topics.