Reading course for graduate students in mathematics. May be repeated to a maximum of nine credits.

Reading course for graduate students in mathematics. May be repeated to a maximum of nine credits.

Reading course for graduate students in mathematics. May be repeated to a maximum of nine credits.

Reading course for graduate students in mathematics. May be repeated to a maximum of nine credits.

Reading course for graduate students in mathematics. May be repeated to a maximum of nine credits.

Reading course for graduate students in mathematics. May be repeated to a maximum of nine credits.

Reading course for graduate students in mathematics. May be repeated to a maximum of nine credits.

Homotopy and homology theories, complexes and applications.

This graduate course is a continuation of MA 661. Topics include modules over principal ideal domains, localization, primary decomposition, associated prime ideals, classes of rings and modules such as Noetherian rings and Dedekind domains, tensor and exterior products, exact sequences and resolutions, ideals and varieties, Hilbert's Nullstellensatz.

Continuation of MA 676. Absolutely continuous functions on the real line, Lebesque spaces, beginning theory of Banach spaces including the Hahn-Banach, closed graph, and open mapping theorems.