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.

General theory of normed linear spaces including the Hahn-Banach separation theorems, principle of uniform boundedness and closed graph theorem. Dual spaces and representation theorems for linear functionals. Abstract measure theory and Riesz representation theorem for C(X).

Review of recent research in discrete mathematics. May be repeated to a maximum of nine credits.

Review of current research in numerical analysis. May be repeated to a maximum of nine credits.

Half-time to full-time work on thesis. May be repeated to a maximum of six semesters.

Reports and discussion on recent advances in group theory, ring theory, and homological algebra. May be repeated to a maximum of nine credits under different subtitles.

Residency credit for dissertation research after the qualifying examination. Students may register for this course in the semester of the qualifying examination. A minimum of two semesters are required as well as continuous enrollment (Fall and Spring) until the dissertation is completed and defended.

May be repeated to a maximum of 12 hours.