Instructor: Alexander Koldobsky

Description: How can one differentiate functions that are not differentiable and compute integrals that do not converge? The theory of distributions offers a way to do it, which has numerous applications to different areas of mathematics, including analysis, differential equations, geometry and others. In this class we start with basic definitions and properties of distributions and go all the way to new research papers in several areas of mathematics. Our main reference will be a series of books "Generalized functions" by I.M.Gelfand and his coauthors. The class will be conducted in the usual lecture-homework format.

Prerequisites: Math 4700 and Math 4900 or any equivalent courses.