The course covers Spaces and
operators including: metric spaces, normed
and Banach spaces, linear operators, inner
product, Hilbert spaces. It also covers
fundamental theorems such as Hahn-Banach theorem, uniform boundedness
theorem, open mapping theorem, closed
graph theorem, and spectral theory including
basic concepts, operators on normed
spaces, compact operators, and self-adjoint
operators. *Prerequisite:* MAT 623.