Hilbert spaces: L^2 spaces, orthogonal complements, dual spaces, Riesz representation theorem, the Fredholm alternative, spectral resolution of compact normal operators. Banach spaces: Hahn-Banach theorem, bounded linear operators, adjoints, closed graph and Banach Steinhaus theorems.

Prerequisite(s): Mathematics 2700A/B or the former Mathematics 2120A/B, Mathematics 3122A/B. Pre-or Corequisite(s): Mathematics 3124A/B.

Extra Information: 3 lecture hours.