MATH 580 Functional Analysis
(Formerly Applicable Analysis MATH 511) Linear spaces, subspaces and linear span, examples of normed linear spaces, linear maps, null spaces, image spaces, invertibility, isomorphisms, normed linear spaces, product spaces, linear functionals, hahn-banach theorem, convergence and continuity, banach spaces, open mapping and closed graph theorems, inner product spaces, contraction mapping principle, orthogonal and complete orthonormal sets, hilbert spaces and linear operators.