Mth 511 Introduction to Real Analysis I

Analysis on metric spaces, Baire Category, Contraction Mapping, and Stone-Weierstrass theorems. Lebesgue measure and integration theory, functions of bounded variation, absolutely continuous functions. Banach and Hilbert spaces. Bases and duality on Hilbert spaces, linear operators on Banach spaces. Introduction to Fourier series. This is the first course in a sequence of three: Mth 511, Mth 512 and Mth 513 which must be taken in sequence.