MA 513 Analysis: Real and Complex 4 cr.  (4-0-0)

​This is an advanced course covering a selection of topics from real analysis and complex analysis. The instructor will ​cover the following topics from real analysis: measurable sets and functions, the Lebesgue Integral, Fourier series, Hilbert spaces, ​and ​the Fourier transform​.  Then the instructor will cover ​the following topics from complex analysis: holomorphic functions, the Cauchy-Riemann equations, the Cauchy-Goursat theorem,​Taylor and Laurent series, and the residue theorem. ​Additionally, the instructor may focus on topics from real and complex analysis such as:​ ​L​p​ spaces, analytic continuation, the Mellin transform, or the Laplace transform.