MA 513 - Analysis: Real and Complex

Offered Fall: No Offered Winter: No Offered Summer: No Offered Other: No

Credits: 4
Hours (Lecture/Discussion/Lab): 4-0-0
Graded: A/F

Prerequisites: Graduate student or accelerated bachelors student in mathematics or instructor permission.
Co-requisites: None

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.