Registration for Spring term opens Thursday, February 23, 2016.
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The course will be an introduction to complex analysis. The following topics will be covered: Holomorphic functions and the Cauchy-Riemann equations, Cauchy's theorem and Cauchy's integral formula, Taylor expansions, entire functions and Liouville's theorem, zeros of holomorphic functions, isolated singularities and Laurent expansions, meromorphic functions, the Residue Theorem, the Maximum Modulus Principle, conformal mappings and linear fractional transformations, harmonic functions, infinite products and the Weierstrass Factorization Theorem, the Gamma function, and the prime number theorem.
Based on homework (70%), and final exam (30%).
Collaboration for solving the homework problems is allowed, however the students should write up the solutions individually. The homework sets should be handed in with a cover sheet that only has the student's first and last names on it, due to privacy policies.
Elias M. Stein and Rami Shakarchi, Complex Analysis (Princeton Lecture Series in Analysis II), ISBN-13: 978-0-691-11385-2.