Complex analysis is beautiful and useful. The course will be a rigorous introduction with examples and proofs foreshadowing modern connections of complex analysis with differential and algebraic geometry and partial differential equations. Acquaintance with analytic arguments at the level of Rudin's Principles of Modern Analysis is necessary. Some knowledge of algebra and point-set topology is useful. A previous "undergraduate" course in complex analysis would also be useful though not necessary. Students who have taken a complex analysis course which carefully discussed a homotopy or homology version of Cauchy's Theorem may not need to take this course.
The text will be Complex Analysis in One Variable (second edition) by R. Narasimhan and Y. Nievergelt. The book is now available in the Rutgers University bookstore for about $68. Narasimhan's excellent text, with many interesting features, such as early presentation of results named for Picard and Runge, and the Corona Theorem, has in the second edition been supplemented with a useful and diverse collection of exercises by Nievergelt. I hope to cover most of Chapters 1 through 7. There will be written homework assignments and a written midterm and final exam.
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