### Course announcement for Math 503,
fall 2004

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.

**
Maintained by **`
greenfie@math.rutgers.edu` and last modified 8/31/2004.