This is a first rigorous course in the theory of functions of one complex variable. Topics include holomorphic (or complex analytic) functions; power series; complex line integrals; Cauchy's integral formula, and some of its applications; singularities of holomorphic functions; Laurent series, and computation of definite integrals by residues; the maximum principle and Schwarz's lemma; conformal mapping; and harmonic functions.
The required textbook is Function Theory of One Complex Variable (2nd Ed) by Robert E. Greene and Steven G. Krantz, AMS, 2002. We will cover chapters 1-7.
The official prerequisite for this course is Math 410 (Advanced Calculus II) or its equivalent. The essential background you need is familiarity with the kind of analytic reasoning used in "epsilon-delta proofs". Prior knowledge of complex analysis is not needed. Math 617 and its successor Math 618 form the basis for the Mathematics Department Qualifying Examination in Complex Analysis.
The course meets Tuesday and Thursday, 9:35-10:50am in BLOC 163. Office Hours are Tuesday and Thursday 11-12 in BLOC 623 and otherwise by appointment (call 845-3261 or e-mail at boggess@math.tamu.edu).
Course grades will be determined by homework (30%); a take-home midterm exam (35%) and an in-class final exam (35%). You may collaborate with other students on the homework. No collaboration is allowed on the take-home mid-term and the final exam. Books and notes are allowed on the mid-term. No books or notes are allowed on the final exam. The idea is that the final exam should be a warm-up for the qualifying exam, where no outside resources are allowed.