Mth 611 Complex Analysis   Term: Spring 2005 Time: MWF 1600-1650 Location: BAT 250

Notes and problems

• Contact Information
• Assignments, Documents, Sample Problems, Old Tests, etc.

Assignments

We will have a few assignments. You are expected to discuss the assigned problems with other people to get ideas (not solutions). Explicitly, you may discuss the assignments with anyone and get help where you can. The goal, after all is to learn some mathematics, and discussion is an effective way to do so. But at some point I expect you to sit down and write up your own work. Please do not share the actual composition of your submissions. Consider how tiresome it would be for me if everyone turns in the same report.

Please try to turn in clear, brief and tidy work and follow the instructions precisely. Otherwise it will not be possible for me to keep up and you will never see your submissions again.

Assignments will be listed here as they become available.

Selected Lecture Notes

1996 Seminar notes: Prime Number Theorem
PDF, 284 KB, 42 pages

These notes are from a seminar on the Riemann hypothesis and related topics offered by Ron Guenther, Mary Flahive and Bent Petersen in 1996. LaTeX-2e was used to prepare the notes.

1993-94 Lecture Notes: Weierstrass Vorbereitungssatz (Preparation Theorem)
PDF 151 KB, 8 pages

These notes are from three lectures from a graduate complex variable (one variable) course offered in 1993-1994. They were prepared using AMS-LaTeX.

1976 Lecture Notes: Riemann Zeta Function
PDF, 131 KB, 13 pages

These notes are from two lectures from a graduate complex variable course offered in 1976. They were prepared (in 1996) using LaTeX 2e.

Syllabus

Mth 611 will cover the topics required for the complex analysis part of the qualifying exam, plus whatever else time allows.

Qualifying exam topics:

• Analytic functions
• Cauchy-Riemann equations
• Conformal mappings
• Möbius tranforms
• Contour integrals
• Cauchy theorem (homotopy)
• Maximum principles
• Open mapping theorem
• Fundamental theorem of algebra
• Rouché theorem, principle of the argument
• Power series (convergence domain = disk)
• Uniqueness theorem, concept of analytic continuation
• Schwarz lemma, estimates of quotients
• Singularities
• Laurent series (convergence domain = annulus)
• Residues, residue theorem

Additional topics (random order):

• Evaluation of some integrals
• Phragmén-Lindelöof and other maximum principles
• Infinite products
• Riemann mapping theorem
• Prime number theorem
• Entire functions

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