MTH562 
Complex Function Theory
 
Tuesday - Thursday 9:30-10:45 AM
Lippitt Hall 201

Instructor    Araceli Bonifant  
Office: Lippitt Hall 202 G
Phone: 874-4394
Email: bonifant@uri.edu

Office Hours:

Book: A Course in Complex Analysis by Saeed Zakeri (not published yet)

Course Description. Rigorus development of the theory of holomorphic (analytic) functions.

Prerequisites. MTH 435-MTH 436 or MTH 437-MTH438 or permission of instructor.


Tentative List of Topics:

  • Rudiments of Complex Analysis: What is a holomorphic function?, Complex analytic functions, Complex integration, Cauchy's theory in a disk, Mapping properties of certain holomorphic functions.

  • Topological Aspects of Cauchy's Theory: Homotopy of curves, Covering properties of the exponential map, The winding number, Cycles and homology, Homology version of Cauchy's theorem.

  • Meromorphic Functions: Isolated singularities, The Riemann sphere, Laurent series, Residues, The argument principle.

  • Moebius Maps and the Schwarz Lemma: The Moebius group, Three automorphism groups, Dynamics of Moebius maps, Conformal metrics, The hyperbolic metric .

  • Convergence and Normality: Compact convergence, Convergence in the space of holomorphic functions, Normal families.

    • Recommended Reading:
    Complex Analysis - Lars V. Alfors, McGraw-Hill, 3rd edition, 1979
    Complex Analysis - Serge Lang, Springer, 4th edition,1999

    Evaluation Policy:

  • Homeworks and Quizzes              25%
  • Midterm                                          35 %    Thursday March 17
  • Final Exam                                     40 %     Tuesday May 10,        11:30 AM - 2:30 PM

    • Standards of behaviour: Students are responsible for being familiar with and adhering to the published "Community Standards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook. If you must come in late, please do not disrupt the class. Please turn off all cell phones, pagers, or any electronic devices.

    Special Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.