Complex Function Theory

(Page Under Construction!!)
Tuesday - Thursday: 12:30PM - 1:45 PM
Lippitt Hall Room 201

Instructor    Araceli Bonifant  
Office: Lippitt Hall 202G
Phone: 874-4394

Office Hours:

Book: Functions of One Complex Variable by J. B. Conway (Second Edition)

Others texts (graduate level):
Complex Analysis - Lars V. Alfors, McGraw-Hill, 3rd edition, 1979
Complex Analysis - Serge Lang, Springer, 4th edition,1999
Function Theory of One Complex Variable - Robert E. Greene, Steven G. Krantz, AMS, 2nd edition, 2002

Course Description. Rigorous development of theory of functions. Topology of plane, complex integration, singularities, conformal mapping.

Prerequisites: MTH435 and MTH436; OR MTH437 and MTH438.

Examinations: There will be a midterm exam scheduled for the week of February 27-March 5 and a final exam scheduled during the final exams period.

List of Topics: (subject to change)

  • The Complex Number System.

  • Metric Spaces and the Topology of the Complex Plane

  • Elementary Properties and Examples of Analytic Functions

  • Complex Integration

  • Singularities

  • The Maximum Modulus Theorem

  • Holomorphic Functions as Geometric Mappings

    Evaluation Policy: The final grade for the course will be determined by your performance on the homework, the midterm exam, and the final exam according to the following algorithm:

  • Homework sets:         30%
  • Midterm:                    30%
  • Final:                         40%
  • Homework: Homework will be assigned almost every week. The due date of the homework will be announced in class. You are encouraged to discuss the homework with your classmates and to work together with them on the problems. However, each student is responsible for the final preparation of his or her own homework papers. No late homework will be accepted. Homework will be graded for correctness, clarity, and justification. For a problem to receive full credit, you must show complete work, explain your work as necessary, and present your work in a clean and clear format that is easily understood. (I do not need type homework just clean and readable!)

    You are expected to abide by the University's civility policy:

    "The University of Rhode Island is committed to developing and actively protecting a class environment in which respect must be shown to everyone in order to facilitate the expression, testing, understanding, and creation of a variety of ideas and opinions. Rude, sarcastic, obscene or disrespectful speech and disruptive behavior have a negative impact on everyone's learning and are considered unacceptable. The course instructor will have disruptive persons removed from the class."

    Cell phones, IPods, beepers and any electronic device must be turned off in class!!

    You are required to do your own work unless specifically told otherwise by your instructor. In support of honest students, those discovered cheating on assignments or exams will receive a grade of zero on the assignment or exam. The Mathematics Department and the University strongly promote academic integrity.

    Special with Disabilities:
    Any student with a documented disability should contact his or her instructor early in the semester so that he or she may work out reasonable accommodations with you to support your success in this course. Students should also contact Disability Services for Students: Office of Student Life, 330 Memorial Union, 874-2098. They will determine what accommodations are necessary and appropriate. All information and documentation is confidential.