MAA5406.01 - Theory of Functions of a Complex Variable I
Fall 2009


Instructor: Dr. Ettore Aldrovandi.
Office: 215 LOV.
Office Hours: Listed at the instructor’s web page.
Course Web Page: http://www.math.fsu.edu/~ealdrov/courses/fall2009/MAA5406.01

SCHEDULE
Class will meet on Tuesday, Thursday, 2:00–3:15 p.m. in 200 LOV.
PREREQUISITES
Graduate standing.
TEXT
Elias M. Stein & Rami Shakarchi, Complex Analysis, Princeton Lectures in Analysis II, Princeton Univ. Press.
COURSE CONTENT
The topics to be covered are roughly as follows: Algebra and geometry of complex numbers; elementary properties and examples of analytic functions; complex integration, integration of analytic functions; Cauchy’s theorem and related theorems; power series and power series representation of analytic functions; singularities and their classification; residues; meromorphic functions. Entire functions. Possibly conformal mappings and Fourier transforms. These topics approximately correspond to chapters 1, 2, 3, 4, 5, and 8 of the textbook.
COURSE OBJECTIVES
The course focuses on theoretical aspects and applications of the theory of functions of a complex variable. The course is the first part of a two semesters-long sequence.

The purpose of this course is to introduce students to the core of the theory of functions of a complex variables in order to: 1) give students solid foundations to base their understanding of more advanced material later on; 2) enable students to acquire computational skills and learn to use new and effective tools they will need in virtually any kind of future mathematical work.

The material to be covered in this course roughly corresponds to the material in the first part of the qualification exam in Complex Analysis. Hence another objective of this course—combined with the second part, MAA5407—is to prepare students for the Qualifier Exam.

Another important objective, not specific to Complex Analysis, is to achieve a good style of mathematical exposition. Hence your work will be graded by taking into account the quality and style of exposition, as well as mathematical content.

ATTENDANCE
I expect you to attend class regularly. A student absent from class bears the full responsibility for all subject matter and information discussed in class.
HOMEWORK
Homework will consist of weekly assignments. Homework assignments will be posted on the course web page. One or two problems per week will be collected for grading.
EXAMS
There will be one midterm and a final exam. A date for the midterm will be communicated in due course.

The final exam date is Friday, Dec. 11, 3:00–5:00 p.m., same location as class meetings.

GRADING
Your grading will be determined by your performance in the written homework, midterm, and final exam, roughly in equal measure.

Cutoff points for A, B, C, etc. will be in the vicinity of 85%, 70%, 55%, etc., but I reserve the right to make (small) adjustements if necessary.

HONOR CODE
A copy of the Academic Honor Code can be found in your current Student Handbook. You are bound by this in all of your academic work. It is based on the premise that each student has the responsibility 1) to uphold the highest standards of academic integrity in the student’s own work, 2) to refuse to tolerate violations of academic integrity in the University community, and 3) to foster a high sense of integrity and social responsibility on the part of the University community. You have successfully completed many mathematics courses and know that on a “test” you may not give or receive any help from a person or written material except as specifically designed acceptable. Out of class you are encouraged to work together on assignments, but plagiarizing of the work of others or study manuals is academically dishonest.
AMERICAN DISABILITIES ACT
Students with disabilities needing academic accommodations should: 1) register with and provide documentation to the Student Disability Resource Center (SDRC); 2) bring a letter to the instructor from SDRC indicating you need academic accommodations. This should be done within the first week of class.