189-249B: Honours Complex Variables

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Professor: Henri Darmon

Classes:
W 11:35-12:55 in Leacock 232.
F 11:35-12:55 in MAASS 112.

Office Hours:

W 13:05-14:25, and F 10:05-11:15 in Burnside Hall 1111, or by appointment.

TA: Vishnu Kadiri

Tutorial Hours: MW 4:35-5:25 in Burnside 1205.

Office Hours: TuTh 2:30-4:00 in Burnside 1031.

Graders: TBA.

See also the Math Help Desk in BH911 operating Mondays to Fridays from noon to 5:00pm. This is a valuable ressource if you need extra help on the material or assignments, and you are strongly encouraged to make use of it.

Main text: We will be following the textbook Complex analysis by Elias Stein as the primary textbook, and will try to stick fairly close to this text as the course unfolds.

Secondary Textbooks:

Functions of one complex variable by John. B. Conway was the primary textbook when I took the class a few years ago, and is still a good solid reference.

Complex Analysis by Lars Ahlfors, one of the towering 20th century figures in the subject, and one of the first winners of the prestigious Fields Medal.

Topics in Complex Analysis by Dan Romik is a more modern and somewhat more advanced (beginning graduate level) textbook which is beautifully written and can be used as a guide to some of the later topics that really bring the subject to life.

Syllabus:

This course will cover the basics of the theory of functions of a single complex variable.
Key topics to be covered will include at least the first 6 chapters of the primary textbook, namely: real and complex numbers, analytic functions and power series, complex integration, singularities of complex functions, the maximum modulus principle. As well as futher topics like, (time permitting) analytic continuation, harmonic functions, the uniformisation theorem.

Assignments:
Assignments will be handed out every other Monday, so there will be a total of 6 assignments in the semester.

Grading Scheme : There will be two possible schemes, and I will take the maximum of those.
1. 20% biweekly assignments, 30% Midterm, 50% Final.
2. 20% biweekly assignments, 80% Final.
In particular, not handing in assignments and going for 100% final is not an option.

Midterm Exam:. The midterm exam will be held, in class, on Friday, March 13 at the usual time (11:35-1:25 PM).

Final Exam:. The final exam will be held on TBA.

The obligatory statements

McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information).

In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.

In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change.