Syllabus for Math 401
Koç University,
Spring 2020
Revised
on March 27, 2020
Title of the Course: Complex Analysis
Instructor: Ali Mostafazadeh
(Office: Sci.154; Office Hours: Tuesdays & Thursdays 17:25-18:25)
Textbook: ‘Complex Analysis,’ J. M. Howie (Springer,
London, 2003)
Website: http://portal.ku.edu.tr/~amostafazadeh/math401/math401_S2020/math401.htm
Topics to be
covered: Review of complete metric spaces, complex numbers, and complex plane
(Chapter 2); Complex plane as a Euclidean metric space, open subsets, limit,
and continuity (Chapter 3); Differentiability of complex-valued functions,
power series (Chapter 4); Complex integration (Chapter 5); Cauchy’s theorem and
its implications (Chapters 6 and 7); Residue Calculus (Chapters 8 and 9);
Open-mapping theorem and winding numbers (Chapter 10)*.
Objective: To provide the
student with a basic knowledge of the differential and integral calculus of
complex-valued functions of a single complex variable and some of their
principal applications.
Evaluation method: Students’ progress
will be evaluated according to their performance in homework assignments, two
extended quizzes (mini exams), and a final exam. These contribute to the
numerical grade as 20%, 20% (10% for each quiz), and 60%, respectively.
Eligibility to take the final exam: Due to the unusual situation related to
the spread of coronavirus all students will be eligible to take the final exam.
Attendance &
Bonus: n bonus points will be added to the final exam grade of
the students who attended 10+n lectures out of the 14 lectures held before March
16, 2020.
Policy for Homeworks: Starting March 30,
2020, scanned PDF copies of the homework papers should be sent as an attachment
to the assistant’s email address before the specified deadlines. The email
should have subject: “Math 401, Homework X” where “X” is the number of the
homework assignment. The same PDF must also be uploaded to Math 401’s page in Blackboard.
No late homeworks will be accepted.
Make-ups: If a student
misses a quiz and has a valid excuse, his (her) grade in the final exam will be
substituted for the grade in the missed quiz. If (s)he also misses the final
exam, (s)he will be given zero in the quiz(zes) that (s)he has missed regardless
of whether (s)he has a valid excuse or not. If a student misses the final exam
and has a valid excuse, (s)he will be given a make-up exam.
Rules for online education: Starting from March
30th and till further notice, the lectures will be pre-recorded and
made available online as videos. The electronic files of these video lectures and their content must
not be made available to third parties; students are not permitted to share any
part of these videos in the social media platforms or post them in the internet.
The video lectures will be made
available online through Blackboard for a period of two weeks. The students
should take notes while watching the video lectures and send their feedback to
the instructor’s email. They can also make appointments for Skype meetings.
Suggested Method of
Study: Students are advised to take notes during the (video)lectures and study
their content immediately after each lecture. Reading the lecture notes and the
book is necessary for grasping the subject, but it is by no means sufficient.
Students must try to reproduce the definitions, proofs of the theorems, and
derivations of the results covered in class on their own. They are expected to
spend an average of five hours per week on studying the material covered
in this course.
* This topic may be
covered depending on the progress of the class.