Syllabus for Complex Analysis, Spring 2016

Instructor: Y.P. Lee, JWB 305
Office Hours: MWF 14:50-15:30 + appointments.

Time. MWF 13:40-14:50.
Room: LCB 323

Course Information
Textbook: Complex Analysis, third edition by Lars Ahlfors. (Note: The book is obscenely expensive, but there are used copies and other means of obtaining a reading copy. Contact me in private if this is a problem for you.)
Catalogue Number: 6310. Class Index Number: 2587.

Course Description: The class will meet 4 hours each week, roughly 50% on lectures and 50% on problem sessions. Because I believe strongly in active learning, the problem solving will be the core of the class. Most examples will be worked out during the problem sessions rather than in the lectures. The pace of the lectures will be brisk and the students are expected to work hard outside the classroom. An average student should plan to study at least 9-12 hours per week to keep up with the class. (The time may vary depending on students' prior exposure to the subject.)

The current plan is to cover the entire book during the semester. Note however that the plan is tentative and the pace will ultimately depends on the class.

Qualifying exam requirements: This is one of the qualifying exam (prelim) classes. Prelim requires solid working knowledge on

Holomorphic functions, Cauchy-Riemann equations, Cauchy's Theorem, Cauchy's integral formula, Maximum principle, Taylor series for holomorphic functions, Liouville's theorem, Runge's Theorem. Normal families, isolated singularities, Laurent series, residue theorem, applications to compute definite integrals, Rouche's Theorem. Conformal mappings, examples, Schwartz lemma, isometries of the hyperbolic plane, Montel's theorem, Riemann mapping theorem. Infinite products, Weirstrass factorization theorem. Analytic continuation, monodromy. Elliptic functions. Picard's theorem.

These topics will form the core of this course. The class is designed in such a way that a student who does well in the class should have no problem passing the complex analysis part of the analysis prelim.

Problem solving is vital for this class. Homework problems will be assigned during the lectures and posted at the class home page afterwards. Problem sessions will be held roughly every 1 to 2 weeks. Students will take turns to present their solutions during the problem sessions and turn in their work on Monday (or Wednesday if Monday is a holiday) after the conclusion of problem sessions. A student volunteer will organize the presentation of HW problems according to students' own preferences.

The current plan is to have one midterm exam and one final exam. This may change depending on how the class goes.(*)
Location: LCB 323, the lecture room, unless otherwise announced.
First Midterm Exam: Wednesday, 24 Feb.
Second Midterm Exam: Friday, 25 Mar.
(*) At the discretion of the instructor, the number of midterm exams might be changed.
Final Exam: Friday, 29 April 2016, 13:00-15:00pm.
Note: All exams are cumulative. Only pencils are allowed during the exams. No calculators, computers, books, notes etc.
Important! Please make sure that you can attend all exams. No makeup exam is possible without a documented exceptional reason. In most cases, it must be authorized by the instructor prior to the exam.

Grading Policy: 10% problem sessions, 20% homework, 40% midterm exams, 30% final exam. (or in case of single midterm exam: 10% problem sessions, 20% homework, 30% midterm exam, 40% final exam.)

How to do well in this class? The answer is straightforward and old-fashioned: Prepare for Class, Keep Up, and Do the Homework Problems. The exams will contain at least 70% from material covered in lecturs and homework problems, with little modification. A sure way to get a good grade is to study for the class, and do the assignments as if you are taking the tests, without the help of the book, notes and computers. It also helps a great deal to ask questions during and after the lectures, especially after you have already (p)reviewed the material.

Instructor's comments: The goal of this class is to have students learn the material well and then to give them fair and accurate grades. To achieve this goal, the instructor belives in serious homework problems and hard exams. Serious problems make students learn more and better. Hard exams give a better evaluation of students' learning. In other words, if you are taking this class just to get a passing grade and with no intention to learn, consider taking another class.

Department Schedule Y.P.'s teaching page Y.P.'s homepage

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