MATH4060 - Complex Analysis - 2018/19

Announcement

• There is no tutorial in the first week.
• Every other question, starting from the second one, of assignment 1 will be marked.
• The midterm will cover Chapter 1 to Chapter 5.2 of the textbook, with the exception of Chapters 2.5.5 and 4.3.
• Week 3 tutorial note was updated.
• The venue of the midterm is AB1 Room 502A. The time is still 23 Oct 1630-1815. Please reserve extra time to go to the new venue.
• The final exam is to be held on Dec 13, 13:30-16:00, at New Asia Gymnasium. It will cover Chapters 1-6 and Chapter 8.1-8.3 of the textbook, with the exceptions of Chapters 2.5.5, 4.3, 8.1.3, Proposition 2.7 in Chapter 6, and Theorem 2.4 in Chapter 8.
• Homework 5 is available for collection.

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General Information

Lecturer

• Yung, Po Lam
  • Office: LSB 234

Teaching Assistant

• Siu, Chun Yin
  • Office: LSB 222A
  • Office Hours: 1630-1730 (Please make an appointment in advance.)

Time and Venue

• Lecture: Tuesdays 5:30pm-6:15pm at AB1 G03, Thursdays 2:30pm-4:15pm, at LSB C2
• Tutorial: Tuesdays 4:30pm-5:15pm, at AB1 G03

Course Description

This is a second course in complex analysis. Topics to be covered include the Poisson summation formula, Weierstrass infinite products, Gamma and zeta functions, the prime number theorem, the Riemann mapping theorem, elliptic functions, and time permitting the sum of two squares theorem. We assume as prerequisite a solid understanding of properties of analytic functions of one complex variable, at the level of Math 2230 or Math 3253.

Textbooks

• E.M. Stein and R. Shakarchi, Complex Analysis, Princeton University Press, 2003.

Pre-class Notes

• Course outline

Lecture Notes

• Review of holomorphic functions
• Poisson summation and periodization
• A characterization of harmonic polynomials
• Order of growth of 1/Gamma
• Basic geometry of holomorphic maps

Tutorial Notes

• week 2
• week 3 (updated on 17 Oct: A typo in the proof of Prop 1 was fixed; part of the argument was amended accordingly.)
• week 5
• week 6
• week 7
• week 9 (updated on 5 Nov: Sources of the examples were added.)
• week 10
• week 11
• week 12
• week 13 (updated on 28 Nov: typos corrected and additional information supplied in boldface.)

Assignments

• Homework 1
• Homework 2
• Homework 3
• Homework 4
• Homework 5 (New due date: Nov 29, 2018)
• Homework 6

Quizzes and Exams

• Midterm 2015
• Midterm 2016
• Midterm 2018

Solutions

• Homework 1 solution
• Homework 2 solution
• Homework 3 solution
• Midterm solution (updated on 24 Oct and 12 Nov, question 2a and 2bi were swapped in the previous version, other editions are marked in the document)
• Homework 4 solution
• Homework 5 solution

Assessment Scheme

Homework		10%
Midterm Exam		40%
Final Exam		50%

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.

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Assessment Policy

Last updated: December 06, 2018 10:49:26