NMAK17002U  Complex Analysis 2

Volume 2017/2018

MSc Programme in Mathematics


The course will cover:

  • Runge's approximation theorem and the Mittag-Leffler theorem
  • The gamma function and the Riemann zeta function
  • Order and type of entire functions
  • Infinite products and the Weierstrass factorization theorem 
  • Normal families and the Riemann mapping theorem 
  • Elliptic functions and the Picard theorem

and related topics. 

Learning Outcome

Knowledge: After completing the course the student is expected to have a thorough knowledge of definitions, theorems and examples related to the topics mentioned in the description of the course content and to have a deeper knowledge of complex analysis, both from an analytic and a geometric/​topological point of view.

Skills: At the end of the course the student is expected to have the ability to use the acquired knowledge to follow arguments and proofs of advanced level as well as to solve relevant problems using complex methods.

Competences: At the end of the course the student is expected to be able to: 
1. reproduce key results presented in the course together with detailed proofs thereof,  
2. construct proofs of results in complex analysis at the level of this course, 
3. use the course content to study relevant examples and to solve concrete problems.

Example of course litterature:

W. Rudin, Real and complex analysis.

Supplementary notes might also be used.

Complex analysis (KomAn) or a similar first course in complex analysis.
Five hours of lectures and three hours of exercise sessions per week for 7 weeks.
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
There will be 30 minutes of preparation time before the oral examination.
Exam registration requirements

To be allowed to take the oral exam the student should have at least 2 out of 3 homework assignments approved.

Only certain aids allowed

All aids allowed during the preparation time. No aids allowed during the examination.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners.

Oral examination, 45 minutes with 45 minutes preparation time. All aids allowed during the preparation time. No aids allowed during the exam.

To be eligible to take the re-exam, students who have not already had 2 out of three mandatory assignments approved must re-submit all three assignments no later than 2 weeks before the beginning of the re-exam week. The mandatory assignment must be approved in order to take the re-exam.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

  • Category
  • Hours
  • Lectures
  • 35
  • Exercises
  • 21
  • Preparation
  • 110
  • Exam Preparation
  • 39
  • Exam
  • 1
  • Total
  • 206