NMAK17002U Complex Analysis 2

Volume 2023/2024

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject


The course covers

  • Holomorphic, harmonic and subharmonic functions
  • Normal families, conformal mapping and Riemann's mapping theorem
  • Infinite products and Weierstrass factorization
  • Growth of entire functions
  • Picard's theorems
  • Eulers Gamma function


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.

Introductory complex analysis (e.g. the course KomAn). We shall occationally use results from introductory measure theory, such as Lebesgue's dominated convergence theorem.

Academic qualifications equivalent to a BSc degree is recommended.
Five hours of lectures and two hours of exercise sessions per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 117
  • Exercises
  • 14
  • Exam Preparation
  • 39
  • Exam
  • 1
  • Total
  • 206
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
Type of assessment details
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 must 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, 30 minutes with 30 minutes preparation time. All aids allowed during the preparation time. No aids allowed during the exam.

To be allowed to take the re-exam, students who have not already had 2 out of the 3 mandatory assignments approved must (re)submit all 3 assignments no later than three weeks before the beginning of the re-exam week and two of these assignments must be approved no later than two weeks before the beginning of the re-exam week.

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.