Complex Analysis 2

Course content

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. 

Education

MSc Programme in Mathematics

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.

Five hours of lectures and three hours of exercise sessions per week for 7 weeks.

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.

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
There will be 30 minutes of preparation time before the oral examination.
Aid
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.
Criteria for exam assessment

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

Single subject courses (day)

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