NMAK15009U Complex analysis 2

Volume 2015/2016
Education

MSc programme in Mathematics

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. 

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.

W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1987.

Supplementary notes might also be used.

Complex analysis (KomAn) or a similar first course in complex analysis.
Five hours of lectures and two hours of exercise sessions per week for 8 weeks.
  • Category
  • Hours
  • Exam
  • 1
  • Exercises
  • 16
  • Lectures
  • 40
  • Preparation
  • 149
  • Total
  • 206
Credit
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. This requirement does not apply to the re-exam.

Aid
All 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.
Re-exam

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

Criteria for exam assesment

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