Mathematics: Complex Analysis 2
This course takes you further into the world of analytic functions, focusing on advanced concepts and methods central to modern mathematical research. It provides a rigorous treatment of analytic functions as well as applications involving conformal mappings and entire functions.
Start
Spring 2027
Level
Master's
Language
English
Place of study
Lund
Course code
MATM32
Building on fundamental complex analysis, the course introduces key theories and techniques for a deeper understanding of the subject. You will learn about specialized concepts like conformal mappings, and compactness theorems for analytic functions. You will study the interplay of analytic, harmonic, and subharmonic functions, and discover the connection between Fourier transforms and entire functions.
The course treats
- Convergence of sequences of analytic functions. Locally uniform convergence, normal families, Montel’s theorem.
- In-depth study of conformal mappings. Riemann sphere, stereographic projection, Möbius transformations, disk automorphisms, Schwarz lemma, Riemann mapping theorem.
- Entire functions. Infinite products, factorization, order, genus. Fourier transforms and Paley-Wiener spaces.
- Harmonic and subharmonic functions. Maximum principle, Harnack’s principle, and application to Dirichlet’s problem in suitable domains.
The course is an alternative-compulsory course within the Master’s programme in Mathematics and Numerical Analysis at Lund University. It may be suitable for interested students at Bachelor’s level. The course is also available as a stand-alone course.
You will learn through a mix of lectures and seminars. The seminars focus on selected exercises and require active participation and preparation.
The assessment includes a written exam and an oral exam at the end of the course. The oral exam is only given for students who pass the written exam. Re-examinations are offered shortly after the regular ones.
This course prepares you for advanced studies in mathematics, science, and technology. You will gain skills that are valuable in research, and analytical roles in both academia and industry. You will also develop skills in logical reasoning, problem-solving, and mathematical communication – valuable in both academic and professional settings.
Entry requirements
For admission to the course, at least 90 credits are required, including basic knowledge in complex analysis corresponding to, for example, MATC21 Analytic Functions 1, 7.5 credits.
Selection criteria
Seats are allocated according to: ECTS (HPAV): 100 %.
Tuition fees for non-EU/EEA citizens
Citizens of countries outside:
- The European Union (EU)
- The European Economic Area (EEA) and
- Switzerland
are required to pay tuition fees. You pay an instalment of the tuition fee in advance of each
semester.
Tuition fees, payments and exemptions
Full programme/course tuition fee: SEK 23,125
First payment: SEK 23,125
Note that you may also need to pay an application fee, or provide proof of exemption.
No tuition fees for citizens of the EU, EEA and Switzerland
There are no tuition fees for citizens of the European Union (EU), the European Economic Area (EEA) and Switzerland.
A shared second home for mathematics
Matematikcentrum gathers students and researchers in mathematics, mathematical statistics, and numerical analysis and computational science. Along Sölvegatan, close to green spaces and the wider university area, you find a shared environment for everyone who uses mathematics as a common language. Research here has led to innovations and companies in areas such as optimisation, image analysis and software, with applications ranging from logistics to video analysis and mobile technology.
