Schedule, syllabus and examination date

Choose semester

Course content

Applications of the residue theorem, Montel's theorem, Cauchy-estimates, solutions to d-bar, Runge's theorem, Cousin I and II, Ahlfors-Schwarz-Pick Lemma, Riemann Mapping Theorem, Möbius transformations, hyperbolicity, metrics of negative curvature, Picard's Theorem, Schottky's Theorem, periodic functions in the plane, compact Riemann surfaces, some sheaf-theory and cohomology, divisors, meromorphic functions and Riemann-Roch.

Learning outcome

The course gives an introduction to classical results in function theory of the complex plane, and an analytic approach to some basic notions in complex/algebraic geometry via compact Riemann surfaces.


Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.


Recommended previous knowledge

MAT2400 – Real Analysis and MAT2410 – Introduction to Complex Analysis.

Overlapping courses

10 credits overlap with MAT9800 – Complex Analysis

* The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department


4 hours of lectures/exercises per week.

Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.


mandatory assignment.

Final oral examination.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who have a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Autumn 2020

Taught according to demand and resources. Contact if you are interested in this course.


Autumn 2020

The same semester as taught.

Teaching language


The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.