MAT4800 – Complex Analysis
Schedule, syllabus and examination date
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.
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.
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Recommended previous knowledge
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.
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.
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.