MAT4810 – Introduction to Several Complex Variables

Schedule, syllabus and examination date

Choose semester

Course content

Holomorphic functions and mappings. Hartog's extension phenomenon, domains of holomorphy and holomorphic convexity. Plurisubharmonic functions. The d-bar equation and the Levi problem. Oka's approximation theorem, Runge pairs and the Cousin problems. Polynomial convexity and applications.

Learning outcome

The course gives an introduction to the most central aspects and methods in the theory of holomorphic functions of several complex variables, and applications of these to approximation and mapping problems.

Admission

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.

Prerequisites

Recommended previous knowledge

MAT4800 – Complex Analysis/MAT9800 – Complex Analysis.

Overlapping courses

10 credits overlap with MAT9810 – Introduction to Several Complex Variables

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

Teaching

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.

Examination

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 can document 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.

Evaluation

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

Credits

10

Level

Master

Teaching

Spring 2020

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.

Examination

Spring 2020

The same semester as taught

Teaching language

English

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