This course is discontinued

Course content

One complex variable: The inhomogeneous Cauchy-Riemann equation and Runge`s theorem. The theorems of Mittag-Leffler and Weierstrass. Riemann`s mapping theorem. Several complex variables: Holomorphic functions and mappings. Zero sets and the Weierstrass preparation theorem. Hartog`s extension, domains of holomorphy, and holomorphic convexity. The d-bar equation with compact support.

Learning outcome

Methods of complex function theory.

Admission

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Prerequisites

Formal prerequisite knowledge

None.

Recommended previous knowledge

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

Overlapping courses

10 credits with MAT365.

10 credits with MAT4310.

*The information about overlaps is not complete. Contact the department for more information if necessary.

Teaching

4 hours of lectures/exercises per week.

Examination

Oral exam.

In addition, each phd student is expected to give a one hour oral presentation on a topic of relevance (chosen in cooperation with the lecturer). The presentation has to be approved by the lecturer for the student to be admitted to the final exam.

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 pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

This subject offers new examination in the beginning of the subsequent term for candidates who withdraw during an ordinary examination or fail an ordinary examination. Deferred examinations for students who due to illness or other valid reason of absence were unable to sit for their final exams will be arranged at the same time. (These valid reasons has to be documented within given deadlines.)

Information about deferred and new examination (also called repeat examination) is found here

More information about examination at the Faculty of Mathematics and Natural Sciences can be found here

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

PhD

Teaching

Autumn 2009

Autumn 2008

Autumn 2007

This version of the course was held for the last time Autumn 2009. MAT9800 - Complex Analysis will still be held.

Examination

Autumn 2009

Autumn 2008

Autumn 2007

Teaching language

Norwegian (English on request)

The course may also be given in English if PhD-students connected to the Department of Mathematics request it within given deadlines.