MAT4810 – Introduction to Several Complex Variables
Course description
Schedule, syllabus and examination date
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 to the course
Students admitted at UiO must?apply for courses?in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may?apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about?admission requirements and procedures for international applicants.
Recommended previous knowledge
Overlapping courses
- 10 credits overlap with MAT9810 – Introduction to Several Complex Variables.
- 4 credits overlap with MAT4310.
- 4 credits overlap with MAT9310 – Complex analysis (discontinued).
- 4 credits overlap with MA365.
- 4 credits overlap with MAT4320 – Several complex variables I (discontinued).
- 4 credits overlap with MAT9320.
- 4 credits overlap with MAT365.
Teaching
4 hours of lectures/exercises per week.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
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
Final oral exam which counts 100 % towards the final grade.
This course has 1 mandatory assignment that must be approved before you can sit the final exam.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT9810 – Introduction to Several Complex Variables
Examination support material
No examination support material is allowed.
Language of examination
Courses 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.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.