Schedule, syllabus and examination date

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Course content

The subject will give a thoroughly introduction to differetiable manifolds. The course will contain topics like the tangent - and the cotangent bundle, vector fields and flows (ordinary differential equations), differential forms, integration. Topological applications will give examples of how analysis on a manifold depends of the global structure.

Learning outcome

The course will give a common background for further studies in topology and geometry and also for parts of real and complex analysis. The course will give proper background for geometry which is important in modern mathematics and theoretical elementary particle physics.


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.


Formal prerequisite knowledge


Recommended previous knowledge

MAT3500 - Topology/MAT4500 - Topology and MAT4510 - Geometric structures.

Overlapping courses

10 credits overlap with MA152

10 credits with MA252/352.

10 credits with MAT4520 - Manifolds.

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


4 hours of lectures/exercises per week.


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

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.


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






Every spring


Every spring

Teaching language


The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.