MAT4520 – Manifolds
Schedule, syllabus and examination date
The course gives an introduction to smooth manifolds. It covers tangent bundles, vector fields and integral curves (ordinary differential equations), Lie groups, differential forms, and integration. This theory is fundamental to both modern geometry and theoretical physics.
After completing the course you:
- understand well the concepts smooth manifold, smoth map, and tangent space;
- know how the inverse function theorem can be used to describe the local structure of immersions and submersions, and you know Sard's theorem;
- can work with submanifolds and know Whitney's embedding theorem;
- know fundamental results about vector fields, Lie brackets, and integral curves, and you know what it means for the flows of two vector fields to commute;
- are familiar with the Lie algebra and exponential map of a Lie group;
- can do calculations with differential forms and characterise the exterior derivative, and you know Stokes' theorem and understand how this generalises classical theorems in calculus.
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.
Recommended previous knowledge
10 credits overlap with MAT9520 – Manifolds
*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.
Final written 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 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.