Schedule, syllabus and examination date

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Course content

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.

Learning outcome

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.

Admission to the course

Students at UiO register for courses and exams in Studentweb.

MAT3500 – Topology/MAT4500 – Topology. It may also be useful to have taken MAT4510 – Geometric structures.

Overlapping courses

  • 10 credits overlap with MAT9520 – Manifolds.
  • 10 credits overlap with MA252.
  • 10 credits overlap with MA352.
  • 10 credits overlap with MA352.
  • 10 credits overlap with MA152.

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

1 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.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Dec. 11, 2019 12:19:08 PM

Facts about this course

Credits
10
Level
Master
Teaching
Spring
Examination
Spring
Teaching language
English