Schedule, syllabus and examination date

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Changes in the course due to coronavirus

Autumn 2020 the exams of most courses at the MN Faculty will be conducted as digital home exams or oral exams, using the normal grading scale. The semester page for your course will be updated with any changes in the form of examination.

See general guidelines for examination at the MN Faculty autumn 2020.

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;
  • will present, on a scientific level, a short thesis on a chosen topic of relevance, selected in collaboration with the lecturer.

Admission to the course

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.

MAT3500 – Topology/MAT4500 – Topology and MAT4510 – Geometric Structures.

Overlapping courses

  • 10 credits overlap with MAT4520 – Manifolds.
  • 10 credits overlap with MA152.
  • 10 credits overlap with MA252.
  • 10 credits overlap with MA352.
  • 10 credits overlap with MA352.

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 examination.

In addition, each PhD candidate 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.

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 pass/fail scale. 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) Nov. 24, 2020 6:20:15 PM

Facts about this course

Credits
10
Level
PhD
Teaching
Spring
Examination
Spring
Teaching language
English