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Differential geometry

  • Number of credits 7.5 credits
  • Level Master’s level
  • Starting Spring Term 2025

About the course

Mathematical models are essential tools in modern science. In this course, we use tools from analysis, linear algebra, and topology to introduce a model that has not only been used in mathematics but also classically is used in physics such as e.g. in Hamiltonian mechanics and Einstein's theory of relativity. Other applications are found in chemistry, economics, engineering, computer graphics and computer vision, as well as recently in statistical learning and machine learning. Some of the key concepts covered in the course are manifolds, tangent spaces, vector fields, tensors, and differential forms. The course concludes with Stokes' theorem on manifolds.

Application and eligibility

Differential geometry, 7.5 credits

Det finns inga tidigare terminer för kursen Spring Term 2025 Det finns inga senare terminer för kursen


20 January 2025


24 March 2025

Study location




Type of studies

Daytime, 50%

Required Knowledge

The course requires 90 ETCS including a course in Real Analysis and a course in Topology or equivalent. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies

Entry requirements


Guaranteed place. Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.

Application code



The online application opens 16 September 2024 at 13:00 CET. Application deadline is 15 October 2024. How to apply

Application and tuition fees

As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.

Application fee

SEK 900

Tuition fee, first instalment

SEK 17,850

Total fee

SEK 17,850

Contact us

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Contactperson for the course is:
Study counselor Lars-Daniel Öhman