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.
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
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 deadline was
19 April 2022.
Please note: This second application round is intended only for EU/EEA/Swiss citizens.