The course provides advanced knowledge of concepts and theorems in advanced analysis. The concept of topology is introduced in metric spaces. The concepts of compactness and continuity are essential. Thereafter real-valued functions defined on metric spaces are studied, with a focus on continuity and function sequences. Central theorems are Heine-Borel covering theorem, Urysohn's lemma and Weierstrass' approximation theorem. The concept of differentiability of vector-valued functions is introduced and the inverse and implicit function theorems are proved.
The information below is only for exchange students
Starts
2 September 2024
Ends
31 October 2024
Study location
Umeå
Language
English
Type of studies
Daytime,
50%
Required Knowledge
The course requires 60 ECTS in mathematics or at least two years university studies. In both cases requires 15 ECTS in Calculus and 7,5 ECTS in Linear Algebra or equivalent. Proficiency in English equivalent to the level required for basic eligibility for higher studies. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
Selection
Students applying for courses within a double degree exchange agreement, within the departments own agreements will be given first priority. Then will - in turn - candidates within the departments own agreements, faculty agreements, central exchange agreements and other departmental agreements be selected.
Application code
UMU-A5801
Application
This application round is only intended for nominated exchange students. Information about deadlines can be found in the e-mail instruction that nominated students receive.
The application period is closed.
