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 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 Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish 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
15 April 2020.
Please note: This second application round is intended only for EU/EEA/Swiss citizens.