Real Analysis

Education facts

Code: 5MA182

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.

Entry requirements

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.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Real Analysis

  Umeå University

  Start date: 31 August 2026

  End date: 1 November 2026

  Pace of study: 50 %