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Umeå University
Real Analysis
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 se…
- Higher education
- Information unavailable
- 31 August 2026
- Information unavailable
- Information unavailable
- 50 %
Overview
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.
Admission scores
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.
The text is reproduced from the Susa source. Antagningsdata does not map GY11 and GY25 or assess personal eligibility.
Source, measure and data quality
- Source
- Skolverket Susa-navet
- Period
- 2026-08-31
- Measure
- Entry-requirement text reproduced from the published Susa data; no personal eligibility assessment is made.
- Population
- Education offering e.uoh.umu.5ma182.5800f.20262
- Last checked
- 2026-09-23T10:39:35.037285+00:00
- Limitation
- Antagningsdata does not map GY11 and GY25. General and specific conditions are not separated without structured source data.
Programme content
Study structure
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- Programme or course starts
- Programme or course ends
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Previous upper-secondary schools and programmes
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About the provider
Sources and data quality
Education facts for the selected offering come from Skolverket Susa-navet.
Retrieved . Published . Times are shown in Swedish local time.
Source identity and publication version
- Publication version
- 8e217193-f5fa-4778-b085-a4521fd03e8d
- Education identity in the source
- i.uoh.umu.5ma182.5800f.20262
- Offering identity in the source
- e.uoh.umu.5ma182.5800f.20262
- Education-form source code
- HS
- Education code in the source
- 5MA182
- Change time according to the source
- 2025-12-11T08:05:34
The provider, education and education offering are separate identities. Application information should be checked on the official website. Supplementary statistics have not been obtained from this source.