Real Analysis 7.5 credits

About the course

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.

Show syllabus

Apply

Autumn 2025
- Real Analysis
  
  Autumn 2025 / Umeå / English / On site
  
  Show more Show less
  
  Starts
  1 September 2025
  
  Ends
  2 November 2025
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  50%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-58026
  
  Eligibility 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
  Guaranteed place
  
  Application
  Application deadline was 15 April 2025. The application period is closed.
  
  Application and tuition fees
  As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.
  
  Application fee: SEK 900
  
  Tuition fee, first instalment: SEK 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

Apply online via universityadmissions.se
You apply to our programmes and courses via universityadmissions.se – the official website for higher education applications in Sweden. There, you can track your application, check that your documents have been registered, and log in to find our your admission results.
 
Late applications
Admissions to most programmes and courses typically close after the final application deadline. However, some programmes and courses may still accept late applications if seats are available. These are marked “Open for late application” on universityadmissions.se. Please note that late applications are not guaranteed to be reviewed.

More about application and admission

Explore your future at Umeå University

Join a vibrant academic community where high-quality education meets groundbreaking research in science, technology, humanities, and the arts. At Umeå University, you will learn from passionate, expert teachers and benefit from a close connection between research, education, collaboration, and innovation.

World's most satisfied international students

#1 globally in the main categories of Living, Support, and Overall Satisfaction.
A university with health at its core

Umeå University is certified as a Healthy Campus, with many initiatives that promote health and well-being.

Questions about the course?

Subject

Describe your enquiry or ask a question

First name

Last name

Email address

Please be aware that the University is a public authority and that what you write here can be included in an official document. Therefore, be careful if you are writing about sensitive or personal matters in this contact form. If you have such an enquiry, please call us instead. All data will be treated in accordance with the General Data Protection Regulation.