Name Cr Method of study Time Location Organiser
Real analysis II 10 Cr General Examination 11.12.2019 - 11.12.2019
Real analysis II 10 Cr Lecture Course 2.9.2019 - 12.12.2019
Real analysis II 5 Cr General Examination 8.8.2018 - 8.8.2018
Real analysis II 5 Cr General Examination 13.6.2018 - 13.6.2018
Real analysis II 5 Cr General Examination 23.5.2018 - 23.5.2018
Real analysis II 10 Cr Lecture Course 15.1.2018 - 30.4.2018

Target group

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

Belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.


Measure and integral, Real analysis I

Learning outcomes

Advanced knowledge on real analysis, incl. fractals.


Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying


Hausdorff measure and dimension, self similar fractals, differentiation of Radon measures, Radon-Nikodym derivative, signed measures.

Activities and teaching methods in support of learning

Lectures and exercise classes.

Study materials

Required: Moderni reaalianalyysi, luentomoniste.

Recommended: Evans-Gariepy: Measure theory and fine properties of functions. K. Falconer: The Geometry of Fractal Sets.

Assessment practices and criteria

Exam and excercises, Course will be graded with grades 1-5.

Recommended optional studies

Barchelor studies

Completion methods

Exam, other methods will be described later