### Instruction

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Real analysis I | 5 Cr | General Examination | 11.12.2019 - 11.12.2019 | ||

Real analysis I | 5 Cr | Lecture Course | 3.9.2019 - 16.10.2019 | ||

Real analysis I | 5 Cr | General Examination | 7.8.2019 - 7.8.2019 | ||

Real analysis I | 5 Cr | General Examination | 12.6.2019 - 12.6.2019 | ||

Real analysis I | 5 Cr | General Examination | 3.4.2019 - 3.4.2019 | ||

Real analysis I | 5 Cr | General Examination | 31.10.2018 - 31.10.2018 | ||

Real analysis I | 5 Cr | Lecture Course | 4.9.2018 - 18.10.2018 | ||

Real analysis I | 5 Cr | General Examination | 8.8.2018 - 8.8.2018 | ||

Real analysis I | 5 Cr | General Examination | 13.6.2018 - 13.6.2018 | ||

Real analysis I | 5 Cr | General Examination | 11.4.2018 - 11.4.2018 | ||

Real analysis I | 5 Cr | General Examination | 7.2.2018 - 7.2.2018 | ||

Real analysis I | 5 Cr | General Examination | 13.12.2017 - 13.12.2017 | ||

Real analysis I | 5 Cr | General Examination | 1.11.2017 - 1.11.2017 | ||

Real analysis I | 5 Cr | Lecture Course | 6.9.2017 - 19.10.2017 |

### Target group

Compulsory 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.

### Prerequisites

Measure and integral

### Learning outcomes

The course gives the basic knowlegde on real analysis that is of fundamental importance on analysis.

### Timing

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

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

### Contents

Basics on real analysis, like L^p spaces, convolution, covering theorems, Lebesgue's differentiation theorem, BV- and absolutely continuous functions.

### Activities and teaching methods in support of learning

Lectures and exercise classes.

### Study materials

Required: Reaalianalyysi I, luentomoniste.

Recommended: R. Gariepy, W. Ziemer: Modern real analysis. F. Jones: Lebesgue integration on Euclidean space.

### 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.