### Timetable

### Description

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.

Analysis I&II, Linear algebra I&II, Topology I

Elements of measure theory and complex analysis

Elements of linear functional analysis including Banach and Hilbert spaces and linear operators between them, three basic principles, and applications to differential equations.

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

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

Introduction to linear functional analysis including Banach and Hilbert spaces and linear operators between them; topology of normed spaces; examples of Banach spaces including sequence and function spaces; three basic principles; Fourier-series; Sobolev spaces; applications to differential equations.

Required:

Funktionaalianalyysin peruskurssi, luentomoniste.

Recommended:

Rynne, B., Youngson, M., Linear Functional Analysis, Springer Undergraduate Mathematics Series, London, 2000. (Introduction to the topic)

Friedman, A., Foundations of Modern Analysis, Dover 1982. Conway, J. A Course in Functional Analysis. Springer, 1990. (Introduction to the topic) Werner, D., Funktionalanalysis, Springer Lehrbuch 1990. (In German)

Lectures and exercise classes

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

Exam, other methods will be described later.