# Mathematics/Applied mathematics

In the field of Mathematics/Applied mathematics, the following third cycle courses are available.

## Measure and Integration Theory, autumn 2023

Measure and Integration Theory is an essential part of education for any PhD student in mathematics. The course gives basis knowledge in the theory and prepares students for further studies in probability and functional analysis.

- Scope: 5 credits
- Starts: November 7, 2023
- Ends: January 9, 2024
- Course coordinator: Anatoliy Malyarenko

The course will start on Tuesday Nov 7 with 6 weekly 2-hours lectures that day and on the following Tuesdays. 15.15-17.00.

Examination date is January 9, 13.15-17.00.

### Enrollment

Inform the course responsible teacher, Anatoliy Malyarenko, by e-mail with the following data:

- name
- male/female
- personal number (or date of birth if the student is from abroad)
- e-mail address
- proof of being a PhD-student (if from abroad)

### Litterature

Jean-François Le Gall. Measure Theory, Probability, and Stochastic Processes, Springer, 2022, **DOI **https://doi.org/10.1007/978-3-031-14205-5 External link., ISBN 978-3-031-14204-8.

The access to the electronic version of the book is provided by the Mälardalen University library from within university computer network at https://link.springer.com/book/10.1007/978-3-031-14205-5 External link..

## Numerical Methods for PDEs, spring 2024

In the course, we will present and discuss basic aspects of such numerical techniques as the finite element method and the finite difference method using elliptic, parabolic, and hyperbolic partial differential equations. Our approach is to integrate naturally the numerical analysis with mathematical analysis of the differential equations. Some modern issues in numerics around the topic will be addressed to as well.

- Scope: 6 credits
- Course code: FOUK014
- Course coordinator: Sergey Korotov

### Lectures + examination date

- 02.04.2024 at 15:15-17.00, lecture 1
- 09.04.2024 at 15:15-17.00, lecture 2
- 16.04.2024 at 15:15-17.00, lecture 3
- 23.04.2024 at 15:15-17.00, lecture 4
- 30.04.2024 at 15:15-17.00, lecture 5
- 07.05.2024 at 15:15-17.00, lecture 6
- 14.05.2024 at 15:15-17.00, lecture 7
- 21.05.2024 at 15:15-17.00, lecture 8
- Seminar: 03.06.2023 at 13:15-17.00

### Enrollment

Inform the course responsible teacher, sergey.korotov@mdu.se, by e-mail with the following data:

- name
- male/female
- personal number (or date of birth if the student is from abroad)
- e-mail address
- proof of being a PhD-student (if from abroad)

### Litterature

Stig Larsson, Vidar Thomee. Partial Differential Equations with Numerical Methods. Springer, 2008.

Course syllabus Pdf, 124.6 kB.

## Applied Algebraic Structures, spring 2024

The course aims to provide research-relevant knowledge of modern algebraic and operator algebraic structures, ideas, concepts and methods important in science and engineering with emphasis on the most important non-commutative and non-associative algebraic structures, non-commutative analysis, operator algebra and representation theory, algebraic analysis and operator methods for solution and symmetry analysis of differential equations, difference equations and integral equations, non-commutative matrix equations and selected applications in science and engineering.

- Scope: 5 credits
- Course code: FOUK016
- Course coordinator: Sergei Silvestrov

### Lectures + examination date

- Start February 16 at 13.15
- March 1 at 13.15
- March 15 at 13.15
- April 5 at 13.15
- April 19 at 13.15
- May 3 at 13.15
- May 17 at 13.15 (examination)

Scheduling of the lessons may be adjusted in agreement with the participants.

### Enrollment

Inform the course responsible teacher, Sergei Silvestrov, by e-mail with the following data:

- name
- male/female
- personal number (or date of birth if the student is from abroad)
- e-mail address
- proof of being a PhD-student (if from abroad)

### Litterature

Relevant literature will be provided during the course.