Course syllabus
Inverse Problems, 7.5 credits
Course code: | MA106A | Credits: | 7.5 |
---|---|---|---|
Main field of study: | Mathematics | Progression: | A1N |
Last revised: | 11/09/2020 | ||
Education cycle: | Second cycle | Approved by: | Head of school |
Established: | 02/12/2019 | Reading list approved: | 11/09/2020 |
Valid from: | Spring semester 2021 | Revision: | 1 |
Aims and objectives
General aims for second cycle education
Second-cycle courses and study programmes shall involve the acquisition of specialist knowledge, competence and skills in relation to first-cycle courses and study programmes, and in addition to the requirements for first-cycle courses and study programmes shall
- further develop the ability of students to integrate and make autonomous use of their knowledge
- develop the students' ability to deal with complex phenomena, issues and situations, and
- develop the students' potential for professional activities that demand considerable autonomy, or for research and development work.
(Higher Education Act, Chapter 1, Section 9)
Course objectives
Knowledge and understanding
After the course the student should have
- knowledge about the most common problem settings in the area of inverse problems,
- knowledge about some of the most used methods for solving inverse problem.
Competence and Skills
After completed studies the student shall be able to
- formulate simple linear inverse problems from applications
- be able to analytically identify that an inverse problem is ill posed and then apply a suitable regularization and solution method
Evaluation Ability and Approach
After completed studies the student shall be able to
- decide that a numerical solution to an inverse problem is reasonable w.r.t. stability, accuracy, efficiency, and applicability.
Main content of the course
- Definitions and examples of ill posed inverse problems,
- general regularization theory and optimization theory,
- tikhonov regularization,
- statistical methods for estimation,
- image analysis,
- parameter estimation,
- choice of regularization parameters, and
- regularization through projection.
Teaching methods
Tutorial via internet-based platforms.
Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.
Examination methods
Examination, 7.5 credits (Code: A001)
Assignments that are reported in writing.
For students with a documented disability, the university may approve applications for adapted or other forms of examinations.
For further information, see the university's local examination regulations (in Swedish).
Grades
According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).
In accordance with university regulations regarding grading systems for first and second-cycle courses (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades shall be used: Fail (U), Pass (G) or Pass with Distinction (VG). For courses that are included in an international Master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the grading scale of A-F shall be used. The vice-chancellor, or a person appointed by the vice-chancellor, may decide on exceptions from this provision for a specific course, if there are special grounds.
Grades used on course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).
Examination
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).
For further information, see the university's local examination regulations (in Swedish).
Specific entry requirements
Computational Mathematics, 9 credits, Optimization, 7.5 credits and Differential Equations, 7.5 credits.
For further information, see the university's admission regulations (in Swedish).
Transfer of credits for previous studies
Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.
For further information, see the university's local credit transfer regulations (in Swedish).
Other provisions
All or part of the course may be given in English.
Reading list and other teaching materials
Required reading
Vogel, Curtis R. (2002)
Computational Methods for Inverse Problems
SIAM, ISBN/ISSN: 0-89871-550-4
Reference literature
Kirsch, Andreas (2011)
An Introduction to the Mathematical Theory of Inverse Problems
Springer, ISBN/ISSN: 978-1-4614-2851-0