MAT-INF2360 – Applications of Linear Algebra
Schedule, syllabus and examination date
The course has a computational approach and gives an introduction to the following:
a) Function spaces and Fourier series, discrete Fourier analysis and change of basis, fast Fourier transform and discrete Cosine transform with effective implementations, digital filters and diagonalisation, eigenvalues and frequency response, sampling, applications to sound and images.
b) Multiresolution analysis, Haar wavelets, linear wavelets, Toeplitz matrices, construction of wavelets with desired properties, tensor products of vector spaces, applications to sound and images.
c) Nonlinear optimization, convexity, numerical solution of nonlinear systems of equations, nonlinear optimization with and without constraints, characterization of extrema, numerical methods, applications in statistics and for calibration of instruments.
The above concepts are learnt through derivation of properties and algorithms for the different mathematical topics, and programming of the algorithms. In the compulsory problems these algorithms are applied to concrete problems like analysis and compression of sound and images, optimization of probabilities, and estimation of parameters in a nonlinear family of functions.
The course gives an introduction to some important applications of linear algebra: Fourier analysis, wavelets and non-linear optimization, all with a computational approach. Fourier analysis and wavelets are useful tools for analyzing frequencies in sound and images, and such applications will be central. Non-linear optimization is a fundamental tool in many applications such as statistics and calibration.
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Formal prerequisite knowledge
In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:
Mathematics R1 (or Mathematics S1 and S2) + R2
And in addition one of these:
- Physics (1+2)
- Chemistry (1+2)
- Biology (1+2)
- Information technology (1+2)
- Geosciences (1+2)
- Technology and theories of research (1+2)
The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).
Recommended previous knowledge
*The information about overlaps is not complete. Contact the Department for more information if necessary.
4 hours of lectures and 2 hours of exercises per week.
Three compulsory assignments need to be passed within given deadlines to be allowed to take the final exam. Final mark based on written examination at the end of the semester.
Examination support material
Permitted aids at final exam: Approved calculator.
Information about approved calculators (Norwegian only)
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
This course offers both postponed and resit of examination. Read more:
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.