DM561: Linear algebra with applications
New courser E2018 (Autumn 2018)
The course is co-read with:The first part of the course is co-read with MM505.
Students taking the course are expected to: The content of DM550 Introduction to Programming should be known.
The course cannot be chosen by students, who have passed MM505 or the first part of MM538.
The main aim of the course is to introduce the student to the basic concepts and methods of linear algebra, with emphasis on matrix manipulations. The material covered is important in many aspects of computer science and has widespread applications throughout the sciences, and another aim of the course is to teach the students how to apply the methods of the course in such practical settings via programming.
This course provides the students with the necessary prerequisites for several courses, in particular DM5XX (Data Mining and Machine Learning), that appears later in the degree.
In relation to the competence profile of the
degree it is the explicit focus of the course to:
- Give skills in
describing, formulating and disseminating problems and results to either other
professional or non-specialists or collaborative partners and users
- Give skills to apply
thinking and terminology from the subject’s basic disciplines.
- Give skills to present
mathematical and computational thinking both in written and oral form.
- Give skills to solve
systems of linear equations, calculate determinants, find inverses of matrices,
find coordinates of vectors, find matrices of linear transformations.
- Give knowledge and
understanding of vector spaces and linear transformations.
- Give the competence to
handle complex and development-oriented situations in study and work contexts
- Give the competence to
identify one's own needs for learning and structure one's own learning in
different learning environments
Expected learning outcome
- Reproduce definitions and results covered in the course.
- Be able to use these results to analyse concrete examples.
- Formulate and present definitions and calculations in a mathematically rigorous way.
- Make programs which uses the methods from the course.
- Systems of linear equations
- Matrix operations, inverses, determinants
- Vector spaces, basis, coordinates, linear independence
- Linear transformations, eigenvalue problems, diagonalisation
- Linear algebra and programming
- Applications of linear algebra in computer science
Applications of linear algebra, such as:
- image processing
- least squares
- graph algorithms
- methods for biology and chemistry
- and others.
Exam element a)
Indicative number of lessons
- Reading from text books
- Solving homeworks
- Applying acquired knowledge to practical projects