DM561: Linear algebra with applications

Discontinued - offered last time Autumn 2022

The course is co-read with:The first part of the course is co-read with MM505.

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

• 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
• pagerank
• least squares
• graph algorithms 
• methods for biology and chemistry
• and others.
  

• Reading from text books
• Solving homeworks
• Applying acquired knowledge to practical projects