Probability Theory and Linear Algebra

2021/2022

Content, progress and pedagogy of the module

Disclaimer.
This is an English translation of the module. In case of discrepancy between the translation and the Danish version, the Danish version of the module is valid.

In order to motivate the students, realistic examples from computer science are used to support the topics. The course includes the use of a programming environment so that the methods can be used.

Learning objectives

Knowledge

  • Grundlæggende sandsynlighedsteori
    • Kombinatorik
    • Sandsynlighedsteori for diskrete udfaldsrum
    • Typer af fordelinger (Bernoulli, Binomial, Uniform,…)
  • Grundlæggende lineær algebra
    • Vektorrum i Rn
    • lineære transformationer og deres sammenhæng med matricer
    • simple matrixoperationer
    • invertibel matrix og invertibel lineær afbildning
    • ortogonale projektioner
  • Mindste kvadraters lineær regression
  • Lineær programmering
  • Diskrettids Markov kæder
    • sandsynligheden for opnåelige tilstande
    • stationære fordelinger

Skills

  • be able to apply the least squares method to linear regression problems
  • represent systems of linear equations by matrix equations and use Gaussian elimination to solve them
  • determine matrix for a given linear plot, and vice versa
  • solve simple matrix equations
  • calculate inverse of small matrices
  • calculate the orthogonal projection of a vector on a subspace of Rn (Gram-Schmidt algorithm)

Competences

  • develop and strengthen knowledge of, understanding of, and application of mathematical theories and methods within other subject areas based on given assumptions
  • be able to reason and argue with mathematical concepts within probability theory and linear algebra

Type of instruction

The teaching is organized in accordance with the general teaching methods for the education, cf. section 17.

Extent and expected workload

The student is expected to spend 27.5 hours per ECTS, which for this activity means 137.5 hours.

Exam

Exams

Name of examProbability Theory and Linear Algebra
Type of exam
Written or oral exam
ECTS5
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Additional information

Contact: Study Board for Computer Science via cs-sn@cs.aau.dk or 9940 8854

Facts about the module

Danish titleSandsynlighedsteori og lineær algebra
Module codeDSNSWCB222
Module typeCourse
Duration1 semester
SemesterSpring
ECTS5
Language of instructionDanish
Empty-place SchemeYes
Location of the lectureCampus Copenhagen
Responsible for the module

Organisation

Study BoardStudy Board of Computer Science
DepartmentDepartment of Computer Science
FacultyTechnical Faculty of IT and Design