Probability Theory and Linear Algebra
2020/2021
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
- Basic probability theory
- Combinatorics
- Probability theory for discrete outcome spaces
- Types of distributions (Bernoulli, Binomial, Uniform,…)
- Basic linear algebra
- Vector room in Rn
- linear transformations and their relationship to matrices
- simple matrix operations
- invertible matrix and invertible linear mapping
- orthogonal projections
- Least squares linear regression
- Linear programming
- Discretionary Markov chains
- the probability of achievable conditions
- stationary distributions
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 exam | Probability Theory and Linear Algebra |
| Type of exam | Written or oral exam |
| ECTS | 5 |
| Assessment | 7-point grading scale |
| Type of grading | Internal examination |
| Criteria of assessment | The criteria of assessment are stated in the Examination Policies and Procedures |
Facts about the module
| Danish title | Sandsynlighedsteori og lineær algebra |
| Module code | DSNDATFB222 |
| Module type | Course |
| Duration | 1 semester |
| Semester | Spring
|
| ECTS | 5 |
| Language of instruction | Danish |
| Empty-place Scheme | Yes |
| Location of the lecture | Campus Aalborg |
| Responsible for the module |
Organisation
| Study Board | Study Board of Computer Science |
| Department | Department of Computer Science |
| Faculty | Technical Faculty of IT and Design |
Litterature
Contact: Study Board for Computer Science via cs-sn@cs.aau.dk or 9940 8854
