# 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.

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