*Official course description, subject to change:*

### Linear Algebra and Probability

##### Course info

##### Programme

##### Staff

##### Course semester

##### Exam

##### Abstract

This is a course in mathematics covering linear algebra and basic probability theory. This course is the first course of the Algorithms and Machine Learning specialisations.##### Description

These topics covered by this course are important in various branches of computer science, in particular in algorithms and machine learning.

Successful students will acquire skills in Linear Algebra and Probability Theory.

The topics covered in the linear algebra part of the course include systems of linear equations, matrices, determinants, vector spaces, bases, dimension, and eigenvectors. The topics covered in the probability theory part include conditional probability, discrete and continuous random variables, as well as the Bernoulli and Poisson processes. A number of applications of the material will be covered in the course, including least squares analysis and Google’s PageRank algorithm.

##### Intended learning outcomes

After the course, the student should be able to:

- Solve systems of linear equations
- Define the basic concepts of linear algebra and probability, e.g., eigenvalues for a matrix or variance of a discrete random variable
- Compute the essential constructions of linear algebra, such as the inverse of a given matrix or the eigenvectors of a given matrix. Compute probabilities, expected values, variances and other concepts from probability theory.
- Apply the tools of linear algebra and probability to solve small mathematical problems.
- Model simple probabilistic problems using the distributions covered in the course.

##### Ordinary exam

**Exam type:**

A: Written exam on premises, external (7-trinsskala)

**Exam variation:**

A22: Written exam on premises with restrictions.

**Exam description:**

The exam is a 4 hour written exam

- Solutions submitted hand written on paper.
- Access to aid in the form of books, own notes, e-books, also on laptops and tablets is permitted.
- Use of internet including email and social media is not permitted.
- Use of any other hardware or software such as MatLab or pocket calculators is not permitted
- Any form of communication between students or with the outside world is not permitted.