After the course, students 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.

Fagligt indhold:

This is a course in mathematics covering linear algebra and basic probability theory. These topics are important in various branches of computer science, in particular in algorithms and machine learning.

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.

Læringsaktiviteter:

14 weeks of lectures and exercises. At the exercise sessions the students will solve and present solutions to mathematical problems. The mandatory assignments are of the form of mathematical problems, but can also involve some programming. The solutions must be submitted in written form.

Obligatoriske aktivititer:

There are 6 mandatory assignments, out of which 5 must be approved for the student to qualify for the exam.
The deadlines are evenly distributed over the semester (approximately one every 2 weeks), exact dates will be posted on learnit the first week of the semester.
If a mandatory assignment is not approved the first time, the student will be allowed to resubmit approximately one week after the first deadline.

Be aware: The student will receive the grade NA (not approved) at the ordinary exam, if the mandatory activities are not approved and the student will use an exam attempt.

Eksamensform og -beskrivelse:

A22: Skriftlig eksamen (stedprøve) med restriktioner., (7-scale, external exam)

The exam is a 4 hour written exam
1. Solutions submitted hand written on paper.
2. Access to aid in the form of books, own notes, e-books, also on laptops and tablets is permitted.
3. Use of internet including email and social media is not permitted.
4. Use of any other hardware or software such as MatLab or pocket calculators is not permitted
5. Any form of communication between students or with the outside world is not permitted.