Linear Algebra and Probability (Spring 2025)

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

The topics covered by this course 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, Bayes theorem, discrete and continuous random variables, as well as the limit theorems. The course focuses on providing a basic understanding of the mathematical concepts covered, but will also include a few illustrative examples of their use.

Formal prerequisites

The course assumes that the students have taken the course Foundation of Computing: Discrete Mathematics from the BSc in Software Development or similar.
Knowledge of single variable calculus, in particular differentiation and the integral is required.

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-point scale)
Exam variation:
A33: Written exam on premises on paper with restrictions