##### 5720 - Mathematical Foundations for Artificial Intelligence

Course information

- Title
- Mathematical Foundations for Artificial Intelligence
- Course number
- 5720.24
- Academic year
- 2024-2025
- ECTS
- 7.50
- Level
- Master
- Faculties
- Educations
- Prerequisites
- Basic knowledge of differential and integral calculus, probability and geometric vectors in two and three dimensions.
- Language of instruction
- The course will be taught in Faroese and English.
- Registration
- .
- Beginning date
- Tuesday, August 27, 2024
- End date
- Thursday, October 10, 2024

Academic content

- Purpose
- This course aims to provide the student with the necessary tools to interpret results produced during data analysis. Therefore, the course covers key concepts and methods from linear algebra, differential calculus and probability theory.
- Learning outcomes
- A student, that successfully has completed this course, should be able to: • Use matrix calculations and Gaussian elimination. • Analyze and explain solution sets of systems of equations. • Analyze and explain the linear structure of solution sets in vector spaces. • Apply linear transformations between general vector spaces. • Calculate analytical properties of vectors. • Examine properties of matrices and perform matrix decompositions. • Explain probabilities in discrete and continuous variables. • Calculate with probability functions and density functions. • Optimization methods, including gradient descent.
- Content
- o Systems of equations and solutions. o Vectors and matrices. o Vector spaces, norms and inner products. o Linear transformations and their properties. o The spectral theorem and matrix decomposition. o Calculus: limits, continuity, differential calculus in several variables, gradients and optimization. o General and advanced probability theory for machine learning: probability spaces and probabilities, sum and product rule, Bayes’ Theorem and the Gaussian distribution.
- Learning and teaching approaches
- Lectures and problem-solving (80 hours). Self-study and three written assignments (126 hours).

Assessment

- Assessment method
- A 4-hour written exam. Electronic aids are not allowed. The assignments must be passed in order to attend the exam. The reexam has the same format.
- Examination (internal/external)
- External
- Grading scale
- 7-scale
- Exam date/dates
- Written assignment.
- Deadline for withdrawal from exam
- Friday, September 27, 2024

Academic responsibility and teachers

- Academic responsibility
- Mortan Janusarson Thomsen
- Teachers
- Mortan Janusarson Thomsen