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Mathematics of Machine Learning (and AI)


Krause R.

Course director

Giordano L.



The theoretical analysis of deep neural networks has made significant progress in the last years. The mathematical language and concepts which provide the basis for this progress can be found in the area of functional analysis. This course provides a thorough introduction to functional analysis and relates these abstract concepts to dep neural networks. Topics are vector spaces, metric spaces, scalar products, Banach- and Hilbert spaces, Sobolev spaces and Hilbert spaces, approximation theory for neural networks, basic theory of bounded linear operators, and reproducing kernel Hilbert spaces.


The students know and understand the basics of functional analysis and can apply these competences in the area of machine learning and artifical intelligence. They understand the theoretical properties of machine learning approaches. They are able to connect practical experience on  the design an behavior of neural networks to their theoretical properties.

Teaching mode

In presence

Learning methods

The course  is based on a mixture of   asynchronous online material (videos and script) for  self study and in person lectures. Guided problem solving classes will help the students to deepen their understanding and to improve their self study abilities. The students will work on regular assignments for practicing. Each student will also give a presentation on a selected topic of the course.

Examination information

At the end of the course, students will do a written exam.