Markus Schweighofer - Aktuelle Lehrveranstaltungen

WS 2025/2026 Linear Algebra in Data Science
9 ECTS credits, 4V+2Ü+P (P stands for programming projects in Julia)
Materials
Target audience: Students of all disciplines
- who like to do computer programming,
- who either know already or are not afraid to learn a tiny bit of linear algebra and machine learning
- who want to experience some basic mathematical techniques for extracting information from data.
The lecture is particularly well suited for the Orientierungsstudium Go.MINt and for the Master's program in Social and Economic Data Science.
Assignments:
- probably three small computer projects to be coded in the programming language Julia and to be presented in the exercise class
Course materials: Selected topics from the following sources:
- Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares by Boyd and Vandenberghe, 2018 (freely available as electronic resource from here)
- Data-Driven Science and Engineering by Brunton and Kutz, 2019 (available as electronic resource from the university library)
- Foundations of Data Science by Blum, Hopcroft and Kannan, 2019 (available as electronic resource from the university library freely or from here)
The topics can be adapted to the participants' interests. Any suggestions are very welcome! A priori possible topics could be a set having a non-empty intersection with the following:
- vectors, norm, distance, angles and matrices
- clustering
- matrix multiplication
- singular value decomposition
- Fourier and wavelet transforms
- sparsity and compressive sensing
- tensor decompositions
- deep neural networks
- learning from graph eigenvalues: sparse cuts in graphs, page ranking
Applications such as image compression and video decomposition could serve as running examples. Here are for example three videos that have been created with a few lines of Julia code by a standard singular value decomposition (which is a technique that applies in a similar way to most kinds of data). The videos show a "rough + details" decomposition where the rough (data-compressed) part is shown in the upper video and the details are shown in the lower video:
Assessment type:
- Successful and active participation in the exercise group
- Oral online presentation of an individually assigned computer project.
Prerequisites:
- Acquaintance with computer programming
- Willingness to learn very basic applied linear algebra