Markus Schweighofer - Aktuelle Lehrveranstaltungen
SS 2025 Proseminar/Seminar für Lehramt Diskrete Optimierung
2S
Unverbindliche Anmeldung frühstmöglich, jedoch allerspätestens bis zum Beginn der Vorlesungszeit des Sommersemesters, per Email an Markus Schweighofer. Die Themen entsprechen grob den neun Kapiteln aus dem Skript
Discrete Optimization von
Thomas Rothvoss und werden in der Reihenfolge der Anmeldung nach Absprache (auch per "zoom") individuell vergeben.
Derzeit sind die meisten Themen noch verfügbar. Als Grundlage reichen die Vorlesungen Analysis I und Lineare Algebra I aus.
Zielgruppe sind vorwiegend Studenten im ersten und zweiten Studienjahr.
SS 2025 Vectors, Matrices, Tensors and Networks for Data Analysis with Julia with David Sawall
4.5 ECTS credits, 2V+1Ü+P (P stands for programming projects in Julia) 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 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:
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
Credits: This course is part of the Advanced Data and Information Literacy Track (ADILT). Whether and how it can be credited depends on the regulations of this track and probably on the field of study. It can also be credited independently of this track in the non-mathematical parts (between 18 and 36 credits) of the bachelor program in mathematics. Description: This course aims at students of all disciplines that have already experience with computer
programming and want to learn the basic mathematical techniques for learning information from data. Students learn to understand sparse vectors, matrix factorizations and tensor decompositions as carriers of information. In the lecture, the theoretical foundations are introduced and explained by means of generally understandable examples. For the aim of accessibility, we abstain from giving complicated mathematical proofs. Instead, we experiment in the exercise class with data stemming from varying areas in order to test the practical power of the presented tenets. In this way, the students develop a deep intuition for the theorems they have learned. The goal is to teach mainly methods that can be applied in manifold contexts are not just designed for a particular problem. This should motivate the students to apply and to deepen the gained knowledge beyond of this lecture within their own projects. Course language: This course and the corresponding exercise course will be offered in English language. If all participants prefer German
we could also switch to German. Course format: Weekly lecture in room D436 on Fridays from 10:00 to 11:30. This weekly slot can be changed on request.
Biweekly programming course with student presentations (date and room will be fixed in accordance with the participants).
SS 2025 Real Algebraic Geometry II with David Sawall
9 credits
flipped classroom
weekly meeting in person with the instructor (planned to be on Fridays from 11:45 to 13:15 in room D404)
weekly exercise session with the exercise tutor (date, time and room to be fixed) Target audience: Master of Science in Mathematics, first year Assignments: weekly exercise sheets Course materials:
successful and independent completion of the exercises
active and frequent participation in the exercise group
passing an oral exam
Prerequisites: This course is the second in a linear
sequence of lectures building one upon the other
that I plan to lecture in four consecutive semesters: Real Algebraic Geometry I, Real Algebraic Geometry II, Geometry of Linear
Matrix Inequalities.
Career changers and incoming students should, with some effort, be able
to jump in due to the available lecture notes and screencasts.
We will study more closely the real spectrum, learn about the geometry of
semialgebraic sets, learn about convex sets in a general framework and apply all these
to study sum-of-squares certificates of nonnegative polynomial especially in the
difficult case where zeros are present. I plan to hold the lecture online in an
asynchronous way similar to last semester. External students are of course welcome
to follow the screencasts and on request might get access to our slack group,
to the questions and answer sessions and
to the exercise course. Creditability: 9 ECTS credits eligible for:
Master of Science in Mathematics, Hauptmodul oder Wahlmodul
Course language: The teaching material is in English, the weekly meeting with the instructor and the exercise tutor will be offered in English or, if agreed by all participants, in German. Subscription: Students interested in the course should immediately subscribe on the
ZEUS platform. Course format: Flipped classroom. Weekly exercise sessions.
