Over the course of two semesters, the participants of the modeling project work in teams on a project in which they are supposed to use the mathematical knowledge they have already acquired in applications outside of mathematics. The project partners can be industrial companies or research institutes.

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2025 will be decided upon with the participants

The lecture addresses Interactive Visualization of Huge Scientific Datasets. More information can also be found on the Homepage: https://www.uni-bremen.de/ag-high-performance-visualization

Die Vorlesung beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Anwendungsbeispiele werden anhand der Open-Source-Software ParaView erläutert.
Homepage zur Veranstaltung: https://www.uni-bremen.de/ag-high-performance-visualization

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2025 will be decided upon with the participants

Profil: SQ, KIKR.
Schwerpunkt: IMA-SQ, IMVT-AI, IMVT-VMC
weitere Studiengänge: M-M-Alg-Num, M-T
https://lvb.informatik.uni-bremen.de/imat/03-imat-apx.pdf

A large number of problems arising in practical scenarios like communication, transportation, planning, logistics etc. can be modeled as combinatorial optimization problems. In most cases, these problems are computationally intractable and one often resorts to heuristics that provide sufficiently good solutions in reasonable amount of runtime. However, in most cases, such heuristics do not provide a worst case guarantee on the performance in comparison to the optimum solution. In this course, we shall study algorithms for combinatorial optimization problems which can provide strong mathematical guarantees on performance. The course aims at developing a toolkit for solving such problems. The lectures will consist of designing polynomial-time algorithms and proving rigorous bounds on their worst case performances.
We review many classical results in the field of approximation algorithms, highlighting different techniques commonly used for the design of such algorithms. Among others, we will treat the following topics:
• Greedy algorithms and Local Search
• Rounding Data and Dynamic Programming
• Deterministic Rounding of Linear Programs (LPs)
• Random Sampling and Randomized Rounding of LPs
• Primal-Dual Methods
• Hardness of Approximation
• Problem Solving under Uncertainty

Many every-day processes can seen as a game between autonomous interacting players, where each player acts stategically in order to pursue her own objectives. This lecture is an introduction to game-theoretic concepts and techniques, mainly with connections to applications. Use-cases are distributed systems, auctions, online-markets, resource allocation, traffic routing, and sports. The goal of the lecture is to provide an overview over state-of-the-art results in the area of algorithmic game theory. Main topics that we will cover in the course are games in normal form, efficiency of equilibria, auctions, truthfulness and VCG-mechanisms, social choice, cake cutting, and cooperative games.

The lectures and homework sheets will be in English language. If all participants agree, the exercise session could be held in German. If there is an oral exam, the language can be chosen by the candidate. In case of a written exam the questions will be in English, answering them in German or English is fine.

The lecture addresses Interactive Visualization of Huge Scientific Datasets. More information can also be found on the Homepage: https://www.uni-bremen.de/ag-high-performance-visualization

Die Vorlesung beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Anwendungsbeispiele werden anhand der Open-Source-Software ParaView erläutert.
Homepage zur Veranstaltung: https://www.uni-bremen.de/ag-high-performance-visualization

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2025 will be decided upon with the participants

Profil: SQ, KIKR.
Schwerpunkt: IMA-SQ, IMVT-AI, IMVT-VMC
weitere Studiengänge: M-M-Alg-Num, M-T
https://lvb.informatik.uni-bremen.de/imat/03-imat-apx.pdf

A large number of problems arising in practical scenarios like communication, transportation, planning, logistics etc. can be modeled as combinatorial optimization problems. In most cases, these problems are computationally intractable and one often resorts to heuristics that provide sufficiently good solutions in reasonable amount of runtime. However, in most cases, such heuristics do not provide a worst case guarantee on the performance in comparison to the optimum solution. In this course, we shall study algorithms for combinatorial optimization problems which can provide strong mathematical guarantees on performance. The course aims at developing a toolkit for solving such problems. The lectures will consist of designing polynomial-time algorithms and proving rigorous bounds on their worst case performances.
We review many classical results in the field of approximation algorithms, highlighting different techniques commonly used for the design of such algorithms. Among others, we will treat the following topics:
• Greedy algorithms and Local Search
• Rounding Data and Dynamic Programming
• Deterministic Rounding of Linear Programs (LPs)
• Random Sampling and Randomized Rounding of LPs
• Primal-Dual Methods
• Hardness of Approximation
• Problem Solving under Uncertainty

Many every-day processes can seen as a game between autonomous interacting players, where each player acts stategically in order to pursue her own objectives. This lecture is an introduction to game-theoretic concepts and techniques, mainly with connections to applications. Use-cases are distributed systems, auctions, online-markets, resource allocation, traffic routing, and sports. The goal of the lecture is to provide an overview over state-of-the-art results in the area of algorithmic game theory. Main topics that we will cover in the course are games in normal form, efficiency of equilibria, auctions, truthfulness and VCG-mechanisms, social choice, cake cutting, and cooperative games.

The lectures and homework sheets will be in English language. If all participants agree, the exercise session could be held in German. If there is an oral exam, the language can be chosen by the candidate. In case of a written exam the questions will be in English, answering them in German or English is fine.

The lecture addresses Interactive Visualization of Huge Scientific Datasets. More information can also be found on the Homepage: https://www.uni-bremen.de/ag-high-performance-visualization

Die Vorlesung beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Anwendungsbeispiele werden anhand der Open-Source-Software ParaView erläutert.
Homepage zur Veranstaltung: https://www.uni-bremen.de/ag-high-performance-visualization

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2025 will be decided upon with the participants

The lecture addresses Interactive Visualization of Huge Scientific Datasets. More information can also be found on the Homepage: https://www.uni-bremen.de/ag-high-performance-visualization

Die Vorlesung beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Anwendungsbeispiele werden anhand der Open-Source-Software ParaView erläutert.
Homepage zur Veranstaltung: https://www.uni-bremen.de/ag-high-performance-visualization

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.