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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

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

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

Homepage zur Veranstaltung: http://zetem.uni-bremen.de/o2c/veranstaltungen

Students study special topics of numerical mathematics in this reading course. The aim is a self-study of selected topics on the basis of textbooks, scientific articles or other monographs. The course may also include an introduction into other associated topics or to special software (e.g. Alberta, WORHP). In addition, aspects of scientific work will b e discussed, e .g. obtaining relevant literature, correct citation, or structure of a scientific a rticle. A ll t his is done under the supervision of a lecturer from the ZeTeM. In addition to the self-study, there will be regular meetings with the supervisor to discuss the topics in an informal or formal way and also written reports on a regular basis are mandatory. The topic will be discussed with the supervisor and, ideally, it is already into the direction of a future Master’s thesis.

Analytical and structured thinking, exact formulation of mathematical facts, comprehension of mathematical proofs and learning of proof techniques, independent and creative solving of mathematical problems, knowledge of real analysis, algorithmic approach to solving mathematical problems.

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

The reading course introduces students to specific topics that may be relevant for the Master's thesis, using mainly original English-language literature (scientific articles and reference books). Students are expected to prepare a seminar talk and an elaboration on the topic.

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Schwerpunkt: AI
https://lvb.informatik.uni-bremen.de/ibap/03-ibap-ml.pdf
Die Übungen starten in der 2. Semesterwoche.
IBAP-MLd (German) or IBAP-MLe (English) can be taken, but the course can only be credited once!

Schwerpunkt: AI
https://lvb.informatik.uni-bremen.de/ibap/03-ibap-mrca.pdf

Robotics is a complex field that emerged at the intersection of multiple disciplines such as physics, mathematics and computer science. New advances in hardware and software design and progress in artificial intelligence enable robotics research to pursue higher goals and achieve increased autonomy in various environments. For instance, robots can operate in disaster zones for search and rescue operations, can be employed in rehabilitation and healthcare, space and underwater exploration, etc. Given the complexity of such scenarios, it is essential to develop robust robotic systems with a high degree of autonomy, able to assist humans in difficult and tedious tasks.

This course aims to provide the fundamentals of modern robot control approaches that enable robots to operate in the environment autonomously. The course introduces a basic understanding of robotics, along with tools and methods to control mobile robotic platforms and manipulators. Firstly, the course presents the basics of modeling robotic systems in terms of geometry, kinematics, and dynamics. Next, real robotic systems are considered with their different types of sensors and actuators. Furthermore, system identification as a means to adapt the robot model to the reality is treated. Finally, the course provides methods and approaches to control robots from a deliberative and reactive point of view. Students will put this knowledge into practice during tutorials and exercise sheets using Python implementation and robot simulations.

Contents

• Introduction to Robotics and AI: long term robot autonomy, artificial intelligence, deliberative vs. reactive control, robotic applications.
• Robot Geometry and Transformations: robot transformations in the 3D space, exponential and logarithmic maps, forward and inverse geometric models.
• Kinematics: definition of twists and wrenches for rigid bodies, geometric Jacobian formulation, forward and inverse kinematics.
• Dynamics: an introduction to Lagrangian and Newtonian mechanics, robot dynamics formulation, recursive Newton-Euler algorithm.
• Sensing and Actuation Modalities: types of sensors and actuators, sensor fusion, actuator control.
• System Identification: methods to identify geometry, kinematic and dyanmic parameters of a robot.
• Localization: direct and probabilistic methods for robot localization, odometry, global localization, particle filter.
• Path Planning: path vs. trajectory generation, graph-based methods for path planning (e.g. Djikstra, A*).
• Dynamic Control: PD gravity compensation control, computed torque control, admittance vs impedance control.

Learning Outcomes

At the end of the course, the student is expected to be able to:

• Have a basic understanding about autonomous robots and AI.
• Compute the coordinate transformations for rigid bodies commonly used in robotics.
• Apply the robot forward and inverse kinematics.
• Describe a robotic system based on its kinematic and dynamic properties.
• Implement and understand the low-level actuator control methods.
• Describe the sensor and actuator modalities used in robotics, and explain their relevance for robot control.
• Apply system identification methods to improve robot models and adapt them to reality.
• Use probabilistic methods for robot localization.
• Generate a path for a mobile robot or manipulator using motion planning methods.
• Apply dynamical control methods on robotic systems such that they are robust against disturbances.
• Assess the strengths and limitations of different control methods presented in the course.
• Identify open challenges in robotics research and current trends in state-of-the-art.
• Communicate confidently using the terminology in the field of robotics.
• Cooperate and work in teams in order to solve tasks.

Examination

During the semester, students are required to complete 6 worksheets in groups of 4.
To pass the course, students must achieve a minimum of 50% on both the worksheets and the written exam.
The final grade is 40% based on worksheets and 60% on the written exam.

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

Profil: KIKR, DMI.
Schwerpunkt: IMVT-AI, IMVT-DMI, IMVT-VMC
https://lvb.informatik.uni-bremen.de/imvt/03-imvt-cgeom.pdf
Die Veranstaltung beginnt am 10.04.2025.
This course looks at a number of algorithms and data structures from computational geometry with a view on their application to computer graphics. You should feel comfortable with geometric-mathematical thinking as well as algorithmic thinking. We will not need, however, complex mathematics. Die Homepage zur Vorlesung befindet sich immer unter http://cgvr.cs.uni-bremen.de -> Teaching

Schwerpunkt: IMA-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-llml.pdf

Profil: KIKR.
Schwerpunkt: IMA-AI, IMVP-VMC
https://lvb.informatik.uni-bremen.de/imap/03-imap-rl.pdf

Profil: KIKR, DMI
Schwerpunkt: IMA-AI, IMVP-DMI, IMVP-VMC
https://lvb.informatik.uni-bremen.de/imap/03-imap-uuw.pdf

Profil: KIKR, DMI, MC.
Schwerpunkt: IMAP-VMC, IMAP-DMI, IMVP-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-acg.pdf
The lecture will be held in German or English, depending on demand. Most of the homework and assignments of this course will be practical ones. Decent programming skills in C++ are required to work on those.
https://cgvr.cs.uni-bremen.de/teaching/

Profil: KIKR
Schwerpunkt: IMVP-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-wawr.pdf
Die Veranstaltung findet im TAB statt.

Schwerpunkt: IMA-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-llml.pdf

https://lvb.informatik.uni-bremen.de/imvp/03-imvp-prosy.pdf
Schwerpunkt: IMVP-SQ

Profil: KIKR.
Schwerpunkt: IMA-AI, IMVP-VMC
https://lvb.informatik.uni-bremen.de/imap/03-imap-rl.pdf

IMVP-AI
Room: TAB Knowledge (0.30)

Learning Outcome:
* Understand and apply concepts of functional programming
* Understand and apply artificial intelligence techniques
* Program an autonomous robot platform using ROS
* Implement failure handling techniques

Contents:
This course gives a solid practical introduction to the Robot Operating System (ROS2) up to advanced topics on how to control robots.
The lecture covers the tools of ROS2 and the cognitive robot architecture CRAM.
Students work in small groups on a TurtleBot to apply the lectures content hands-on to the robot.
Eventually the students will be able to design an autonomously driving vehicle, being evaluated in a final competition.

Profile: KIKR
https://lvb.informatik.uni-bremen.de/imvp/03-imvp-rpros.pdf

https://lvb.informatik.uni-bremen.de/imap/03-imap-secoro.pdf

Profil: KIKR, DMI
Schwerpunkt: IMA-AI, IMVP-DMI, IMVP-VMC
https://lvb.informatik.uni-bremen.de/imap/03-imap-uuw.pdf

Profil: DMI
Schwerpunkt: IMK-DMI, IMA-VMC
https://lvb.informatik.uni-bremen.de/imaa/03-imaa-ec.pdf

Profil: KIKR, DMI, MC.
Schwerpunkt: IMAP-VMC, IMAP-DMI, IMVP-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-acg.pdf
The lecture will be held in German or English, depending on demand. Most of the homework and assignments of this course will be practical ones. Decent programming skills in C++ are required to work on those.
https://cgvr.cs.uni-bremen.de/teaching/

Profil: KIKR, DMI, MC.
Schwerpunkt: IMAP-VMC, IMAP-DMI, IMVP-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-acg.pdf
The lecture will be held in German or English, depending on demand. Most of the homework and assignments of this course will be practical ones. Decent programming skills in C++ are required to work on those.
https://cgvr.cs.uni-bremen.de/teaching/

Profil: DMI
Schwerpunkt: IMK-DMI, IMA-VMC
https://lvb.informatik.uni-bremen.de/imaa/03-imaa-ec.pdf

Schwerpunkt: IMVA-AI, IMVA-DMI
https://lvb.informatik.uni-bremen.de/imva/03-imva-acss.pdf
The aim of this course is to create an understanding of the major aspects of sports applications. The course is split into two parts: the first half has a classic lecture/tutorial style, whereas the second half will focus on the creation of individual sports applications.

The lectures will explain the necessary fundamentals, such as sensor technology, user feedback, and the conduction of empirical studies, along with a number of inspiring examples.

In the project part, own prototypes for sports applications are developed in small groups. The exact application as well as the technical implementation approach can be chosen freely. The final graded outcome of the course will be a small sports application about which a presentation has to be held and a documentation in a scientific paper style has to be written.

The course will be held in English.

Schwerpunkt: AI, DMI

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

Profil: SQ.
Schwerpunkt: IMAP-SQ
https://lvb.informatik.uni-bremen.de/imap/03-imap-qse.pdf

Profil: KIKR, DMI, MC.
Schwerpunkt: IMAP-VMC, IMAP-DMI, IMVP-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-acg.pdf
The lecture will be held in German or English, depending on demand. Most of the homework and assignments of this course will be practical ones. Decent programming skills in C++ are required to work on those.
https://cgvr.cs.uni-bremen.de/teaching/

Profil: KIKR.
Schwerpunkt: IMA-AI, IMVP-VMC
https://lvb.informatik.uni-bremen.de/imap/03-imap-rl.pdf

Profil: KIKR, DMI
Schwerpunkt: IMA-AI, IMVP-DMI, IMVP-VMC
https://lvb.informatik.uni-bremen.de/imap/03-imap-uuw.pdf

Profil: SQ.
Schwerpunkt: IMVP-DMI, IMVP-SQ
https://lvb.informatik.uni-bremen.de/imap/03-imap-dis.pdf
Die Veranstaltung ist inhaltlich identisch mit "Entwurf von Informationssystemen" (keine Doppelanerkennung möglich).

https://lvb.informatik.uni-bremen.de/imvp/03-imvp-prosy.pdf
Schwerpunkt: IMVP-SQ

Profil: SQ.
Schwerpunkt: IMAP-SQ
https://lvb.informatik.uni-bremen.de/imap/03-imap-qse.pdf

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

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

Profil: KIKR, DMI.
Schwerpunkt: IMVT-AI, IMVT-DMI, IMVT-VMC
https://lvb.informatik.uni-bremen.de/imvt/03-imvt-cgeom.pdf
Die Veranstaltung beginnt am 10.04.2025.
This course looks at a number of algorithms and data structures from computational geometry with a view on their application to computer graphics. You should feel comfortable with geometric-mathematical thinking as well as algorithmic thinking. We will not need, however, complex mathematics. Die Homepage zur Vorlesung befindet sich immer unter http://cgvr.cs.uni-bremen.de -> Teaching

Profil: DMI.
Schwerpunkt: IMVA-DMI, IMVA-VMC
https://lvb.informatik.uni-bremen.de/imva/03-imva-ei.pdf

Profil: DMI
Schwerpunkt: IMK-DMI, IMA-VMC
https://lvb.informatik.uni-bremen.de/imaa/03-imaa-ec.pdf

Profil: KIKR, DMI, MC.
Schwerpunkt: IMAP-VMC, IMAP-DMI, IMVP-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-acg.pdf
The lecture will be held in German or English, depending on demand. Most of the homework and assignments of this course will be practical ones. Decent programming skills in C++ are required to work on those.
https://cgvr.cs.uni-bremen.de/teaching/

Profil: DMI
Schwerpunkt: IMA-DMI, IMVA-DMI
https://lvb.informatik.uni-bremen.de/imva/03-imva-mad.pdf
Die Veranstaltung richtet sich an Studenten der Informatik und Digitalen Medien. In Gruppenarbeit sollen die Studierenden semesterbegleitend ein App-Projekt umsetzen. In der Vorlesung werden alle relevanten Informationen der modernen Softwareentwicklung, mit Fokus auf die mobile App-Entwickung, vermittelt. Dazu gehören Themen wie mobiles Testing, Scrum, UX Design, Evaluation & Nutzertests, Design Patterns und Cross-Plattform-Entwicklung. Das Ziel dabei ist die Vermittlung von praxisrelevantem Wissen aus dem Alltag eines erfolgreichen Unternehmens.

Profil: SQ.
Schwerpunkt: IMVP-DMI, IMVP-SQ
https://lvb.informatik.uni-bremen.de/imap/03-imap-dis.pdf
Die Veranstaltung ist inhaltlich identisch mit "Entwurf von Informationssystemen" (keine Doppelanerkennung möglich).

Profil: KIKR, DMI
Schwerpunkt: IMA-AI, IMVP-DMI, IMVP-VMC
https://lvb.informatik.uni-bremen.de/imap/03-imap-uuw.pdf

4 SWS, Profil: DMI
Schwerpunkt: IMVA-DMI
https://lvb.informatik.uni-bremen.de/imva/03-imva-3dmft.pdf
Kurzbeschreibung unter: http://dimeb.informatik.uni-bremen.de/FabLab/GenerativeDesign.pdf
Präsenz-Meeting mittwochs 10-12h und anschließend 2 Std Übungen im FabLab wöchentlich.

Schwerpunkt: IMVA-AI, IMVA-DMI
https://lvb.informatik.uni-bremen.de/imva/03-imva-acss.pdf
The aim of this course is to create an understanding of the major aspects of sports applications. The course is split into two parts: the first half has a classic lecture/tutorial style, whereas the second half will focus on the creation of individual sports applications.

The lectures will explain the necessary fundamentals, such as sensor technology, user feedback, and the conduction of empirical studies, along with a number of inspiring examples.

In the project part, own prototypes for sports applications are developed in small groups. The exact application as well as the technical implementation approach can be chosen freely. The final graded outcome of the course will be a small sports application about which a presentation has to be held and a documentation in a scientific paper style has to be written.

The course will be held in English.

Schwerpunkt: AI, DMI

Profil: DMI.
Schwerpunkt: IMVA-DMI, IMVA-VMC
https://lvb.informatik.uni-bremen.de/imva/03-imva-ei.pdf

Profil: DMI
Schwerpunkt: IMA-DMI, IMVA-DMI
https://lvb.informatik.uni-bremen.de/imva/03-imva-mad.pdf
Die Veranstaltung richtet sich an Studenten der Informatik und Digitalen Medien. In Gruppenarbeit sollen die Studierenden semesterbegleitend ein App-Projekt umsetzen. In der Vorlesung werden alle relevanten Informationen der modernen Softwareentwicklung, mit Fokus auf die mobile App-Entwickung, vermittelt. Dazu gehören Themen wie mobiles Testing, Scrum, UX Design, Evaluation & Nutzertests, Design Patterns und Cross-Plattform-Entwicklung. Das Ziel dabei ist die Vermittlung von praxisrelevantem Wissen aus dem Alltag eines erfolgreichen Unternehmens.

Profil: KIKR, DMI, MC.
Schwerpunkt: IMAP-VMC, IMAP-DMI, IMVP-AI
https://lvb.informatik.uni-bremen.de/imap/03-imap-acg.pdf
The lecture will be held in German or English, depending on demand. Most of the homework and assignments of this course will be practical ones. Decent programming skills in C++ are required to work on those.
https://cgvr.cs.uni-bremen.de/teaching/

Profil: SQ.
Schwerpunkt: IMAP-SQ
https://lvb.informatik.uni-bremen.de/imap/03-imap-qse.pdf

Profil: KIKR, DMI.
Schwerpunkt: IMVT-AI, IMVT-DMI, IMVT-VMC
https://lvb.informatik.uni-bremen.de/imvt/03-imvt-cgeom.pdf
Die Veranstaltung beginnt am 10.04.2025.
This course looks at a number of algorithms and data structures from computational geometry with a view on their application to computer graphics. You should feel comfortable with geometric-mathematical thinking as well as algorithmic thinking. We will not need, however, complex mathematics. Die Homepage zur Vorlesung befindet sich immer unter http://cgvr.cs.uni-bremen.de -> Teaching

Registration for this lab must be done via Stud.IP.
Participants are selected on the basis of the exam passed in Control Theory I.
Please remember that this lab is in English. The preparation tasks therefore also have to be answered in English. Answers in German can not be accepted.
Registration period until 28.03.2025

Registration in the groups can then take place from 29.03.2025 to 14.04.2025.

If there are questions, please contact A. Niaz (0421 218 62727).
-
Anmeldung ausschließlich über Stud.IP..
Die Auswahl der Teilnehmer erfolgt auf der Grundlage der in der Kontrolltheorie I bestandene Klausur.
Bitte denken Sie daran, dass dieses Labor in Englisch ist. Die Vorbereitungsaufgaben müssen daher auch auf Englisch beantwortet werden. Antworten auf Deutsch können nicht akzeptiert werden.
Anmeldezeitraum bis zum 28.03.2025

Ab dem 29.03.2025 bis zum 14.04.2025 können dann die Eintragung in den Gruppen stattfinden.

Bei Fragen kontaktieren Sie bitte A. Niaz (0421 218 62727).



Termine nach Vereinbarung.

The ICT lab consists of multiple parts, which are organized by three departments: the RF department, ComNets and the dept. of communications engineering. Please refer to the individual departments for further information:

http://www.hf.uni-bremen.de/
http://www.comnets.uni-bremen.de/
http://www.ant.uni-bremen.de/courses/ictlab/

Registration for this lab must be done via Stud.IP.
Participants are selected on the basis of the exam passed in Control Theory I.
Please remember that this lab is in English. The preparation tasks therefore also have to be answered in English. Answers in German can not be accepted.
Registration period until 28.03.2025

Registration in the groups can then take place from 29.03.2025 to 14.04.2025.

If there are questions, please contact A. Niaz (0421 218 62727).
-
Anmeldung ausschließlich über Stud.IP..
Die Auswahl der Teilnehmer erfolgt auf der Grundlage der in der Kontrolltheorie I bestandene Klausur.
Bitte denken Sie daran, dass dieses Labor in Englisch ist. Die Vorbereitungsaufgaben müssen daher auch auf Englisch beantwortet werden. Antworten auf Deutsch können nicht akzeptiert werden.
Anmeldezeitraum bis zum 28.03.2025

Ab dem 29.03.2025 bis zum 14.04.2025 können dann die Eintragung in den Gruppen stattfinden.

Bei Fragen kontaktieren Sie bitte A. Niaz (0421 218 62727).



Termine nach Vereinbarung.

In the first 3 weeks, the lectures will be in room N3130. All further weekly appointments: Rooms depending on the respective experiment. / (4 SWS)
Please check the PEP homepage for further course details (lecture + practical).

In the first 3 weeks, the lectures will be in room N3130. All further weekly appointments: Rooms depending on the respective experiment. / (2 SWS) / Please check the PEP homepage for further course details (lecture + practicals).

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem

Many every-day processes can seen as a game between autonomous interacting players, where each player acts strategically 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, and traffic networks. 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 \begin{itemize} \item Strategic Games and Efficiency of Equilibria \item Auctions, Truthfulness and VCG-mechanisms \item Cooperative Games \item Social Choice \end{itemize}

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.

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

In this course we will delve into the fascinating world of Ergodic Theory, a branch of mathematics that studies the asymptotic properties of transformations on topological and measurable spaces. From the origins of the ergodic hypothesis, which laid the foundation for classical statistical mechanics, to modern applications such as hyperbolic geometry or metric number theory, we will uncover the intricate relationships between measure-preserving systems, recurrence, entropy, and stochastic characterisations of dynamical systems. Through a combination of theoretical foundations and illuminating examples, we will explore the fundamental concepts of ergodic theory, including Measure-preserving systems and their properties Several ergodic theorems and their implications Recurrence and its role in understanding the behaviour of dynamical systems Dynamical spectra and their connections to number theory Entropy and its role in the study of dynamical systems Ergodic theory has far-reaching implications in many different fields outside mathematics, including physics, biology, economics and computer science (machine learning). The study of dynamical systems and ergodic theory has led to numerous breakthroughs in mathematics and has been recognised by several Fields Medals in recent years. By studying ergodic theory, you will gain a deeper understanding of the underlying mathematical structures and principles that govern complex systems. This course is an excellent starting point for further research in the field of dynamical systems, leading to exciting topics for master theses in the areas of the analysis/stochastics group. Join us on this journey into the fascinating world of Ergodic Theory!

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

Inverse problems are problems where one would like to find an unknown cause for which one can only measure observed effects. This situation occurs, for example, if one can only make indirect measurements of the quantity of interest. Two simple examples: \begin{itemize} \item We measure the position of an object, but would like to know the speed. \item In tomography we measure several projections (X-ray images) of an object, but would like to know the absorption spectrum of said object. \end{itemize} Inverse problems usually suffer from ill-posedness: Solutions may not be unique, they may not exist (for example due to measurement noise), and, most drastically, their solution is unstable in the sense that it does not depend continuously on the data. We will analyze the phenomenon on ill-posedness for linear inverse problems (modeled as linear and continuous maps between Hilbert spaces) to understand the reason for instability. A central goal of the course is to establish the notion of regularization of ill-posed problems (which roughly means the approximate solution by stable methods) and to derive and analyze regularization methods such as Tikhonov regularization, or the Landweber method with early stopping. We will also treat the numerical solution of inverse problems in the lecture and the exercises.

This course introduces quantum computing, covering the mathematical principles needed to understand and implement quantum algorithms. Topics include qubits, entanglement, quantum gates, and circuits. Students will explore algorithms like Deutsch-Jozsa and Shor’s, and problems such as secure communication. The course also addresses error correction and adiabatic algorithms, and includes hands-on practice using Qiskit to build and simulate quantum circuits on IBM’s Quantum Lab.

Die Veranstaltung findet im KKSB Raum 40010 statt.

Die Veranstaltung findet im KKSB LINZ 4 statt.

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

Advanced Communication Analysis is a master seminar in which advanced topics in the area of analysis are discussed. The precise topics for the Summer Semester 2025 will be decided upon with the participants.

This is the research seminar of our working group. It is open to all students with interest in the mathematical foundation of AI. As prerequisite, the students should have successfully finished an introductory course in data analysis including the basics of neural networks.

This seminar will treat methods of convex optimization that are suitable for large problems with millions of variables (the size is basically restricted that the computer memory can hold a small finite number of vectors). The guiding principle of these methods is to exploit suitable additive \emph{splitting} of the objective function and then use simple building blocks for the splitted parts to assemble an algorithm. Recently there has been much progress in this areas and in this seminar we will explore the following directions, for example: \begin{itemize} \item Stochastic optimization (stochastic gradient descent, stochastic proximal gradient method), [Chapter 7, 1] \item Accelerated methods (Accelerated gradient descent, accelerated proximal point methods), [Chapter 12, 1] \item Degenerate preconditioned proximal point methods [2] \item Kaczmarz (row-action) methods with mismatched adjoint [3] \end{itemize}

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

Commutative algebra is a branch of algebra which studies commutative rings, ideals and modules. We will discuss the theory of ideals of a polynomial ring, graded and multigraded modules, Gröbner bases, presentations and resolutions of modules. Topics are: Polynomial rings, ideals and varieties Gröbner bases and Buchberger’s algorithm Hilbert’s Nullstellensatz Multigraded modules and Betti numbers Rank invariants Presentations and resolutions Hilbert’s syzygy theorem Schreyer’s theorem