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

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2024 will be decided upon with the participants

Seminar on advanced numerical methods for partial differential equations

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

Convex Geometry plays an essential role in several branches of Mathematics, from Discrete Mathematics to Harmonic Analysis. We will discuss some major analytic and discrete aspects of convex geometry and some applications. Our topics will range from the boundary structure of convex bodies, particularly polytopes, to Hadwiger's volume characterisation, via geometric and functional inequalities, as well as geometric and analytic symmetrization techniques.

This course deals with the mathematical foundations of machine learning with a strong focus on classical theory and well-established algorithms like, for example, support vector machines for classification, ridge regression, principal component analysis for dimensionality reduction and k-means clustering. In addition, deep learning with neural networks will be briefly discussed towards the end of the course.

Die Veranstaltung findet im KKSB statt.

The course will provide an introduction into the theory of semiparametric models. We will introduce and discuss the mathematical statistical theory for such models and will illustrate the utility of semiparametric models with a number of concrete models and data examples. Hence, the lecture and exercises will cover theoretical and practical aspects of semiparametric models. We will use the open statistical software R for the data applications.

This course will cover manifolds, vector bundles, embeddings and submersions, integral curves and flows, basics of Lie groups, differential forms and integration, Riemannian metrics, geodesics, connections, curvature, and further topics.

The course will discuss convex optimisation problems and present and analyse algorithms that solve them. Topics will include proximal splitting, acceleration, stochastic algorithms, and performance estimation.

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2024 will be decided upon with the participants

Seminar on advanced numerical methods for partial differential equations

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

This course provides an introduction to the practice of scientific programming.

This course deals with the mathematical foundations of machine learning with a strong focus on classical theory and well-established algorithms like, for example, support vector machines for classification, ridge regression, principal component analysis for dimensionality reduction and k-means clustering. In addition, deep learning with neural networks will be briefly discussed towards the end of the course.

Die Veranstaltung findet im NEOS Gebäude statt.

This course will cover manifolds, vector bundles, embeddings and submersions, integral curves and flows, basics of Lie groups, differential forms and integration, Riemannian metrics, geodesics, connections, curvature, and further topics.

The course will discuss convex optimisation problems and present and analyse algorithms that solve them. Topics will include proximal splitting, acceleration, stochastic algorithms, and performance estimation.

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2024 will be decided upon with the participants

Seminar on advanced numerical methods for partial differential equations

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

This course provides an introduction to the practice of scientific programming.

This course deals with the mathematical foundations of machine learning with a strong focus on classical theory and well-established algorithms like, for example, support vector machines for classification, ridge regression, principal component analysis for dimensionality reduction and k-means clustering. In addition, deep learning with neural networks will be briefly discussed towards the end of the course.

Die Veranstaltung findet im NEOS Gebäude statt.

This course will cover manifolds, vector bundles, embeddings and submersions, integral curves and flows, basics of Lie groups, differential forms and integration, Riemannian metrics, geodesics, connections, curvature, and further topics.

The course will discuss convex optimisation problems and present and analyse algorithms that solve them. Topics will include proximal splitting, acceleration, stochastic algorithms, and performance estimation.

In the Seminar Analysis advanced topics in the area of analysis are discussed. The precise topic for Summer semester 2024 will be decided upon with the participants

Seminar on advanced numerical methods for partial differential equations

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

Convex Geometry plays an essential role in several branches of Mathematics, from Discrete Mathematics to Harmonic Analysis. We will discuss some major analytic and discrete aspects of convex geometry and some applications. Our topics will range from the boundary structure of convex bodies, particularly polytopes, to Hadwiger's volume characterisation, via geometric and functional inequalities, as well as geometric and analytic symmetrization techniques.

This course deals with the mathematical foundations of machine learning with a strong focus on classical theory and well-established algorithms like, for example, support vector machines for classification, ridge regression, principal component analysis for dimensionality reduction and k-means clustering. In addition, deep learning with neural networks will be briefly discussed towards the end of the course.

Die Veranstaltung findet im KKSB statt.

The course will provide an introduction into the theory of semiparametric models. We will introduce and discuss the mathematical statistical theory for such models and will illustrate the utility of semiparametric models with a number of concrete models and data examples. Hence, the lecture and exercises will cover theoretical and practical aspects of semiparametric models. We will use the open statistical software R for the data applications.

This course will cover manifolds, vector bundles, embeddings and submersions, integral curves and flows, basics of Lie groups, differential forms and integration, Riemannian metrics, geodesics, connections, curvature, and further topics.

The course will discuss convex optimisation problems and present and analyse algorithms that solve them. Topics will include proximal splitting, acceleration, stochastic algorithms, and performance estimation.