Der Kurs findet in der zweiten und dritten Märzwoche statt. Details werden noch bekanntgegeben.

Die Funktionalanalysis untersucht unendlichdimensionale Räume und die darauf definierten Operatoren.

Fortsetzung von Numerik~1: Entwicklung und Analyse von Algorithmen zur approximativen Lösung mathematischer Probleme, die insbesondere in industriellen Anwendungen auftreten.

Aktuelle Informationsbroschüren finden Sie unter www.szmathe.uni-bremen.de

Einblicke in die Industriemathematik: mathematische Modellierung, Analyse und numerische Simulationen zu wöchentlich wechselnden Anwendungsproblemen.

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.

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.

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 NEOS Gebäude statt.

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.

Aktuelle Informationsbroschüren finden Sie unter www.szmathe.uni-bremen.de

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

Homepage zur Veranstaltung: https://www.uni-bremen.de/rtg-pi3/qualification/rtg-seminar

https://lvb.informatik.uni-bremen.de/igs/03-ibfw-hto.pdf
A large number of problems arising in practical scenarios like communication, transportation, planning, logistics etc. can be formulated as discrete linear optimization problems. This course briefly introduces the theory of such problems. We develop a toolkit to model real-world problems as (discrete) linear programs. We also explore several ways to find integer solutions such as cutting planes, branch & bound, and column generation.

Throughout the course, we learn these skills by modeling and solving, for example, scheduling, packing, matching, routing, and network-design problems. We focus on translating practical examples into mixed-integer linear programs. We learn how to use solvers (such as CPLEX and Gurobi) and tailor the solution process to certain properties of the problem.

This course consists of two phases:

• One week Mon-Fri (full day, 9-5) of lectures and practical labs: September 23-27, in MZH.
• A subsequent project period: One problem has to be modeled, implemented, and solved individually or in a group of at most three students. The topic will be provided by the lecturers and will be discussed on the last day of the block course. The project including the implementation has to be presented in the beginning of the winter semester.

There are no prerequisites except some basic programming skills to participate.

Die Mathematik lebt davon, dass abstrahiert wird. Im Studium der Mathematik und der Industriemathematik erlernt man dieses abstrakte Denken und übersieht vielleicht, wie gut dieses Studium für den Arbeitsmarkt qualifiziert. Daher soll dieses Seminar Impulse setzen und Hilfen geben, um sich mit der eigenen beruflichen Karriere auseinanderzusetzen.

3 SWS Seminar
Raum wird nach Anmeldung in Stud.IP bekannt gegeben.
Homepage des KKSB und Uni-Lageplan

Zu den Themen, die in diesem Kurs behandelt werden, gehören:

• Mengenlehre, d.h. Schreibweisen, Mengenoperationen, Produkt- und Potenzmengen
• Beweise und Logik
• Kombinatorik (Variationen, Permutationen, Kombinationen, Binomialkoeffizienten, u.a.)
• Graphentheorie (Planare Graphen, Wege in Graphen, Färbungen, Bäume)

Kursinformationen und Onlineanmeldung unter:
https://kurse.sprachenzentrum-bremen.de/course/summer-2024/282d1a14-8b09-42f2-8e14-fd3e8107a1df