In this lecture we will concentrate on 3 basic types of partial differential equations: the Poisson equation, the wave equation and the heat equation – which are prototypes of elliptic, hyperbolic and parabolic differential equations. They are linear equations, and for the solution theory we will make some use of linear functional analysis. See also http://www.math.uni-bremen.de/~hvogt/pde26.html

Field Trip and Exercise

3 SWS Seminar
Raum im KKSB Linz 4
Homepage des KKSB und Uni-Lageplan

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, Gurobi, Xpress and free ones) 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: July 14-18, 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.

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.

https://lvb.informatik.uni-bremen.de/ims/03-ims-apks.pdf
Termine:
Auftakttermin: 07.04.2026 um 12:00 Uhr in Raum 2.43 Rotunde Cartesium.

This course in commutative algebra covers the theory of ideals in polynomial rings, affine algebraic varieties, Gröbner bases, and the Buchberger algorithm, providing a basic introduction to algebraic geometry. It also develops concepts from homological algebra, including the theory of R-modules, injective and projective modules, chain complexes, homology, presentations and free resolutions, multigraded modules, and the decomposition theorem of R-modules.

Die Veranstaltung findet im NEOS Gebäude statt.

The lecture addresses Interactive Visualization of huge scientific Datasets. More information can also be found on the Homepage: https://www.uni-bremen.de/ag-hpvis

3 SWS Seminar
Raum im KKSB Linz 4
Homepage des KKSB und Uni-Lageplan

We will discuss linear and generalized linear regression models. While the models studied in Statistics I are mainly models for stochastically independent and identically distributed observables, regression models are used to model stochastically independent, but not identically distributed observables. In addition to the theoretical investigations, we will discuss real-life applications and software solutions (in R).

In this lecture we will concentrate on 3 basic types of partial differential equations: the Poisson equation, the wave equation and the heat equation – which are prototypes of elliptic, hyperbolic and parabolic differential equations. They are linear equations, and for the solution theory we will make some use of linear functional analysis. See also http://www.math.uni-bremen.de/~hvogt/pde26.html

In this lecture we will concentrate on 3 basic types of partial differential equations: the Poisson equation, the wave equation and the heat equation – which are prototypes of elliptic, hyperbolic and parabolic differential equations. They are linear equations, and for the solution theory we will make some use of linear functional analysis. See also http://www.math.uni-bremen.de/~hvogt/pde26.html

In the focus of this lecture are modern numerical tools for modeling applications and the corresponding research software. In the lecture, modern numerical methods and their demands on implementations are given. In the seminar exercises, principles of numerical software design are introduced and implementations are tested interactively. As third element, in a project week students focus on the practical implementation for a selected application case.

Statistical problems are described by statistical models. This means interpreting the data as realizations of random variables whose unconditional or conditional densities are described and estimated by statistical (regression) models. These models are usually identified by a set of parameters, which can be finite but also infinite dimensional. For this purpose, there are usually three types of possible models, depending on the structure of the data and the problem at hand: parametric, nonparametric, and semiparametric. A semiparametric model is characterized by the inclusion of both finite dimensional parametric and infinite dimensional nonparametric components. The main interest is usually in the finite dimensional parametric component, with the infinite dimensional component being co-estimated for the purpose of statistical inference and efficiency. In this seminar we will study the definition, properties, and applications of semiparametric models. Examples of semiparametric models include single-index models and Cox regression models for censored survival time data. We will also consider approaches to dealing with missing information in data sets. The use of semiparametric models plays a major role for medical studies, for example.

Prerequisites for participation in the seminar are basic knowledge of mathematical statistics (e.g. from Statistics 1) and of regression models (e.g. from Statistics 2). English speaking students are welcome.

In order to gain a good insight into the extensive theory of semi-parametric models, we will use the master thesis by Karel Vermeulen as our primary literature and study the chapters that are important for us in more detail, presenting the knowledge gained through the thesis in the form of individual presentations.

A list with the name of the thesis and further literature can be found below.

• Master thesis of Karel Vermeulen. Semiparametric Efficiency
• A. W. van der Vaart. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 1998.
• A. W. van der Vaart. ”On Differentiable Functionals“. In: Ann. Statist. 19.1 (März 1991), S. 178–204.
• Tsiatis, Anastasios. Semiparametric Theory and Missing Data. Vereinigtes Königreich, Springer New York, 2010.