Are you fascinated by geometric shapes and their properties?
Are you an Bachelor's or Masters's student in mathematics looking to deepen your understanding of polytopes?
Then this seminar is for you!

In this seminar, we will delve into the fascinating world of polytopes, which are geometric objects that generalize the idea of a convex polygon or a convex polyhedron.
Polytopes have a wide range of applications in various fields, such as computer graphics, physics, and optimization.

We will cover a variety of topics related to polytopes, including:

• Basics of polytopes: We will begin by discussing the basic properties of polytopes. We will also explore the different types of polytopes, including simplices, cubes, and cross-polytopes.
• Combinatorial properties: We will delve into the combinatorial properties of polytopes, including the Euler characteristic, face numbers, and the Dehn-Sommerville equations.
• Algebraic properties: We will examine the algebraic properties of polytopes, including their symmetry groups and the representation of polytopes by linear inequalities.

- Applications: We will explore the different applications of polytopes in other areas of mathematics and science, such as linear programming, coding theory, and computer graphics.

• Computational methods: We will learn about computational methods for dealing with polytopes, including convex hull algorithms, triangulation algorithms and algorithms for counting the number of faces of a polytope.

Throughout the seminar, we will use examples and case studies to illustrate the concepts and theories discussed.
The seminar will also touch on the recent developments in the study of polytopes, including new results and open problems.

But this seminar is not just about listening and taking notes, we want you to actively participate in the class.
Each student is expected to give a talk on a specific topic related to polytopes, allowing you to not only deepen your own understanding but also share your knowledge with your peers.
This seminar is also a great opportunity for students to connect with other students with similar interests and to learn from each other.

Join us on a journey of discovery and exploration as we uncover the hidden beauty and complexity of polytopes.

Sign up now and be ready to be amazed!

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

Course homepage: http://www.math.uni-bremen.de/~hvogt/evolution23.html

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

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

Die Veransaltungen 03-M-SP-17 "Deep Learning for Inverse Problems"und 03-M-SP-18 "Nonlinear Inverse Problems" bilden zwei einzeln belegbare Veranstaltungsblöcke im Themenbereich von inversen Problemen (Woche 1-7: Deep Learning for Inverse Problems; Woche 8-14: Nonlinear Inverse Problems), die hintereinander stattfinden. Sie können zusammen oder separat belegt belegt werden.

Die Veransaltungen 03-M-SP-17 "Deep Learning for Inverse Problems"und 03-M-SP-18 "Nonlinear Inverse Problems" bilden zwei einzeln belegbare Veranstaltungsblöcke im Themenbereich von inversen Problemen (Woche 1-7: Deep Learning for Inverse Problems; Woche 8-14: Nonlinear Inverse Problems), die hintereinander stattfinden. Sie können zusammen oder separat belegt belegt werden.

Are you fascinated by geometric shapes and their properties?
Are you an Bachelor's or Masters's student in mathematics looking to deepen your understanding of polytopes?
Then this seminar is for you!

In this seminar, we will delve into the fascinating world of polytopes, which are geometric objects that generalize the idea of a convex polygon or a convex polyhedron.
Polytopes have a wide range of applications in various fields, such as computer graphics, physics, and optimization.

We will cover a variety of topics related to polytopes, including:

• Basics of polytopes: We will begin by discussing the basic properties of polytopes. We will also explore the different types of polytopes, including simplices, cubes, and cross-polytopes.
• Combinatorial properties: We will delve into the combinatorial properties of polytopes, including the Euler characteristic, face numbers, and the Dehn-Sommerville equations.
• Algebraic properties: We will examine the algebraic properties of polytopes, including their symmetry groups and the representation of polytopes by linear inequalities.

- Applications: We will explore the different applications of polytopes in other areas of mathematics and science, such as linear programming, coding theory, and computer graphics.

• Computational methods: We will learn about computational methods for dealing with polytopes, including convex hull algorithms, triangulation algorithms and algorithms for counting the number of faces of a polytope.

Throughout the seminar, we will use examples and case studies to illustrate the concepts and theories discussed.
The seminar will also touch on the recent developments in the study of polytopes, including new results and open problems.

But this seminar is not just about listening and taking notes, we want you to actively participate in the class.
Each student is expected to give a talk on a specific topic related to polytopes, allowing you to not only deepen your own understanding but also share your knowledge with your peers.
This seminar is also a great opportunity for students to connect with other students with similar interests and to learn from each other.

Join us on a journey of discovery and exploration as we uncover the hidden beauty and complexity of polytopes.

Sign up now and be ready to be amazed!

In real data analysis, researchers are often interested in using the same data set to make inference on multiple hypotheses. For instance, they may want to identify brain regions that are activated by a stimulus in brain imaging data, or biological pathways that are differentially expressed in genomics data. However, testing multiple hypotheses simultaneously is a non-trivial extension of the individual case.

Indeed, any hypothesis test carries the risk of making a type I error, i.e., falsely rejecting a true hypothesis; this leads to a ‘false discovery’ and so a potentially misleading scientific result. Standard methods for testing an individual hypothesis allow to bound the probability of making such an error by an ‘acceptable’ risk, usually set at 0.05. When performing multiple tests, however, each one has a probability of producing a type I error. As a result, the risk of having at least one error among the findings may become unmanageable.

In this seminar we will introduce the problem of multiple testing and explore different techniques that have been proposed to control the flood of type I errors that arise in this context. We will see that different procedures aim at controlling different generalizations of the type I error. First, we will focus on procedures that control either the familywise error rate (FWER) or the false discovery rate (FDR), a class that includes many of the most popular multiple testing methods. Subsequently, we will introduce recent proposals that estimate the false discovery proportion (FDP) or provide confidence intervals for it.

The seminar is held in English.

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

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

Kursinformationen und Onlineanmeldung unter https://www.fremdsprachenzentrum-bremen.de/1375.0.html?&no_cache=1&user_kursdb_pi1%5BshowUid%5D=14917

Dieser Kurs behandelt die Grundlagen der mathematischen Statistik für Studierende der Masterprogramme im Vollfach. Es können sich keine Credit Points für die Teilnahme angerkannt werden!