Preliminary course catalogue - changes and additions are still possible.
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New (and partly not yet in den annotated course catalogue):
Please note the registration modalities for the individual seminars published in the comments to the course catalog: As a rule, places are allocated after pre-registration by e-mail at the preliminary meeting at the end of the lecture period of the summer semester. You must then register online for the exam; the registration period runs from August 1, 2025 to October 8, 2025.
Seminar: Computational PDEs – Gradient Flows and Descent Methods
Lecturer: Sören Bartels
Language: Talk/participation possible in German and English
Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 15.07., 12:30, Raum 209, Hermann-Herder-Str. 10
Preparation meetings for talks: Dates by arrangement
The seminar will be devoted to the development of reliable and efficient discretizations of time stepping methods for parabolic evolution problems. The considered model problems either result from minimization problems or dynamical systems and are typically constrained or nondifferentiable. Criteria that allow to adjust the step sizes and strategies that lead to an acceleration of the convergence to stationary configurations will be addressed in the seminar. Specific topics and literature will be assigned in the preliminary meeting.
Elective in Data
Mathematical Seminar
Seminar: Medical Data Science
Lecturer: Harald Binder
Language: Talk/participation possible in German and English
Seminar: Mi, 10:15-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary Meeting 23.07., 10:15, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
To answer complex biomedical questions from large amounts of data, a wide range of analysis tools is often necessary, e.g. deep learning or general machine learning techniques, which is often summarized under the term ``Medical Data Science''. Statistical approaches play an important rôle as the basis for this. A selection of approaches is to be presented in the seminar lectures that are based on recent original work. The exact thematic orientation is still to be determined.
Good knowledge of probability theory and mathematical statistics.
Elective in Data
Mathematical Seminar
Seminar: Random Walks
Lecturer: Angelika Rohde
Assistant: Johannes Brutsche
Language: Talk/participation possible in German and English
Seminar: Mo, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Preliminary Meeting 22.07., Raum 232, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Preregistration: If your are interested in the seminar, please write an email to Johannes Brutsche listing your prerequisites in probability and note if you plan to attend the Probability Theory II.
Random walks are stochastic processes (in discrete time) formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. Many results that are part of this seminar also carry over to Brownian motion and related processes in continuous time. In particular, the theory for random walks contains many central and elegant proof ideas which can be extended to various other settings. We start the theory at the very beginning but quickly move on to proving local central limit theorems, study Green's function and recurrence properties, hitting times and the Gambler's ruin estimate. Further topics may include a dyadic coupling with Brownian motion, Dirichlet problems, random walks that are not indexed in \(\mathbb{N}\) but the lattice \(\mathbb{Z}^d\), and intersection probabilities for multidimensional random walks (which are processes \(X:\mathbb{N}\rightarrow\mathbb{R}^d\)). Here, we will see that in dimension \(d=1,2,3\) two paths hit each other with positive probability, while for \(d\geq 4\) they avoid each other almost surely.
Probability Theory I \
Some talks only require knowledge of Stochastics I, so if you are interested in the seminar and have not taken part in the probability theory I class, do not hesitate to reach out to us regarding a suitable topic.
Elective in Data
Mathematical Seminar
Seminar: Data-Driven Medicine from Routine Data
Lecturer: Nadine Binder
Note: Only for the degree programme "Mathematics in Data and Technology"
Imagine being able to use routine data such as diagnoses, lab results, and medication plans to answer medical questions in innovative ways and improve patient care. In this seminar, we will learn to identify relevant data, understand suitable analysis methods, and what to consider when applying them in practice. Together, we will analyze scientific studies on routine data and discuss clinical questions, the methods used, and their feasibility for implementation.
What makes this seminar special: Medical and mathematics students collaborate to understand scientific studies from both perspectives. When possible, you will work in pairs (or individually if no pair can be formed) to analyze a study from your respective viewpoints and prepare related presentations. You may test available programming code or develop your own approaches to replicate the methods and apply them to your own questions. The pairs can be formed during the preliminary meeting.
necessary: Basics in Applied Mathematics \
useful: Probability Theory I
Elective in Data
Mathematical Seminar