Attention: There are some short-term room changes!
Lecture: Mo, 12-14h, HS II, Albertstr. 23b, Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Sir-in Exam: Date to be announced
Attention: Change of time and room!
Teacher: Patrick Dondl
Assistant: Luciano Sciaraffia
Language: in German
Linear functional analysis, which is the subject of the lecture, uses concepts of linear algebra such as vector space, linear operator, dual space, scalar product, adjoint map, eigenvalue, spectrum to solve equations in infinite-dimensional function spaces, especially linear differential equations. The algebraic concepts have to be extended by topological concepts such as convergence, completeness and compactness.
This approach was developed at the beginning of the 20th century by Hilbert, among others, and is now part of the methodological foundation of analysis, numerics and mathematical physics, in particular quantum mechanics, and is also indispensable in other mathematical areas.
Linear Algebra I+II, Analysis I–III
Elective in Data
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, date to be determined
22.09., 10:00-12:00
Teacher: Angelika Rohde
Assistant: Johannes Brutsche
Language: in English
The problem of axiomatising probability theory was solved by Kolmogorov in 1933: a probability is a measure of the set of all possible outcomes of a random experiment. From this starting point, the entire modern theory of probability develops with numerous references to current applications.
The lecture is a systematic introduction to this area based on measure theory and includes, among other things, the central limit theorem in the Lindeberg-Feller version, conditional expectations and regular versions, martingales and martingale convergence theorems, the strong law of large numbers and the ergodic theorem as well as Brownian motion.
necessary: Analysis I+II, Linear Algebra I, Elementary Probability Theory I
useful: Analysis III
Advanced Lecture in Stochastics
Elective in Data
Lecture: Mi, 14-16h, HS II, Albertstr. 23b, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: David Criens
Assistant: Samuel Adeosun
Language: in English
This lecture builds the foundation of one of the key areas of probability theory: stochastic analysis. We start with a rigorous construction of the It^o integral that integrates against a Brownian motion (or, more generally, a continuous local martingale). In this connection, we learn about It^o's celebrated formula, Girsanov’s theorem, representation theorems for continuous local martingales and about the exciting theory of local times. Then, we discuss the relation of Brownian motion and Dirichlet problems. In the final part of the lecture, we study stochastic differential equations, which provide a rich class of stochastic models that are of interest in many areas of applied probability theory, such as mathematical finance, physics or biology. We discuss the main existence and uniqueness results, the connection to the martingale problem of Stroock-Varadhan and the important Yamada-Watanabe theory.
Probability Theory I and II (Stochastic Processes)
Advanced Lecture in Stochastics
Elective in Data
Lecture: Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English
The lecture addresses algorithmic aspects in the practical realization of mathematical methods in big data analytics and machine learning. The first part will be devoted to the development of recommendation systems, clustering methods and sparse recovery techniques. The architecture and approximation properties as well as the training of neural networks are the subject of the second part. Convergence results for accelerated gradient descent methods for nonsmooth problems will be analyzed in the third part of the course. The lecture is accompanied by weekly tutorials which will involve both, practical and theoretical exercises.
Lectures "Numerik I, II" or lecture "Basics in Applied Mathematics"
Elective in Data
Lecture: Mo, 14-16h, HS II, Albertstr. 23b
Exercise session: Mi, 16-18h, SR 403, Ernst-Zermelo-Str. 1
Teacher: Ernst August v. Hammerstein
Assistant: Sebastian Hahn
Language: in English
Lévy processes are the continuous-time analogues of random walks in discrete time as they possess, by definition, independent and stationary increments. They form a fundamental class of stochastic processes which has widespread applications in financial and insurance mathematics, queuing theory, physics and telecommunication. The Brownian motion and the Poisson process, which may already be known from other lectures, also belong to this class. Despite their richness and flexibility, Lévy processes are usually analytically and numerically very tractable because their distributions are generated by a single univariate distribution which has the property of infinite divisibility.
The lecture starts with an introduction into infinitely divisible distributions and the derivation of the famous Lévy-Khintchine formula. Then it will be explained how the Lévy processes emerge from these distributions and how the characteristics of the latter influence the path properties of the corresponding processes. Finally, after a short look at the method of subordination, option pricing in Lévy-driven financial models will be discussed.
necessary: Probability Theory I
useful: Probability Theory II (Stochastic Processes)
Elective in Data
Lecture: Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Thorsten Schmidt
Assistant: Simone Pavarana
Language: in English
In this lecture we will study new and highly efficient tools from machine learning which are applied to stochastic problems. This includes neural SDEs as a generalisation of stochastic differential equations relying on neural networks, transformers as a versatile tool not only for languages but also for time series, transformers and GANs as generator of time series and a variety of applications in Finance and insurance such as (robust) deep hedging, signature methods and the application of reinforcement learning.
The prerequisites are stochastics, for some parts we will require a good understanding of stochastic processes. A (very) short introduction will be given in the lectures – so for fast learners it would be possible to follow the lectures even without the courses on stochastic processes.
Elective in Data
Lecture: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Patrick Dondl
Assistant: Eric Trébuchon
Language: in English
This course provides a comprehensive introduction to mathematical modeling. We will learn the systematic process of translating real-world problems into mathematical frameworks, analyzing them using appropriate mathematical tools, and interpreting the results in practical contexts. The course covers both discrete and continuous modeling approaches, with emphasis on differential equations, variational problems, and optimization techniques. Through case studies in physics, biology, engineering, and economics, students will develop skills in model formulation, validation, and refinement. Special attention is given to dimensional analysis, stability theory, and numerical methods necessary for implementing solutions with a focus on numerical methods for ordinary differential equations. The course combines theoretical foundations with hands-on experience in computational tools for model simulation and analysis.
Analysis I, II, Linear Algebra I, II, Numerics I, II
Elective in Data
Numerical Optimization
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Sir-in Exam: Date to be announced
Teacher: Moritz Diehl
Assistant: Léo Simpson
Language: in English
The aim of the course is to give an introduction into numerical methods for the solution of optimization problems in science and engineering. The focus is on continuous nonlinear optimization in finite dimensions, covering both convex and nonconvex problems. The course divided into four major parts:
The course is organized as inverted classroom based on lecture recordings and a lecture manuscript, with weekly alternating Q&A sessions and exercise sessions. The lecture is accompanied by intensive computer exercises offered in Python (6 ECTS) and an optional project (3 ECTS). The project consists in the formulation and implementation of a self-chosen optimization problem or numerical solution method, resulting in documented computer code, a project report, and a public presentation. Please check the website for further information.
necessary: Analysis I–II, Linear Algebra I–II
useful: Introduction to Numerics
Elective in Data
Seminar: Mo, 12-14h, online, -
Preregistration: by e-mail to Diyora Salimova
Preliminary Meeting 14.04., 15:00, via zoom (please write the lecturer in case the time slot does not fit you)
Preparation meetings for talks: Dates by arrangement
Teacher: Diyora Salimova
Language: Talk/participation possible in German and English
In recent years, deep learning have been successfully employed for a multitude of computational problems including object and face recognition, natural language processing, fraud detection, computational advertisement, and numerical approximations of differential equations. Such simulations indicate that neural networks seem to admit the fundamental power to efficiently approximate high-dimensional functions appearing in these applications.
The seminar will review some classical and recent mathematical results on approximation properties of deep learning. We will focus on mathematical proof techniques to obtain approximation estimates on various classes of data including, in particular, certain types of PDE solutions.
Basics of functional analysis, numerics of differential equations, and probability theory
Elective in Data
Mathematical Seminar
Teacher: Harald Binder
Language: Talk/participation possible in German and English
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: Numerics of Partial Differential Equations
Seminar: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 04.02., 12:00, Raum 209, Hermann-Herder-Str. 10, Or registration by e-mail to Sören Bartels.
Teacher: Sören Bartels
Assistant: Vera Jackisch, Tatjana Schreiber
Language: Talk/participation possible in German and English
The seminar will cover advanced topics in the theory and numerics of partial differential equations. This includes the iterative solution of the resulting linear systems of equations with multigrid and domain decomposition methods, the adaptive refinement of finite element grids, the derivation of an approximation theory with explicit constants, and the solution of nonlinear problems.
Introduction to Theory and Numerics of Partial Differential Equations
Elective in Data
Mathematical Seminar
Seminar: The Wiener Chaos Decomposition and (Non-)Central Limit Theorems
Teacher: Angelika Rohde
Language: Talk/participation possible in German and English
Elective in Data
Mathematical Seminar
Note: Only for the degree programme "Mathematics in Data and Technology"
Teacher: Nadine Binder
Language: Talk/participation possible in German and English
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 Appiled Mathematics
useful: Probability Theory I
Elective in Data
Mathematical Seminar
Details: please click on the title and follow the link!
Computational Economics
Lecture: Mi, 14-16h, Paulussaal, Pauluskirche
Exercise session: Mi, 8-10h, HS 1098, KG I
Course offered by the Institute for Economics
Teacher: Dirk Neumann
Elective in Data
Foundations of Artificial Intelligence
Lecture: Mi, 14-16h, HS 00-026, Georges-Köhler-Allee 101
Exercise session: Fr, 10-12h, verschiedene Räume, -
Course offered by the Faculty of Engineering
Teacher: Joschka Boedecker, Abhinav Valada
Elective in Data
Image Processing and Computer Graphics
Lecture (3 hours): Di, 14-16h, HS 00-036, Georges-Köhler-Allee 101, Mi, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Tutorial (1 hour): Mi, 10-12h, verschiedene Räume, -
Course offered by the Faculty of Engineering
Teacher: Thomas Brox, Matthias Teschner
Elective in Data
Course offered by the Institute for Economics
Teacher: Ekaterina Kazak
Elective in Data
Further courses can be admitted as Elective in Data or as Elective after consultation with the Examination Board.