Preliminary course catalogue - changes and additions are likely.
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Basics in Applied Mathematics
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Computer exercise: 2 hours, date to be determined
Teacher: Sören Bartels, Moritz Diehl, Thorsten Schmidt
Language: in English
This course provides an introduction into the basic concepts, notions, definitions and results in probability theory, numerics and optimization, accompanied with programming projects in Python. Besides deepen mathematical skills in principle, the course lays the foundation of further classes in these three areas.
None that go beyond admission to the degree programme.
Basics in Applied Mathematics
Algebra and Number Theory
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Language: in German
This lecture continues the linear algebra courses. It treats groups, rings, fields and applications in the number theory and geometry. The highlights of the lecture are the classification of finite fields, the impossibility of the trisection of angles with circle and ruler, the non-existence of a solution formula for the general equations of fifth degree and the quadratic reciprocity law.
Required: Linear Algebra~I and II
Elective
Algebraic Topology
Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Maximilian Stegemeyer
Language: in German
Elective
Analysis III
Lecture: Mo, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
Teacher: Michael Růžička
Language: in German
Lebesgue measure and measure theory, Lebesgue integral on measure spaces and Fubini's theorem, Fourier series and Fourier transform, Hilbert spaces. Differential forms, their integration and outer derivative. Stokes' theorem and Gauss' theorem.
Required: Analysis I and II, Linear Algebra I
Elective in Data
Complex Analysis
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Stefan Kebekus
Language: in German
Complex analysis deals with functions \(f : \mathbb C \to \mathbb C\) , which map complex numbers to complex numbers. Many concepts of Analysis~I can be directly transferred to this case, e.\,g. the definition of differentiability. One might expect that this would lead to a theory analogous to Analysis~I but much more is true: in many respects you get a more elegant and simpler theory. For example, complex differentiability on an open set implies that a function is even infinitely often differentiable, and this is further consistent with analyticity. For real functions, all these notions are different. However, some new ideas are also necessary: For real numbers \(a\), \(b\) one integrates for \[\int_a^b f(x) \mathrm dx\] over the elements of the interval \([a, b]\) or \([b, a]\). However, if \(a\), \(b\) are complex numbers, it is no longer so clear clear how such an integral is to be calculated. One could, for example, in the complex numbers along the line that connects \(a, b \in \mathbb C\), or along another curve that leads from \(a\) to \(b\). Does this lead to a well-defined integral term or does such a curve integral depend on the choice of the curve?
Required: Analysis I+II, Linear Algebra I
Elective
Introduction to Theory and Numerics of Partial Differential Equations
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Patrick Dondl
Language: in English
The aim of this course is to give an introduction into theory of linear partial differential equations and their finite difference as well as finite element approximations. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensable tool in science and technology. We provide an introduction to the construction, analysis, and implementation of finite element methods for different model problems. We will address elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.
Required: Analysis~I and II, Linear Algebra~I and II as well as knowledge about higher-dimensional integration (e.g. from Analysis~III or Extensions of Analysis) \ Recommended: Numerics for differential equations, Functional analysis
Advanced Lecture in Numerics
Elective in Data
Mathematical Statistics
Lecture: Di, Do, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Ernst August v. Hammerstein
Language: in English
The lecture builds on basic knowledge about Probability Theory. The fundamental problem of statistics is to infer from a sample of observations as precise as possible statements about the data-generating process or the underlying distributions of the data. For this purpose, the most important methods from statistical decision theory such as test and estimation methods are introduced in the lecture. \\ Key words hereto include Bayes estimators and tests, Neyman-Pearson test theory, maximum likelihood estimators, UMVU estimators, exponential families, linear models. Other topics include ordering principles for reducing the complexity of models (sufficiency and invariance). Statistical methods and procedures are used not only in the natural sciences and medicine, but in almost all areas in which data is collected and analyzed This includes, for example, economics (“econometrics”) and the social sciences (especially psychology). However, in the context of this lecture, we will focus less on applications, but---as the name suggests---more on the mathematical justification of the methods.
Required: Probability Theory (in particular measure theory and conditional probabilities/expectations)
Advanced Lecture in Stochastics
Elective in Data
Model Theory
Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Elective
Probabilistic Machine Learning
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Giuseppe Genovese
Assistant: Sebastian Stroppel
Advanced Lecture in Stochastics
Elective in Data
Probability Theory II – Stochastic Processes
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Angelika Rohde
Language: in English
Advanced Lecture in Stochastics
Elective in Data
Calculus of Variations
Lecture: Mo, Mi, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Guofang Wang
Assistant: Florian Johne
Language: in German
Elective
Futures and Options
Lecture: Mo, 10-12h, -, -
Exercise session: Di, 8-10h, -, -
Teacher: Eva Lütkebohmert-Holtz
Language: in English
This course covers an introduction to financial markets and products. Besides futures and standard put and call options of European and American type we also discuss interest-rate sensitive instruments such as swaps.
For the valuation of financial derivatives we first introduce financial models in discrete time as the Cox--Ross--Rubinstein model and explain basic principles of risk-neutral valuation. Finally, we will discuss the famous Black--Scholes model which represents a continuous time model for option pricing.
Required: Elementary Probability Theory~I
Elective in Data
Machine Learning and Mathematical Logic
Lecture: Do, 14-16h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Maxwell Levine
Language: in English
Elective in Data
Markov Chains
Lecture: Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: David Criens
Language: in English
The class of Markov chains is an important class of (discrete-time) stochastic processes that are used frequently to model for example the spread of infections, queuing systems or switches of economic scenarios. Their main characteristic is the Markov property, which roughly means that the future depends on the past only through the current state. In this lecture we provide the mathematical foundation of the theory of Markov chains. In particular, we learn about path properties, such as recurrence and transience, state classifications and discuss convergence to the equilibrium. We also study extensions to continuous time. On the way we discuss applications to biology, queuing systems and resource management. If the time allows, we also take a look at Markov chains with random transition probabilities, so-called random walks in random environment, which is a prominent model in the field of random media.
Required: Elementary Probability Theory~I \ Recommended: Analysis~III, Probability Theory~I
Elective in Data
Measure Theory
Teacher: Peter Pfaffelhuber
Assistant: Samuel Adeosun
Language: in English
Measure Theory is the foundation of advanced probability theory. In this course, we build on knowledge in analysis and provide all necessary results for later classes in statistics, probabilistic machine learning and stochastic processes. It contains set systems, constructions of measures using outer measures, the integral, and product measures.
Required: Basic courses in analysis, and an understanding of mathematical proofs.
Elective in Data
Mathematical Introduction to Deep Neural Networks
Lecture: Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Diyora Salimova
Language: in English
Elective in Data
Numerical Optimal Control
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Teacher: Moritz Diehl
Language: in English
The aim of the course is to give an introduction to numerical methods for the solution of optimal control problems in science and engineering. The focus is on both discrete time and continuous time optimal control in continuous state spaces. It is intended for a mixed audience of students from mathematics, engineering and computer science.
The course covers the following topics:
The lecture is accompanied by intensive weekly computer exercises offered both in MATLAB and Python (6~ECTS) and an optional project (3~ECTS). The project consists in the formulation and implementation of a self-chosen optimal control problem and numerical solution method, resulting in documented computer code, a project report, and a public presentation.
Required: Analysis~I and II, Linear Algebra~I and II \ Recommended: Numerics I, Ordinary Differential Equations, Numerical Optimization
Elective in Data
Theory and Numerics for Partial Differential Equations – ??
Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Sören Bartels
Language: in English
Elective in Data
Learning by Teaching
Organisation: Susanne Knies
Language: in German
What characterizes a good tutorial? This question will be discussed in the first workshop and tips and suggestions will be given. Experiences will be shared in the second workshop.
Elective
Computer exercises for 'Introduction to Theory and Numerics of Partial Differential Equations'
Teacher: Patrick Dondl
Language: in English
Elective
Computer exercises for 'Theory and Numerics of Partial Differential Equations'
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
Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Sören Bartels
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: Medical Data Science
Seminar: Mi, 10:15-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary Meeting 17.07., HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
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: Minimal Surfaces
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Guofang Wang
Elective
Seminar
Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Elective
Seminar
Seminar: Mo, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Angelika Rohde
Elective in Data
Mathematical Seminar
Graduate Student Speaker Series
Mi, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Organisation: Sören Bartels, Ernst August v. Hammerstein
In the Graduate Student Speaker Series, students of the M.Sc. degreee programme ‘Mathematics in Data and Technology’ talk about their Master's thesis or their programming projects, and the lecturers of the programme talk about their fields of work.
Graduate Student Speaker Series