Preliminary course catalogue - changes and additions are likely.
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Analysis I
Lecture: Di, Mi, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
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Teacher: Ernst Kuwert
Assistant: Xuwen Zhang
Language: in German
Analysis I is one of the two basic lectures in the mathematics course. It deals with concepts based on the notion of limit. The central topics are: induction, real and complex numbers, convergence of sequences and series, completeness, exponential function and trigonometric functions, continuity, derivation of functions of one variable and regulated integrals.
Required: High school mathematics. \ Attendance of the preliminary course (for students in mathematics) is recommended.
Analysis
Linear Algebra I
Lecture: Mo, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
Teacher: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: in German
Linear Algebra I is one of the two introductory lectures in the mathematics degree program that form the basis for further courses. Topics covered include: fundamental concepts (in particular fundamental concepts of set theory and equivalence relations), groups, fields, vector spaces over arbitrary fields, basis and dimension, linear mappings and transformation matrix, matrix calculus, linear systems of equations, Gaussian elimination, linear forms, dual space, quotient vector spaces and homomorphism theorem, determinant, eigenvalues, polynomials, characteristic polynomial, diagonalizability, affine spaces. The background to the mathematical content is explained in terms of ideas and the history of mathematics.
Required: High school mathematics. \ Attendance of the preliminary course (for students in mathematics) is recommended.
Linear Algebra
Numerics I
Lecture: Mi, 14-16h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
Teacher: Patrick Dondl
Language: in German
Numerics is a sub-discipline of mathematics that deals with the practical solution of mathematical problems. As a rule, problems are not solved exactly but approximately, for which a sensible compromise between accuracy and computational effort must be found. The first part of the two-semester course focuses on questions of linear algebra such as solving linear systems of equations and determining the eigenvalues of a matrix. Attendance at the accompanying practical exercises ({\em Praktische Übung zur Numerik}) is recommended. These take place every 14 days, alternating with the lecture's tutorial.
Required: Linear Algebra~I \ Recommended: Linear Algebra~II and Analysis~I (required for Numerics~II)
Numerics
Elementary Probability Theory I
Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
Sir-in Exam: Date to be announced
Teacher: Thorsten Schmidt
Language: in German
Stochastic is, to put it loosely, the “mathematics of chance”, about which---possibly contrary to first impressions---many precise and not at all random statements can be formulated and proven. The aim of the lecture is to give an introduction to stochastic modeling, to explain some basic concepts and results of Stochastic and to illustrate them with examples. It is also intended as a motivating preparation for the lecture “Probability Theory” in the summer semester, especially for students in the B.Sc. in Mathematics. Topics covered include: Discrete and continuous random variables, probability spaces and measures, combinatorics, expected value, variance, correlation, generating functions, conditional probability, independence, weak law of large numbers, central limit theorem. The lecture Elementary Probability Theory~II in the summer semester will mainly be devoted to statistical topics. If you are interested in a practical, computer-supported implementation of individual lecture contents, participation in the regularly offered practical excercise “Praktischen Übung Stochastik" is also recommended (in parallel or subsequently).
Required: Linear Algebra~I, Analysis~I and II. \ Note that Linear Algebra~I can be attended in parallel.
Elementary Probability Theory I
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Analysis III
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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)
Compulsory Elective in Mathematics
Model Theory
Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
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 in Numerics
Teacher: Patrick Dondl
Language: in German
Numerics
Computer exercises for 'Theory and Numerics of Partial Differential Equations'
Please note the registration modalities for the individual proseminars 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 examination; the registration period runs from August 1, 2025 to October 8, 2025; if you would like to attend a proseminar but have not been allocated a place, please contact the degree program coordinator immediately.
Undergraduate seminar: Elementary Number Theory
Seminar: Mi, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer
Undergraduate Seminar
Undergraduate seminar: Ordinary Differential Equations
Seminar: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Diyora Salimova
Undergraduate Seminar
Undergraduate seminar: Graph Theroy
Seminar: Di, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Heike Mildenberger
Undergraduate Seminar
Seminar
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.
M.Ed.-Seminar (nach Praxissemester)
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
Compulsory Elective in Mathematics
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.
Compulsory Elective in Mathematics
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
Compulsory Elective in Mathematics
Mathematical Seminar
Seminar
Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Compulsory Elective in Mathematics
Mathematical Seminar
Seminar
Seminar: Mo, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Angelika Rohde
Compulsory Elective in Mathematics
Mathematical Seminar