Preliminary course catalogue - changes and additions are still possible.
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New (and partly not yet in den annotated course catalogue):
Lecturer: Eva Lütkebohmert-Holtz
Language: in English
Lecture: Mo, 10-12h, HS 1015, KG I
Exercise session: Di, 8-10h, HS 1098, KG I
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
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.
Elementary Probability Theory I
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Linear Algebraic Groups
Lecturer: Abhishek Oswal
Assistant: Damian Sercombe
Language: in English
Lecture: Mo, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
There is no information available yet.
There is no information available yet.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Maxwell Levine
Language: in English
Lecture: Do, 14-16h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
Developments in artificial intelligence have boomed in recent years, holding the potential to reshape not just our daily routines but also society at large. Many bold claims have been made regarding the power and reach of AI. From a mathematical perspective, one is led to ask: What are its limitations? To what extent does our knowledge of reasoning systems in general apply to AI?
This course is intended to provide some applications of mathematical logic to the field of machine learning, a field within artificial intelligence. The goal of the course is to present a breadth of approachable examples.
The course will include a gentle introduction to machine learning in a somewhat abstract setting, including the notions of PAC learning and VC dimension. Connections to set theory and computability theory will be explored through statements in machine learning that are provably undecidable. We will also study some applications of model theory to machine learning.
The literature indicated in the announcement is representative but tentative. A continuously written PDF of course notes will be the main resource for students.
Background in basic mathematical logic is strongly recommended. Students should be familiar with the following notions: ordinals, cardinals, transfinite induction, the axioms of ZFC, the notion of a computable function, computable and computably enumerable sets (a.k.a. recursive and recursively enumerable sets), the notions of languages and theories and structures as understood in model theory, atomic diagrams, elementarity, and types. The concepts will be reviewed briefly in the lectures. Students are not expected to be familiar with the notion of forcing in set theory.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Markov Chains
Lecturer: David Criens
Language: in English
Lecture: Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
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
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Diyora Salimova
Assistant: Ilkhom Mukhammadiev
Language: in English
Lecture: Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
The course will provide an introduction to deep learning algorithms with a focus on the mathematical understanding of the objects and methods used. Essential components of deep learning algorithms will be reviewed, including different neural network architectures and optimization algorithms. The course will cover theoretical aspects of deep learning algorithms, including their approximation capabilities, optimization theory, and error analysis.
Analysis I and II, Lineare Algebra I and II
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematical Time Series Analysis
Lecturer: Rainer Dahlhaus
Lecture: Do, 10-12h, SR 127, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
From a narrow perspective, time series analysis is the statistical study of the properties of stochastic processes in discrete time. In this lecture, we will take a broader view: First we will examine the important probabilistic properties of stationary processes, including strong laws of large numbers (based on the Ergodic theorem) and various versions of the central limit theorem (for processes with strong dependence, even the rate of convergence can change). Another exciting topic is the relation between stationary processes and Fourier analysis based on the Cramér-representation, in which a stationary process is represented as a Fourier-integral of a stochastic process in continuous time (such as the Brownian motion). This later leads, on the statistical side, to a quasi-maximum likelihood method in the frequency domain. Furthermore, we investigate linear and nonlinear time series models, the prediction of time series, linear filters, linear state space models, model selection, maximum likelihood and quasi maximum likelihood methods, the Toeplitz-theory for quadratic forms of stationary processes. Finally, we provide an outlook on locally stationary processes, where the process can be locally apprximated by stationary processes.
Elementary Probability Theory I (Stochastik I) and Probability Theory (Wahrscheinlichkeitstheorie)
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Moritz Diehl
Language: in English
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Lecture: asynchronous (videos)
Sit-in exam: date to be announced
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
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
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English
Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
The lecture addresses the development and analysis of numerical methods for the approximation of certain nonlinear partial differential equations. The considered model problems include harmonic maps into spheres and total-variation regularized minimization problems. For each of the problems, a suitable finite element discretization is devised, its convergence is analyzed and iterative solution procedures are developed. The lecture is complemented by theoretical and practical lab tutorials in which the results are deepened and experimentally tested.
'Introduction to Theory and Numerics for PDEs' or 'Introduction to PDEs'
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Topics in Mathematical Physics
Lecturer: Chiara Saffirio
Language: in English
Lecture: Mo, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
This course provides an introduction to analytical methods in mathematical physics, with a particular emphasis on many-body quantum mechanics. A central focus is the rigorous proof of the stability of matter for Coulomb systems, such as atoms and molecules. The key question - why macroscopic objects made of charged particles do not collapse under electromagnetic forces - remained unresolved in classical physics and lacked even a heuristic explanation in early quantum theory. Remarkably, the proof of stability of matter marked the first time that mathematics offered a definitive answer to a fundamental physical and stands as one of the early triumphs of quantum mechanics.
Content:
Analysis III and Linear Algebra are required. \
No prior knowledge of physics is assumed; all relevant physical concepts will be introduced from scratch.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Mikhail Tëmkin
Language: in English
Lecture: Mo, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
Real-world data is often given as a finite set of points in ℝⁿ, called a point cloud. Topological data analysis aims to extract features of a point cloud algorithmically. At its core, it is a pipeline of tools from pure mathematics. These tools are of fundamental theoretical importance, and many have practical applications of their own (which the course will briefly discuss). The tools span geometry (convex sets, Delaunay triangulation), topology (simplicial and chain complexes, homology), and algebra (quivers). The course provides a thorough introduction to them and culminates by assembling them into persistent homology, the main object of study in topological data analysis. Although targeted at students in the “Mathematics in Data and Technology” program, it may also interest pure mathematicians because of the close interplay between the two areas.
Linear Algebra
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Organisation: Susanne Knies
Language: in German
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
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.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.School Mathematical Aspects of Analysis and Linear Algebra
Lecturer: Katharina Böcherer-Linder, Markus Junker
Language: in German
Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Computer exercises for 'Introduction to Theory and Numerics of Partial Differential Equations'
Lecturer: Patrick Dondl
Assistant: Ludwig Striet, Oliver Suchan
Language: in English
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
The computer tutorial accompanies the lecture with programming exercises.
See the lecture – additionally: programming knowledge.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Patrick Dondl
Assistant: Alen Kushova
Language: in German
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
In the computer tutorial accompanying the Numerics (first term) lecture the algorithms developed and analyzed in the lecture are put into practice and and tested experimentally. The implementation is carried out in the programming languages Matlab, C++ and Python. Elementary programming knowledge is assumed.
See the lecture {\em Numerics I} (which should be attended in parallel or should already have been completed). \ Additionally: Elementary programming knowledge.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Computer exercises for 'Theory and Numerics of Partial Differential Equations – Selected Nonlinear Problems'
Lecturer: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
In the practical exercises accompanying the lecture 'Theory and Numerics for Partial Differential Equations – Selected Nonlinear Problems', the algorithms developed and analyzed in the lecture are implemented and tested experimentally. The implementation can be carried out in the programming languages Matlab, C++ or Python. Elementary programming knowledge is assumed.
see lecture
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.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.
Lecturer: Susanne Knies
Assistant: Jonah Reuß
Language: in German
Remaining places in the M.Ed. seminar after the school practical semester can be allocated as undergraduate seminar places. For more information see there!
In HISinOne: no course registration, but exam registration until 8 October 2025.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.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.
Lecturer: Susanne Knies
Assistant: Jonah Reuß
Language: in German
The seminar is preferably intended for M.Ed. students. Remaining places can be allocated as undergraduate seminar places.
In HISinOne: no course registration, but exam registration until 8 October 2025.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.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
In HISinOne: no course registration, but exam registration until 8 October 2025.
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.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Wolfgang Soergel
Assistant: Niklas Müller
Language: Talk/participation possible in German and English
Seminar: Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Preregistration: In case of interest, please email to Wolfgang Soergel
Preliminary Meeting 17.07., 12:15, SR 403, Ernst-Zermelo-Str. 1
In HISinOne: no course registration, but exam registration until 8 October 2025.
Structure of noncommutative rings with applications to representations of finite groups.
necessary: Linear Algebra I and II \
useful: Algebra and Number Theory
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
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
In HISinOne: no course registration, but exam registration until 8 October 2025.
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.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Guofang Wang
Language: Talk/participation possible in German and English
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 30.07., SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
In HISinOne: no course registration, but exam registration until 8 October 2025.
Minimal surfaces are surfaces in space with a ‘minimal’ area and can be described using holomorphic functions. They appear, for example, in the investigation of soap skins and the construction of stable objects (e.g. in architecture). Elegant methods from various mathematical fields such as complex analysis, calculus of variations, differential geometry, and partial differential equations are used to analyse minimal surfaces.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.
Lecturer: Angelika Rohde
Assistant: Johannes Brutsche
Language: Talk/participation possible in German and English
Seminar: Mo, 16-18h, SR 127, Ernst-Zermelo-Str. 1
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.
Preliminary Meeting 22.07., 14:00, Raum 232, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
In HISinOne: no course registration, but exam registration until 8 October 2025.
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.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.