Preliminary course catalogue - changes and additions are likely.
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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
Pure Mathematics
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module
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)
Applied Mathematics
Elective
Mathematics
Concentration Module
Model Theory
Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Pure Mathematics
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module
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
Pure Mathematics
Elective
Mathematics
Concentration Module
Reading courses
Teacher: All professors and 'Privatdozenten' of the Mathematical Institute
Language: Talk/participation possible in German and English
In a reading course, the material of a four-hour lecture is studied in supervised self-study. In rare cases, this may take place as part of a course; however, reading courses are not usually listed in the course catalog. If you are interested, please contact a professor or a private lecturer before the start of the course; typically, this will be the supervisor of your Master's thesis, as the reading course ideally serves as preparation for the Master's thesis (both in the M.Sc. and the M.Ed. programs).
The content of the reading course, the specific details, and the coursework requirements will be determined by the supervisor at the beginning of the lecture period. The workload should be equivalent to that of a four-hour lecture with exercises.
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module
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
Pure Mathematics
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module
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
Applied Mathematics
Elective
Mathematics
Concentration Module