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Functional Analysis
Lecturer: Guofang Wang
Language: in English
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
Attention: Change of time and room!
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
Pure Mathematics
Applied Mathematics
Elective
Commutative Algebra and Introduction to Algebraic Geometry
Lecturer: Abhishek Oswal
Language: in English
Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
In linear algebra you studied linear systems of equations. In commutative algebra, we study polynomial equation systems such as \(x^2+y^2 = \) 1 and their solution sets, the algebraic varieties. It will turn out that such a variety is closely related to the ring of the restrictions of polynomial functions on that variety, and that we can extrapolate this relationship to a geometric understanding of any commutative rings, in particular the ring of the integers. Commutative algebra, algebraic geometry, and number theory grow together in this conceptual building. The lecture aims to introduce into this conceptual world. We will especially focus on the dimension of algebraic varieties and their cutting behavior, which generalizes the phenomena known from the linear algebra on the case of polynomial equation systems.
necessary: Linear Algebra I+II
useful: Algebra and Number Theory
Pure Mathematics
Elective
Mathematics
Concentration Module
Mathematical Logic
Lecturer: Markus Junker
Language: in German
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
This introductory course in mathematical logic consists of several parts. It the basics of predicate logic and a brief introduction to model theory and the axiom system as well as the axiom system of set theory. The aim of the lecture is to explain the recursion-theoretical content of the predicate calculus, in particular the so-called Peano-arithmetic and Gödel's incompleteness theorems.
Basic knowledge of mathematics from first semester lectures
Pure Mathematics
Elective
Probability Theory
Lecturer: Thorsten Schmidt
Language: in English
Lecture: Fr, 8-10h, HS II, Albertstr. 23b, Do, 12-14h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
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
Applied Mathematics
Elective
Probability Theory III: Stochastic Analysis
Lecturer: Angelika Rohde
Language: in English
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
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)
Applied Mathematics
Elective
Mathematics
Concentration Module
Topology
Lecturer: Heike Mildenberger
Assistant: Simon Klemm
Language: in German
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
A topological space consists of a basic set \(X\) and a family of open subsets of the basic set, which is called topology on \(X\). Examples over the basic sets \(\mathbb R\) and \({\mathbb R}^n\) are given in the analysis lectures. The mathematical subject \glqq{}Topology\grqq\ is the study of topological spaces and the investigation of topological spaces. Our lecture is an introduction to set-theoretic and algebraic topology.
Analysis I and II, Linear Algebra I
Pure Mathematics
Elective
Reading courses
Lecturer: 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
Algorithmic Aspects of Data Analytics and Machine Learning
Lecturer: Sören Bartels
Language: in English
Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
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"
Applied Mathematics
Elective
Mathematics
Concentration Module
Introduction to Theory and Numerics of Stochastic Differential Equations
Lecturer: Diyora Salimova
Language: in English
Lecture: Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
Applied Mathematics
Elective
Mathematics
Concentration Module
Mathematical Physics II
Lecturer: Chiara Saffirio
Language: in English
Lecture: Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
Applied Mathematics
Elective
Mathematics
Concentration Module
Mathematical Time Series Analysis II
Lecturer: Rainer Dahlhaus
Language: in English
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.
Applied Mathematics
Elective
Mathematics
Concentration Module
Numerical Optimization
Lecturer: Moritz Diehl
Language: in English
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Sit-in exam: date to be announced
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
Applied Mathematics
Elective
Mathematics
Concentration Module
Learning by Teaching
Organisation: Katharina Böcherer-Linder, 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
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Computer Exercises
Lecturer: Peter Pfaffelhuber
Language: in English
Mo, 12-14h, SR 127, Ernst-Zermelo-Str. 1
Elective
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 course catalogue: As a rule, places are allocated at the preliminary meeting at the end of the summer semester lecture period. You must then register for the examination in HISinOne; the registration period is expected to run from 1 March to 15 April 2026.
Seminar: Algebraic D-Modules
Lecturer: Annette Huber-Klawitter
Assistant: Ben Snodgrass
Language: Talk/participation possible in German and English
Seminar: Mo, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Preliminary Meeting
Mathematical Seminar
Elective
Seminar: Approximation Properties of Deep Learning
Lecturer: Diyora Salimova
Language: Talk/participation possible in German and English
Seminar: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration: by e-mail to Diyora Salimova
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Mathematical Seminar
Elective
Seminar on representation theory
Lecturer: Wolfgang Soergel
Language: Talk/participation possible in German and English
Seminar: Do, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preregistration: by e-mail to Wolfgang Soergel
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Mathematical Seminar
Elective
Seminar: Strong Homologies, Derived Limites, and Set Theory
Lecturer: Heike Mildenberger
Assistant: Maxwell Levine
Language: Talk/participation possible in German and English
Seminar: Di, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Mathematical Seminar
Elective
Seminar on probability theory
Lecturer: Angelika Rohde
Language: Talk/participation possible in German and English
Mathematical Seminar
Elective
Seminar: String Topology
Lecturer: Nadine Große
Assistant: Maximilian Stegemeyer
Language: Talk/participation possible in German and English
Seminar: Di, 12-14h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Mathematical Seminar
Elective
Seminar: Topics in the Calculus of Variations
Lecturer: Patrick Dondl, Guofang Wang
Language: Talk/participation possible in German and English
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
In HISinOne: no course registration, but exam registration until 15 April 2026.
Mathematical Seminar
Elective
Seminar: Medical Data Science
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 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.
Mathematical Seminar
Elective