Organisation: Susanne Knies
Language: in German

The bridge course is aimed at students in a double major bachelor's programme who are taking Analysis II without having taken Linear Algebra I. Please register by 14 April in HISInOne!

Content

The course consists of self-study lecture notes and accompanying tutorials. The bridge course covers the basic knowledge of linear algebra required for Analysis II. It does not replace the linear algebra lectures.

Language: in German

Lecturer: Ernst Kuwert
Assistant: Xuwen Zhang
Language: in German

Time and place

Lecture: Mo, Mi, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

Content

Analysis II is the continuation of Analysis I from the winter semester and one of the basic lectures of the study programmes in Mathematics.

Previous knowledge

Analysis I, Linear Algebra I (or bridge course linear algebra)

Usability

Analysis (2HfB21, BSc21, MEH21, MEB21)
Analysis II (BScInfo, BScPhys)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: in German

Time and place

Lecture: Di, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

Content

Linear algebra II is the continuation of the lecture linear algebra I from the winter semester and one of the basic courses of math studies.

Central topics are: Jordan’s normal form of endomorphisms, symmetrical bilinear forms with especially the Sylvester’s theorem, Euclidian and Hermitian vector spaces, skalar products, orthonormal bases, orthogonal and (self-) adjugated , spectral theorem, principal axis theorem.

Previous knowledge

Linear Algebra I

Usability

Linear Algebra (2HfB21, BSc21, MEH21)
Linear Algebra (MEB21)
Linear Algebra II (BScInfo, BScPhys)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Wolfgang Soergel
Assistant: Damian Sercombe
Language: in German

Time and place

Lecture: Fr, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 24.07., 14:00-17:00, HS Rundbau, Albertstr. 21
Sit-in exam (resit) 16.10., 14:00-17:00, HS Rundbau, Albertstr. 21

Content

The lecture gives an introduction to elementary geometry in Euclidian and non-Euclidian space and its mathematical foundations. We get to know Euclidean, hyperbolic, and projective geometry as examples of incidence geometries, and study their symmetry groups.

The next main topic is the axiomatic characterization of the Euclidean plane. The focus is on the story of the fifth Euclidian axiom (and the attempts to get rid of it).

Previous knowledge

Linear Algebra I

Usability

Elementary Geometry (2HfB21, MEH21, MEB21, MEdual24)
Compulsory Elective in Mathematics (BSc21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Patrick Dondl
Assistant: Jonathan Brugger
Language: in German

Time and place

Lecture: Mi, 14-16h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours fortnightly, various dates
Sit-in exam 30.07., 15:00-17:00, HS Rundbau, Albertstr. 21

Content

Numerics is a discipline of mathematics that deals with the practical solution of mathematical problems. As a rule, problems are not precisely solved but approximated, for which a sensible compromise of accuracy and computing effort has to be found. In the second part of the two -semester course, questions of the analysis such as the approximation of functions by polynomials, the approximately solution of non -linear equations and the practical calculation of integrals are treated. Attendance at the accompanying computer exercise sessions is recommended. These take place fortnightly, alternating with the tutorial for the lecture.

Previous knowledge

necessary: Linear Algebra I and Analysis I

useful: Linear Algebra II, Analysis II

Usability

Numerics (2HfB21, MEH21)
Numerics (BSc21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Thorsten Schmidt
Assistant: Simone Pavarana
Language: in German

Time and place

Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours fortnightly, various dates
Sit-in exam 06.08., 10:00-12:00

Content

After gaining an insight into the basics and various methods and questions of stochastics and probability theory in the Stochastics I lecture, this lecture will mainly focus on statistical topics, especially those that are relevant for students studying to become secondary school teachers. However, the lecture can also be a (hopefully) useful supplement and a good basis for later attendance of the course lecture ‘Mathematical Statistics’ for students in the B.Sc. in Mathematics with an interest in stochastics.

After clarifying the term ‘statistical model’, methods for constructing estimators (e.g. maximum likelihood principle, method of moments) and quality criteria for these (reliability of expectations, consistency) are discussed. Confidence intervals and hypothesis tests are also introduced. Linear models are considered as further applications and, if time permits, other statistical methods. The properties of exponential families and multivariate normal distributions, which are useful for many test and estimation methods, are also introduced.

Previous knowledge

Linear Algebra I+II and Analysis I+II

Usability

Elementary Probabilty Theory (2HfB21, MEH21)
Elementary Probability Theory II (MEdual24)
Compulsory Elective in Mathematics (BSc21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Abhishek Oswal
Language: in English

Time and place

Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class

Content

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.

Previous knowledge

necessary: Linear Algebra I+II

useful: Algebra and Number Theory

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Nadine Große
Assistant: Jonah Reuß
Language: in English if requested, otherwise in German

Time and place

Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class

Content

Eigenvalues of geometric differential operators play a central role in Riemannian geometry, linking analytic, geometric, and topological properties of manifolds. In this lecture we give an introduction to spectral theory on Riemannian manifolds, with particular emphasis on the Laplace–Beltrami operator. Some results from spectral theory and functional analysis will necessarily be taken as black boxes. We discuss fundamental results on eigenvalue estimates and their dependence on the Riemannian metric. Through classical examples and key inequalities (such as those due to Cheeger, Lichnerowicz, and Weyl), we illustrate how curvature, volume, and topology influence the spectrum.

Previous knowledge

Differential geometry I is required; knowledge of Riemannian metrics and integration on manifolds is desirable.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Guofang Wang
Assistant: Florian Johne
Language: in English

Time and place

Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam 31.07., 09:00-12:00, SR 404, Ernst-Zermelo-Str. 1

Attention: Change of time and room!

Content

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.

Previous knowledge

Linear Algebra I+II, Analysis I–III

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Applied Mathematics (MSc14)
Pure Mathematics (MSc14)
Elective (MSc14)
Advanced Lecture in Numerics (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Ernst Kuwert
Assistant: Yuchen Bi
Language: in German

Time and place

Lecture: Mo, Mi, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam 03.08., 10:00

Content

The lecture studies the geometry of curves and surfaces in Euclidean space. The main topic is the definition of curvature and the understanding of its geometric meaning. The lecture addresses Bachelor students in Mathematics, as well as students in the Master of Education. The subject may relevance in the fields Analysis, Geometry, and Applied Mathematics.

Previous knowledge

Basic lectures in Analysis and Linear Algebra

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Wolfgang Soergel
Assistant: Leon Blattmann
Language: in English if requested, otherwise in German

Time and place

Lecture: Mo, Mi, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class

Content

A Lie group is a manifold with a group structure. The lecture begins with the study of closed subgroups of the matrix groups \(GL(n;\mathbb R)\). It is shown that they are always manifolds and their tangent spaces are examined. Abstract manifolds and non-embedded Lie groups are discussed further on. The ultimate goal is the classification of compact Lie groups.

Previous knowledge

The lecture builds on the basic lectures in lineare algebra and analysis. No further knowledge of differential geometry or group theory is required.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Markus Junker
Assistant: Stefan Ludwig
Language: in German

Time and place

Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam 14.09., 10:00-13:00, HS Weismann-Haus, Albertstr. 21a

Content

The aim of mathematical logic is first and foremost to clarify the fundamentals of mathematics: What is a proof? Which methods of proof are permissible? Which axioms are needed? In order to provide meaningful answers to these questions, one must first formalise what mathematical statements and proofs are in what is known as predicate logic. Once this has been achieved, statements and proofs themselves can become the object of mathematical investigation, and one can prove theorems about the possibilities and limits of provability: the most important of these are Kurt Gödel's completeness theorem and incompleteness theorems. On the way there, the lecture introduces the basic concepts of important subfields of mathematical logic: set theory, model theory and computability theory (recursion theory).

Previous knowledge

Basic knowledge of mathematics from first semester lectures

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Language: in English

Time and place

Lecture: Mo, Mi, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class

Content

The proof of Baldwin and Lachlan of Morley's theorem introduces the notion of \(\omega\)-stability, which lies in the core of many applications of model theory to algebraic geometry and number theory. In this lecture we will introduce Morley rank, a meaningful dimension in \(\omega\)-stable theories, and prove, among others, Macintyre's theorem, which states that an infinite \(\omega\)-stable field must be algebraically closed. Similarly, we will prove Reineke's theorem, which states that a connected \(\omega\)-stable group of rank \(1\) is abelian. In order to give a full proof of these two theorems, we need to introduce the notions of generic types in \(\omega\)-stable groups as well as imaginaries.

Previous knowledge

required: Model theory

useful: Algebra and Number Theory

For the algebraic aspects of this lecture, we will need only some notions from the course “Algebra und Zahlentheorie” (in particular Galois theory). No advanced notions from commutative algebra will be needed.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Thorsten Schmidt
Assistant: Donatien Wilfried Kuissi Kamdem
Language: in English

Time and place

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 04.09., 10:00-12:00, HS Weismann-Haus, Albertstr. 21a

Content

This lecture lays the foundation for a systematic treatment of random phenomena. The aim is to develop methods of stochastic modelling and analysis and to derive the classical limit theorems. In addition, the extremely important concept of martingales is studied in general terms and an initial look is taken at stochastic processes.

The knowledge gained in this lecture forms the basis for later special lectures and seminars in the field of stochastics and financial mathematics.

Previous knowledge

necessary: Analysis I+II, Linear Algebra I, Elementary Probability Theory I

useful: Analysis III

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Applied Mathematics (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Angelika Rohde
Assistant: Johannes Brutsche
Language: in English

Time and place

Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class

Content

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.

Previous knowledge

Probability Theory I and II (Stochastic Processes)

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Stefan Kebekus
Assistant: Riccardo Tosi
Language: in English if requested, otherwise in German

Time and place

Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class

Content

For complex numbers, the logarithm can no longer be defined with all the properties known from real numbers because the exponential function is not injective: \(\exp(\bullet) = \exp(\bullet + 2\pi i)\). We say that ‘the logarithm is multivalued’. This problem gave Bernhard Riemann the idea of studying holomorphic functions not only on the complex number plane, but on more general manifolds, the ‘Riemannian surfaces’. The aim of the lecture is to understand these surfaces geometrically using methods from function theory and algebraic topology.

Previous knowledge

Complex Analysis

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Heike Mildenberger
Assistant: Simon Klemm
Language: in German

Time and place

Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam 23.07., 10:00-12:00

Content

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 ``Topology'' is the study of topological spaces and the investigation of topological spaces. Our lecture is an introduction to set-theoretic and algebraic topology.

Previous knowledge

Analysis I and II, Linear Algebra I

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: All professors and 'Privatdozenten' of the Mathematical Institute
Language: Talk/participation possible in German and English

Time and place

Dates by arrangement

Content

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.

Usability

Reading Course (MEd18, MEH21)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Annette Huber-Klawitter
Assistant: Ben Snodgrass
Language: in English

Time and place

Mo, 10-12h, SR 404, Ernst-Zermelo-Str. 1

The seminar of the same name can also be attended without giving a talk and can be credited as a two-hour lecture with 3 ECTS credits.

Content

The course will partly take the form of a seminar. For details on the content etc., please see the seminar of the same name!

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Part of the course is a seminar.

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English

Time and place

Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class

Content

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.

Previous knowledge

Lectures "Numerik I, II" or lecture "Basics in Applied Mathematics"

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Sören Bartels, Giuseppe Buttazzo
Language: in English

Usability

Elective in Data (MScData24)
Elective (MSc14)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Diyora Salimova
Assistant: Ilkhom Mukhammadiev
Language: in English

Time and place

Lecture: Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class

Content

The aim of this course is to enable the students to carry out simulations and their mathematical analysis for stochastic models originating from applications such as mathematical finance and physics. For this, the course teaches a decent knowledge on stochastic differential equations (SDEs) and their solutions. Furthermore, different numerical methods for SDEs, their underlying ideas, convergence properties, and implementation issues are studied. The topics we will cover \\ - Preliminaries from measure and probability theory \\ - Generation of random numbers \\ - Monte Carlo integration methods \\ - Stochastic processes and Ito calculus \\ - SDEs \\ - Numerical approximations for SDEs \\ - Applications to computational finance: Option valuation

Previous knowledge

Probability and measure theory, basic numerical analysis and basics of MATLAB programming.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Chiara Saffirio
Assistant: Phillip Pflaum
Language: in English

Time and place

Lecture: Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class

Content

• Introduction: short review on classical, basic notions of quantum mechanics, semiclassical analysis;

• Semiclassical pseudo-differential calculus: motivation, oscillatory integrals and symbol classes, Schwartz kernels of pseudo-differenial operators and symbolic calculus;

• Applications to static and dynamical problems in physics.

Previous knowledge

necessary: Analysis I and II, Measure and Integration Theory, Probability Theory I and II.

useful: Functional Analysis, Introduction to Mathematical Physics.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Rainer Dahlhaus
Assistant: Moritz Meyer
Language: in English

Time and place

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.

Content

In the second part, we cover various topics, including Toeplitz theory for quadratic forms of stationary processes, the cumulant method for proving central limit theorems in complex situations, likelihood theory for stationary processes including maximum likelihood and quasi-maximum likelihood methods (using Toeplitz theory and cumulants to prove asymptotic results), and various aspects of locally stationary processes where the process can be locally approximated by stationary processes. Furthermore, we discuss model misspecification and model selection.

Previous knowledge

Elementary Probability Theory I and Probability Theory (Wahrscheinlichkeitstheorie), Mathematical Time Series Analysis 1 (at least knowledge of ergodic theory, linear models, spectral representation and spectral estimation,central limit theorems)

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Moritz Diehl
Language: in English

Time and place

Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Sit-in exam 16.09., 10:00-12:00, G.-Köhler-Allee 101, SR 01-009/13

Content

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:

1. Fundamental Concepts of Optimization: Definitions, Types of Optimization Problems, Convexity, Duality, Compu- ting Derivatives
2. Unconstrained Optimization and Newton-Type Algorithms: Exact Newton, Quasi-Newton, BFGS, Gauss-Newton, Globalization
3. Equality Constrained Optimization: Optimality Conditions, Newton-Lagrange and Constrained Gauss–Newton, Quasi-Newton, Globalization
4. Inequality Constrained Optimization Algorithms: Karush-Kuhn-Tucker Conditions, Active Set Methods, Interior Point Methods, Sequential Quadratic Programming

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.

Previous knowledge

necessary: Analysis I–II, Linear Algebra I–II

useful: Introduction to Numerics

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Giuseppe Genovese
Assistant: Roger Bader
Language: in English

Time and place

Lecture: Mi, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class

Content

Randomised algorithms use probabilistic ideas to improve and simplify existing algorithms in a way sometimes quite surprising. To familiarise with the methods, we will study some of the main examples arising for discrete structures, such as graphs, trees and random walks on discrete groups. The second part of the corse will focus mainly on sampling algorithms based on probabilistic ideas, such as Markov chain Montecarlo and stochastic localisation.

Previous knowledge

necessary: Elementary Probability Theory I

useful: Markov chains

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Katharina Böcherer-Linder
Language: in German

Time and place

Mo, 10-12h, SR 226, Hermann-Herder-Str. 10
Exercise session: Do, 10-12h, SR 226, Hermann-Herder-Str. 10
Sit-in exam 27.07., 10:00-12:00, HS Weismann-Haus, Albertstr. 21a

Content

Mathematics didactic principles and their learning theory foundations and possibilities of teaching implementation (also e.g. with the help of digital media). \\ Theoretical concepts on central mathematical thinking activities such as concept formation, modeling, problem solving and reasoning. \\ Mathematics didactic constructs: Barriers to understanding, pre-concepts, basic ideas, specific difficulties with selected mathematical content. \\ Concepts for dealing with heterogeneity, taking into account subject-specific characteristics particularities (e.g. dyscalculia or mathematical giftedness).\\ Levels of conceptual rigour and formalization as well as their age-appropriate implementation.

Previous knowledge

Required: Analysis~I, Linear Algebra~I

Usability

(Introduction to) Mathematics Education (2HfB21, MEH21, MEB21)
Introduction to Mathematics Education (MEdual24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Jürgen Kury
Language: in German

Time and place

Seminar: Mi, 14-17h, SR 404, Ernst-Zermelo-Str. 1

Content

Exemplary implementations of the theoretical concepts of central mathematical thought processes such as concept formation, modeling, problem solving and reasoning for the content areas of functions and analysis. \\ Barriers to understanding, pre-concepts, basic ideas, specific difficulties for the content areas of functions and analysis. \\ Fundamental possibilities and limitations of media, in particular of computer-aided mathematical tools mathematical tools and their application for the content areas of functions and analysis. Analysis of individual mathematical learning processes and errors as well as development individual support measures for the content areas of functions and analysis.

Previous knowledge

Required: Introduction to Mathematics Education, Knowledge about analysis and numerics

Usability

Mathematics Education for Specific Areas of Mathematics (MEd18, MEH21, MEB21)

A request has been made to change the examination format to an oral exam (instead of the previous written exam), but this still needs to be formally approved by the Senate (expected in May).

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Katharina Böcherer-Linder
Language: in German

Time and place

Seminar: Di, 9-12h, SR 226, Hermann-Herder-Str. 10

Content

Exemplary implementations of the theoretical concepts of central mathematical thought processes such as concept formation, modeling, problem solving and reasoning for the content areas of stochastics and algebra. \\ Barriers to understanding, pre-concepts, basic ideas, specific difficulties for the content areas of stochastics and algebra.\ Basic possibilities and limitations of media, especially computer-based mathematical tools and their mathematical tools and their application for the content areas of stochastics and algebra. and algebra. \\ Analysis of individual mathematical learning processes and errors as well as development individual support measures for the content areas of stochastics and algebra.

Previous knowledge

Required: Introduction to Mathematics Education, knowledge from stochastics and algebra.

Usability

Mathematics Education for Specific Areas of Mathematics (MEd18, MEH21, MEB21)

A request has been made to change the examination format to an oral exam (instead of the previous written exam), but this still needs to be formally approved by the Senate (expected in May).

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Holger Dietz
Language: in German

Time and place

Seminar: Do, 14-17h, genauer Raum wird später bekanntgegeben, Goethe-Gymnasium Freiburg

Content

As a high school student, you have no idea what it means to study mathematics. While studying mathematics at the university, the imagination of what it means to teach mathematics at school is similarly vague . This seminar would like to provide concrete insights into the practice of math teaching and tries to build on experiences e.g. B. from the practical semester.

Selected contents and aspects of mathematics lessons (from worksheet to the extension of number systems) are analyzed and questioned – not only from the point of view of the scientist, but also from the point of view of the lecturers, teachers, pupils. Mathematically simple topics often hide unexpected didactic challenges. Therefore, in addition to dealing with existing content and framework conditions, teaching should also be planned and – if possible – carried out at the school.

Previous knowledge

Basic lectures

Usability

Supplementary Module in Mathematics Education (MEd18, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Lecturers of the University of Education Freiburg
Language: in German

For the module "Fachdidaktische Entwicklung", suitable courses can also be completed at the PH Freiburg if places are available there. Please check with Ms. Böcherer-Linder whether courses are suitable, and with the lecturers whether places are available. Courses are usually offered in German.

Usability

Supplementary Module in Mathematics Education (MEd18, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Lecturers of the University of Education Freiburg, Anselm Strohmaier
Language: in German

Time and place

Part 1: Seminar 'Development Research in Mathematics Education ‒ Selected Topics': Mo, 14-16h, -, -, – please refer to the PH Freiburg course catalogue for any last-minute time or room changes.
Part 2: Seminar 'Research Methods in Mathematics Education': Mo, 10-13h, Mensa 3 / Zwischendeck SR 032, PH Freiburg, –please refer to the PH Freiburg course catalogue for any last-minute time or room changes.
Part 3: Master's thesis seminar: Development and Optimisation of a Research Project in Mathematics Education Appointments by arrangement

Registration: see course descriptions

Content

The three related courses of the module prepare students for an empirical Master thesis in mathematics didactics. The course is jointly designed by all professors at the PH with mathematics didactics research projects at secondary levels 1 and 2 and is carried out by one of these researchers. Afterwards, students have the opportunity to start Master thesis with one of these supervisors - usually integrated into larger ongoing research projects.

The first course of the module provides an introduction to strategies of empirical didactic research (research questions, research status, research designs). Students deepen their skills in scientific research and the evaluation of subject-specific didactic research. In the second course (in the last third of the semester) students are introduced to central qualitative and quantitative research methods through concrete work with existing data (interviews, student products, experimental data), students are introduced to central qualitative and quantitative research methods. The third course is an accompanying seminar for the Master thesis.

The main objectives of the module are the ability to receive mathematics didactic research in order to didactic research to clarify questions of practical relevance and to plan an empirical mathematics didactics Master thesis. It will be held as a mixture of seminar, development of research topics in groups and active work with research data. Recommended literature will be depending on the research topics offered within the respective courses. The parts can also be attended in different semesters, for example part~1 in the second Master semester and part~2 in the compact phase of the third Master semester after the practical semester.

Usability

Research in Mathematics Education (MEd18, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Organisation: Katharina Böcherer-Linder, Susanne Knies
Language: in German

Time and place

1st workshop 22.04., 16:00-18:00, Raum 232, Ernst-Zermelo-Str. 1, (Please check the time in HISinOne due to possible last-minute changes.)

If you are interested, please register for the course in HISinOne up to one week before the start of lectures.

Content

What makes a good tutorial? This question will be discussed in an initial workshop, where tips and suggestions will be provided to help participants start the semester better prepared. Participating tutors will gain further experience and provide each other with feedback through mutual observation. The experiences will be shared in the second workshop.

The date of the first workshop is entered in HISinOne, and the date of the second workshop will be agreed upon during the first workshop.

Usability

Elective (Option Area) (2HfB21)
Elective (BSc21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Stefan Kater
Language: in German

Time and place

Lecture: Mo, 16-18h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates

Previous knowledge

none

Usability

Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
BOK course (BSc21)
Supplementary Module in Mathematics (MEd18)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Patrick Dondl
Assistant: Jonathan Brugger
Language: in German

Time and place

Programming exercise: 2 hours fortnightly, various dates

Content

In the practical exercises accompanying the Numerics II lecture, the algorithms developed and analysed in the lecture are implemented in practice and tested experimentally. The implementation is carried out in the programming languages Matlab, C++ and Python. Elementary programming skills are assumed.

Previous knowledge

See the lecture Numerics II.

In addition elementary programming knowledge.

Usability

Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Numerics (BSc21)
Supplementary Module in Mathematics (MEd18)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Peter Pfaffelhuber
Assistant: Samuel Ayomide Adeosun

Time and place

Di, 12-14h, SR 127, Ernst-Zermelo-Str. 1

Cannot be credited together with Prorgramming Exercises in Stochastics in Python.

Content

This course is designed for students without prior knowledge in programming, but students who have already taken a first programming course might benefit as well . We will start with basic syntax and the standard library of python, including data types, functions, loops, regular expressions, and interacting with the operating system. For data analysis we learn dataframes using packages such as pandas (and relatives), see how we can interact with freely available APIs, make plots using matplotlib, and use numpy and scipy for standard procedures including numerical computations.

Within this course, you will pick a programming task of your interest, and implement your ideas based on your gained knowledge.

Previous knowledge

none

Usability

Elective (MScData24)
Computer Exercise (2HfB21, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Sören Bartels
Assistant: Dominik Schneider
Language: in German

Time and place

Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration: by email to Sören Bartels, but you can also simply come to the preliminary meeting.
Preliminary seminar meeting 29.01., 12:45, Raum 209, Hermann-Herder-Str. 10
Individual preparation meetings for the talks: Dates by arrangement

Usability

Introductory Student Seminar (2HfB21, BSc21, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Susanne Knies, Maxwell Levine
Language: in German

Time and place

Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 28.01., 12:15, Raum 232, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

How many guards does a museum need? How can I estimate \(\pi\) by throwing a needle? How much evidence is there for the infinity of the set of prime numbers? These and other questions are answered by classical mathematical results with particularly elegant proofs. These (and others) have been compiled by Aigner and Ziegler in the BOOK of Proofs, from which selected chapters will be presented in this proseminar. A list of possible lecture topics can be found here.

Previous knowledge

Analysis I and II, Linear Algebra I and II

Usability

Introductory Student Seminar (2HfB21, BSc21, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Ernst August v. Hammerstein
Language: in German

Time and place

Di, 10-12h, SR 127, Ernst-Zermelo-Str. 1
Preregistration: until February 2, 2026, via email to Ernst August v. Hammerstein
Preliminary seminar meeting 04.02., 16:00, SR 127, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

Coding theory is classically understood to mean techniques and procedures for summarizing information in a “compact and transmission-secure” manner. Compact here means accommodating as much information as possible in as few code words as possible (such as author, book title, and publisher in an ISBN number), and transmission-secure means that errors in transmitted code words can be detected and, ideally, corrected, i.e., the originally intended code word can be restored if necessary. In addition, the keyword “encoding” often brings to mind “hard-to-crack codes,” i.e., encryption techniques used to protect transmitted information from unauthorized access.

This proseminar will consider both of the above aspects, with greater emphasis on the former. The mathematical foundations of the individual methods will also be examined and explained in more detail. Key terms in this context include: calculation in residue classes/modulo, Fermat's little theorem and the Chinese remainder theorem, encryption using RSA methods and discrete logarithms, (perfect) linear codes, cyclic codes, Reed-Solomon and BCH codes.

Previous knowledge

Analysis I,II, Linear Algebra I,II

Usability

Introductory Student Seminar (2HfB21, BSc21, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Annette Huber-Klawitter
Assistant: Ben Snodgrass
Language: in English

Time and place

Seminar: Mo, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Preregistration: Please sign up in the list with Frau Frei, room 421
Preliminary seminar meeting 04.02., 12:15-14:00, SR 403, Ernst-Zermelo-Str. 1

Content

In this seminar, we shall learn about algebraic \(\mathcal D\)-modules. These are modules over a certain class of non-commutative rings, consisting of polynomials and differential operators. The simplest example is \(\mathbb C[z, \partial]\), where \(\partial \cdot z = z \cdot \partial + 1\). These modules can be seen as a generalisation of systems of linear partial differential equations with polynomial coefficients, in the sense that each such system defines a \(\mathcal D\)-module from which the system can be recovered.

In \(\mathcal D\)-module theory, one is typically less interested in finding explicit solutions of systems of differential equations and more interested in applying techniques from commutative algebra and algebraic geometry to understand the systems themselves. We shall learn about certain invariants associated to a given \(\mathcal D\)-module and their geometric interpretations, including holonomicity. Time-allowing, we will also look at solution spaces of \(\mathcal D\)-modules and the statement of the Riemann-Hilbert correspondence, with some instructive examples.

Previous knowledge

Commutative Algebra

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Diyora Salimova
Assistant: Ilkhom Mukhammadiev
Language: Talk/participation possible in German and English

Time and place

Seminar: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration: by e-mail to Diyora Salimova
Preliminary seminar meeting 04.02., 13:15, SR 226, Hermann-Herder-Str. 10
Individual preparation meetings for the talks: Dates by arrangement

Content

In recent years, deep learning have been successfully employed for a multitude of computational problems including object and face recognition, natural language processing, fraud detection, computational advertisement, and numerical approximations of differential equations. Such simulations indicate that neural networks seem to admit the fundamental power to efficiently approximate high-dimensional functions appearing in these applications.

The seminar will review some classical and recent mathematical results on approximation properties of deep learning. We will focus on mathematical proof techniques to obtain approximation estimates on various classes of data.

Previous knowledge

required: Analysis I/II, Linear Algebra I/II \ useful: Functional Analysis, Numerics, basics of Deep Learning.

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Mathematical Seminar (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Wolfgang Soergel
Assistant: Xier Ren
Language: Talk/participation possible in German and English

Time and place

Seminar: Do, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preregistration: by e-mail to Wolfgang Soergel
Preliminary seminar meeting 04.02., 12:15, SR 218, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

In this seminar, we will discuss the theory of Lie algebras. A Lie algebra is a vector space \(L\) with a bilinear operation \(L \times L \to L\) denoted \((x, y) \mapsto [x, y]\) with \([x, x] = 0\) and \([x, [y, z]] + [y, [z, x]] + [z, [x, y]] = 0\) for all \(x, y, z \in L\). This algebraic structure is of fundamental importance for the study of continuous symmetries, also known as Lie groups, but has its own theory that does not require differential geometry and can be developed entirely within the framework of algebra. The goal is the classification of simple complex Lie algebras according to Killing and Cartan. Participants with the appropriate prerequisites are also very welcome to receive lecture topics that report on the relationships to Lie groups.

Previous knowledge

required: Linear Algebra I–II \ useful: Algebra and Number Theory

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Heike Mildenberger
Assistant: Maxwell Levine
Language: Talk/participation possible in German and English

Time and place

Seminar: Di, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 27.01., 13:30, Raum 313, Ernst-Zermelo-Str. 1, No preregistration required!
Individual preparation meetings for the talks: Dates by arrangement

Content

In this seminar, we will focus on combinatorial questions that belong simultaneously to algebraic geometry, topology and set theory. Among other things, homology theory investigates structural features using limit constructions from mappings into Abelian groups, modules or other reference structures. Often there are \(\mathbb N\)-many different limits (which can be seen as dimensions) and relatives of derivatives between them. Certain quotient groups and limits are to be calculated, or at least it is to be determined whether they are isomorphic to the one-element group. Compactness properties of directed systems of structures can imply the one-element nature of such a quotient. In this seminar, we are interested in structural features of families of two-argument functions, such as those found in Hawaiian earring-based chain complexes. Surprisingly, already the question of the disappearance of \(\lim^1\) is independent of ZFC.

Previous knowledge

Basic knowledge of topology as well as the definition of ordinal numbers and cardinal numbers is useful. Some talks will require only one of these. The necessary fundamentals of algebraic geometry and homology theory will be introduced in the talks.

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Angelika Rohde
Assistant: Dario Kieffer
Language: Talk/participation possible in German and English

Time and place

Block seminar
Preregistration: by email to Dario Kieffer, but you can also simply come to the preliminary meeting.
Preliminary seminar meeting 05.02., 14:00, SR 318, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

While on the one hand linear models---such as the linear regression model known from the introductory course Stochastics II---are easy to interpret, they are typically unsuitable for modeling complex statistical relationships. On the other hand, 'black-box' models such as deep learning, which can model complex situations very well, are often difficult to interpret. Additive models allow the modeling of nonlinear relationships between the response variable and the observations while maintaining a high level of interpretability of the results. For this reason, they are of great importance when the justification of decisions plays a central role. The mathematical analysis is, however, demanding, though also fascinating, since it connects mathematical stochastics with the theory of optimization and functional analysis.

In the additive model, let \((X_{1}, Y_{1}), \dots, (X_{n}, Y_{n}) \colon \Omega \to \mathbb{R}^{d} \times \mathcal{Y}\) be independent and identically distributed with \[\mathbb{E}\big[ Y_{1} \mid X_{1} = (x^{1}, \dots, x^{d}) \big] = \eta_{0} + \sum_{i=1}^{d} \eta_{i}(x^{i}),\] for suitable unknown functions \(\eta_{i} : \mathbb{R} \to \mathbb{R}\), \(i = 1, \dots, d\), and an unknown constant \(\eta_{0} \in \mathbb{R}\). We will study recursive nonparametric algorithms for estimating the unknown quantities \((\eta_{i})_{i=0,\dots,d}\) and investigate their probabilistic properties. Based on Hilbert space theory, the so-called backfitting algorithm is derived, which allows us to study the consistency of the estimator as well as to determine its asymptotic distribution. Furthermore, so-called generalized additive models are considered, in which \[\mathbb{E}\big[ Y\ |\ X = (x^{1}, \dots, x^{d}) \big] = g\bigg( \eta_{0} + \sum_{i=1}^{d} \eta_{i}(x^{i}) \bigg)\] is assumed for a known function \(g:\mathbb{R} \to \mathbb{R}\).

Previous knowledge

necessary: Probability Theory I

useful: Probability Theory II (Stochastic Processes), Functional Analysis

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Mathematical Seminar (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Nadine Große
Assistant: Maximilian Stegemeyer
Language: Talk/participation possible in German and English

Time and place

Seminar: Di, 12-14h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 03.02., 12:00, SR 318, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

Algebraic topology studies how topological spaces can be assigned algebraic objects, such as homology and cohomology groups. The homology and cohomology of a compact manifold have a special property that other spaces generally do not fulfil. The homology and cohomology of a compact manifold together satisfy what is known as Poincaré duality. This special structure has many interesting consequences; for example, there is now a product on the homology groups, the intersection product. In this seminar, we will first learn about the algebraic topology of manifolds and study Poincaré duality and the intersection product. The ideas behind the intersection product can then be transferred to the free loop space of a manifold. The homology of the free loop space thus also obtains a product, as well as other algebraic structures. The study of these additional algebraic structures on the loop space is called string topology. In this seminar, we will learn about some aspects and applications of string topology and finally see what string topology can tell us about the geometry and topology of the underlying manifold.

Previous knowledge

Algebraic topology, in particular basic knowledge of singular homology and cohomology. Other courses, such as Differential Geometry I, are helpful but not a prerequisite for participation in the seminar.

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Patrick Dondl, Guofang Wang
Assistant: Florian Johne
Language: Talk/participation possible in German and English

Time and place

Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 04.02., 16:00, SR 125, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

In HISinOne: no course registration, but exam registration until 15 April 2026.

Content

Further information on the topics of the talks will be provided at the preliminary meeting.

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Mathematical Seminar (MScData24)
Elective in Data (MScData24)

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

Time and place

Seminar: Mi, 10:15-11:45h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration: via e-mail to bemb.imbi.sek@list.uniklinik-freiburg.de
Preliminary seminar meeting 04.02., 10:15-11:15, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26

In HISinOne: no course registration, but exam registration until 8 October 2025.

Content

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.

Previous knowledge

Good knowledge of probability theory and mathematical statistics.

Usability

Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Mathematical Seminar (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Nadine Binder
Language: Talk/participation possible in German and English

Time and place

Seminar: Do, 16:30-18h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration: by e-mail to Nadine Binder
Preliminary seminar meeting 01.04., 16:30-17:15, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26

Note: Only for the degree programme "Mathematics in Data and Technology"

Content

The seminar is a journal‑club style meeting where we critically read and discuss recent papers that use routine health‑care data. You’ll dissect the statistical or computational models, incl. survival analysis, causal‑effects methods, or machine learning, that turn raw diagnoses, labs, or medication records into clinical insights. You’ll work individually or potentially in pairs with medical students to prepare a presentation that summarizes the study, evaluates its methodology, and reflects on how the mathematics could be refined or applied elsewhere. The seminar format will allow you to sharpen your ability for interpreting quantitative research, bridge theory with practice, and experience the interdisciplinary dialogue that drives modern evidence‑based medicine.

Previous knowledge

None that go beyond admission to the degree program.

Usability

Mathematical Seminar (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Organisation: Sören Bartels, Ernst August v. Hammerstein
Language: in English

Time and place

Mi, 14-16h, SR 125, Ernst-Zermelo-Str. 1

Content

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.

Usability

Graduate Student Speaker Series (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

general course catalogue see https://vorlesungsverzeichnis.unibas.ch/de/semester-planung

course catalogue for mathematics see https://www.math.kit.edu/vvz

Master Mathématiques Fondamentales et Appliquées see https://irma.math.unistra.fr/linstitut/lmd_enseignement.html#masters

Lecturer: André Biedenkapp, Frank Hutter
Language: in English

Time and place

Lecture: Mi, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Exercise session: Do, 14-16h, HS 00-036, Georges-Köhler-Allee 101

Course offered by the Faculty of Engineering. For contents, prerequisites, and requirements see the module handbook M.Sc. Computer Science.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Abhinav Valada
Language: in English

Time and place

Lecture: Mo, 14-16h, HS 00-026, Georges-Köhler-Allee 101
Exercise session: Fr, 10-12h, R 00 006, Georges-Köhler-Allee 082

Course offered by the Faculty of Engineering. For contents, prerequisites, and requirements see the module handbook M.Sc. Computer Science.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Andrea Mazzoran
Language: in English

Time and place

Lecture: Di, 10-12h, Max-Kade Auditorium 2, Alte Uni
Exercise session: Do, 16-18h, Max-Kade Auditorium 2, Alte Uni

Course offered by the Institute for Economics. For contents, prerequisites, and requirements see the module handbook M.Sc. VWL and additionally also the course website.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Saswat Patra
Language: in English

Time and place

Block course 02.06. bis 26.06., different rooms and times, see course webpage

Course offered by the Institute for Economics. For contents, prerequisites, and requirements see the module handbook M.Sc. VWL.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Joschka Bödecker
Language: in English

Time and place

Lecture: Di, Fr, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Exercise session: Fr, 14-16h, HS 00-026, Georges-Köhler-Allee 101

Course offered by the Faculty of Engineering. For contents, prerequisites, and requirements see the module handbook M.Sc. Computer Science.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Thomas Brox
Language: in English

Time and place

Lecture: Mo, Mi, 10-12h, HS 00-006, Georges-Köhler-Allee 082
Exercise session: Mi, 10-12h, verschiedene Räume, -, Lectures and tutorials alternate and do not take place on all days!

Course offered by the Faculty of Engineering. For contents, prerequisites, and requirements see the module handbook M.Sc. Computer Science.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Maria Kalweit
Language: in English

Time and place

Lecture: Di, 14-16h, SR 00-010/14, Georges-Köhler-Allee 101

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Joschka Bödecker
Language: in English

Time and place

Lecture: Di, 16-18h, SR 01-016/18, Georges-Köhler-Allee 101
Exercise session: Fr, 12-14h, SR 01-016/18, Georges-Köhler-Allee 101

Course offered by the Faculty of Engineering. For contents, prerequisites, and requirements see the module handbook M.Sc. Computer Science.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Joschka Bödecker, Gabriel Kalweit
Language: in English

Time and place

Lecture: Mo, 16-18h, R 00 006, Georges-Köhler-Allee 082
Exercise session: Fr, 8-10h, R 00 006, Georges-Köhler-Allee 082

Course offered by the Faculty of Engineering. For contents, prerequisites, and requirements see the module handbook M.Sc. Computer Science.

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Lecturer: Ernst August v. Hammerstein
Assistant: Lukas Riepl
Language: in German

Time and place

Lecture: Mo, Mi, 10-12h, HS 00-026, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates

This course is offered for Computer Science and cannot be taken as part of any Mathematics degree programmes, not even as an elective module!

Content

This course builds on Mathematics I for Computer Science and Engineering Students from the winter semester, with a selection of topics tailored more specifically to computer science. The main topics are

• Linear Algebra: vector spaces, linear mappings, matrices, systems of linear equations, determinants, eigenvalues, scalar product and norm, symmetric matrices, diagonalization and singular value decomposition, applications: coding theory and linear codes
• Algebra: groups, rings, and fields; structure of finite cyclic groups; Euclid’s algorithm; the Chinese Remainder Theorem; Fermat’s Little Theorem
  Applications: RSA algorithm
• Analysis: Curves, real-valued functions of several variables, vector-valued functions, derivatives, partial derivatives, gradient, Jacobi matrix, Hessian matrix, local extrema, vector fields, divergence, Laplace operator, integrals of several variables

Previous knowledge

Mathematics I for Computer Science and Engineering Students

Lecturer: Peter Pfaffelhuber
Assistant: Sebastian Stroppel
Language: in German

Time and place

Lecture: Mo, Mi, 16-18h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

This course is offered for the Faculty of Engineering and cannot be taken as part of any Mathematics degree programmes, not even as an elective module!

Lecturer: Susanne Knies
Assistant: Alen Kushova
Language: in German

Time and place

Lecture: Di, Do, 10-12h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

This course is offered for several study programmes in Sciences and cannot be taken as part of any Mathematics degree programmes, not even as an elective module!

Lecturer: David Criens
Assistant: Nils Kober
Language: in German

Time and place

Lecture: Mo, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates

This course is offered for Computer Science and cannot be taken as part of any Mathematics degree programmes, not even as an elective module!

Lecturer: Ernst Kuwert, Guofang Wang

Time and place

Di, 16-18h, SR 404, Ernst-Zermelo-Str. 1

Lecturer: Chiara Saffirio
Language: in English

Time and place

Mo, 13-14h, Raum 337, Ernst-Zermelo-Str. 1

Organisation: Annette Huber-Klawitter, Stefan Kebekus, Abhishek Oswal, Wolfgang Soergel

Time and place

Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1

Content

The research seminar consists of research talks from the respective specialisation area. The single talks are usually announced in the weekly programme and on the homepage.

Organisation: Sören Bartels, Patrick Dondl, Diyora Salimova

Time and place

Di, 14-16h, SR 226, Hermann-Herder-Str. 10

Content

The research seminar consists of research talks from the respective specialisation area. The single talks are usually announced in the weekly programme and on the homepage.

Organisation: Sebastian Goette, Nadine Große

Time and place

Mo, 16-18h, SR 404, Ernst-Zermelo-Str. 1

Content

The research seminar consists of research talks from the respective specialisation area. The single talks are usually announced in the weekly programme and on the homepage.

Organisation: Amador Martín Pizarro, Heike Mildenberger

Time and place

Di, 14:30-16h, SR 404, Ernst-Zermelo-Str. 1

Content

The research seminar consists of research talks from the respective specialisation area. The single talks are usually announced in the weekly programme and on the homepage.

Organisation: Harald Binder

Time and place

Do, 13-14h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26

Organisation: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Content

The research seminar consists of research talks from the respective specialisation area. The single talks are usually announced in the weekly programme and on the homepage.

Organisation: Katharina Böcherer-Linder, Heike Mildenberger

Time and place

Di, 18:30-20h, HS II, Albertstr. 23b

Content

The Mathematics Education Colloquium aims to show concrete examples, to further develop existing concepts and to encourage didactic experimentation. It is aimed at teachers of all school types, students, trainee teachers and anyone interested.

Organisation: Nadine Große, Amador Martín Pizarro

Time and place

Do, 15-16h, HS II, Albertstr. 23b

Organisation: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Content

Current, interdisciplinary research is presented here, in which mathematical models enable the understanding of natural and social science issues.