Attention: There are some short-term room changes!
Organisation: Susanne Knies
Language: in German
Supervised Exercising
Mo 14-16h, SR 414, Ernst-Zermelo-Str. 1, Mi, 16-18h, SR 414, Ernst-Zermelo-Str. 1
Organisation: Fachschaft
Lecture: Mo, Mi, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Michael Růžička
Assistant: Maximilian Stegemeyer
Language: in German
Analysis II is the continuation of Analysis I from the winter semester and one of the basic lectures of the study programmes in Mathematics. Central concepts of Analysis I (limits and derivations) will be generalized to the case of higher dimension.
Central topics are the topology of \(\mathbb R^n\), metrics and norms, differential calculs in several variables, ordinary differential equations and in particular linear differential equations.
Analysis I, Linear Algebra I (or bridge course linear algebra)
Analysis (2HfB21, BSc21, MEH21, MEB21)
Analysis II (BScInfo19, BScPhys20)
Linear Algebra II
Lecture: Di, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Stefan Kebekus
Assistant: Christoph Brackenhofer
Language: in German
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.
Linear Algebra I
Linear Algebra (2HfB21, BSc21, MEH21)
Linear Algebra (MEB21)
Linear Algebra II (BScInfo19, BScPhys20)
Lecture: Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
29.07., 08:30-11:30, HS Rundbau, Albertstr. 21
Sit-in exam (resit) 08.10., 08:30-11:30, HS Weismann-Haus, Albertstr. 21a
Teacher: Nadine Große
Assistant: Jonah Reuß
Language: in German
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).
Linear Algebra I
Elementary Geometry (2HfB21, MEH21, MEB21, MEdual24)
Compulsory Elective in Mathematics (BSc21)
Lecture: Mi, 14-16h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
31.07., 10:00-12:00
Teacher: Sören Bartels
Assistant: Vera Jackisch
Language: in German
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.
necessary: Linear Algebra I and Analysis I
useful: Linear Algebra II, Analysis II
Numerics (2HfB21, MEH21)
Numerics (BSc21)
Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
05.09.
Teacher: Johannes Brutsche
Assistant: Dario Kieffer
Language: in German
Linear Algebra I+II and Analysis I+II
Elementary Probabilty Theory (2HfB21, MEH21)
Elementary Probability Theory II (MEdual24)
Compulsory Elective in Mathematics (BSc21)
Differential Geometry II – Geometry of Submanifolds
Lecture: Mo, Mi, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Guofang Wang
Assistant: Xuwen Zhang
Language: in German
In the lecture, we discuss the geometry of the sub-manifolds of Euclidian spaces. Examples of such sub-manifolds are curves in the plane and surfaces in the 3-dimensional space. In the 1st part we introduce the external geometry of the sub-manifold, e.g. the second fundamental form, the mean curvature, the first variation of the area, the equations of Gauss, Codazzi and Ricci. In the 2nd part we examine tminimal hypersurfaces (minimal surfaces), the hypersurface with constant mean curvature and the geometric inequalities, the isoperimetric inequality and its generalisations.
Analysis III and "Differential Geometry" or "Curves and Surfaces"
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Mo, 12-14h, HS II, Albertstr. 23b, Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Sir-in Exam: Date to be announced
Attention: Change of time and room!
Teacher: Patrick Dondl
Assistant: Luciano Sciaraffia
Language: in German
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
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Wolfgang Soergel
Assistant: Xier Ren
Language: in German
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
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Sir-in Exam: Date to be announced
Teacher: Amador Martín Pizarro
Assistant: Stefan Ludwig
Language: in German
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
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
22.07.
Teacher: Heike Mildenberger
Assistant: Hannes Jakob
Language: in German
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
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, date to be determined
22.09., 10:00-12:00
Teacher: Angelika Rohde
Assistant: Johannes Brutsche
Language: in English
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
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)
Lecture: Mi, 14-16h, HS II, Albertstr. 23b, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: David Criens
Assistant: Samuel Adeosun
Language: in English
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)
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)
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.
Reading Course (MEd18, MEH21)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Lecture: Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English
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"
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Lecture: Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Mikhail Tëmkin
Language: in English
The notion of a manifold is fundamental importance. On one hand, it is a common ground for many branches of pure and applied mathematics, as well as mathematical physics. On the other hand, it itself is a lush source of elegant, unexpected and structural results. Next, algebraic topology is to mathematics what the periodic table is to chemistry: it offers order to what seems to be chaotic (more precisely, to topological spaces of which manifolds is an important example). Finally, differential topology studies smooth manifolds using topological tools. As it turns out, narrowing the scope to manifolds provides many new beautiful methods, structure and strong results, that are applicable elsewhere -- as we will see in the course. Necessary notions from algebraic topology will be covered in the beginning.
Point-set topology (e.g. "Topology" from summer semester of 2024)
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Mi, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Language: in German
Groups without any non-trivial normal subgroup are called simple groups. Similar to prime numbers for the natural numbers, simple groups form the building blocks for finite groups. It is easy to see that Abelian finite simple groups are cyclic. Non-Abelian examples are alternating groups and Lie-type groups.
The classification of finite simple groups is far beyond the scope of this course. However, we will illustrate some of the recurring ideas of classification and, in particular, prove the following result of Brauer and Fowler:
Theorem: Let G be a finite group of even order such that the centre is of odd order. Then there is an element \(g \neq 1_G\) with \(|G| < |C_G (g)|^3\) .
This theorem had a particularly large impact on the classification of finite simple groups, as it suggests that these could be classified by examining the centralisers of elements of order 2.
Algebra and Number Theory
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Mo, 14-16h, HS II, Albertstr. 23b
Exercise session: Mi, 16-18h, SR 403, Ernst-Zermelo-Str. 1
Teacher: Ernst August v. Hammerstein
Assistant: Sebastian Hahn
Language: in English
Lévy processes are the continuous-time analogues of random walks in discrete time as they possess, by definition, independent and stationary increments. They form a fundamental class of stochastic processes which has widespread applications in financial and insurance mathematics, queuing theory, physics and telecommunication. The Brownian motion and the Poisson process, which may already be known from other lectures, also belong to this class. Despite their richness and flexibility, Lévy processes are usually analytically and numerically very tractable because their distributions are generated by a single univariate distribution which has the property of infinite divisibility.
The lecture starts with an introduction into infinitely divisible distributions and the derivation of the famous Lévy-Khintchine formula. Then it will be explained how the Lévy processes emerge from these distributions and how the characteristics of the latter influence the path properties of the corresponding processes. Finally, after a short look at the method of subordination, option pricing in Lévy-driven financial models will be discussed.
necessary: Probability Theory I
useful: Probability Theory II (Stochastic Processes)
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Lecture: Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Thorsten Schmidt
Assistant: Simone Pavarana
Language: in English
In this lecture we will study new and highly efficient tools from machine learning which are applied to stochastic problems. This includes neural SDEs as a generalisation of stochastic differential equations relying on neural networks, transformers as a versatile tool not only for languages but also for time series, transformers and GANs as generator of time series and a variety of applications in Finance and insurance such as (robust) deep hedging, signature methods and the application of reinforcement learning.
The prerequisites are stochastics, for some parts we will require a good understanding of stochastic processes. A (very) short introduction will be given in the lectures – so for fast learners it would be possible to follow the lectures even without the courses on stochastic processes.
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Lecture: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Patrick Dondl
Assistant: Eric Trébuchon
Language: in English
This course provides a comprehensive introduction to mathematical modeling. We will learn the systematic process of translating real-world problems into mathematical frameworks, analyzing them using appropriate mathematical tools, and interpreting the results in practical contexts. The course covers both discrete and continuous modeling approaches, with emphasis on differential equations, variational problems, and optimization techniques. Through case studies in physics, biology, engineering, and economics, students will develop skills in model formulation, validation, and refinement. Special attention is given to dimensional analysis, stability theory, and numerical methods necessary for implementing solutions with a focus on numerical methods for ordinary differential equations. The course combines theoretical foundations with hands-on experience in computational tools for model simulation and analysis.
Analysis I, II, Linear Algebra I, II, Numerics I, II
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Numerical Optimization
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Sir-in Exam: Date to be announced
Teacher: Moritz Diehl
Assistant: Léo Simpson
Language: in English
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
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Advanced Course in Schemes
Lecture: Mo, 12-14h, SR 403, Ernst-Zermelo-Str. 1
Exercise session: Do, 14-16h, -, -
Teacher: Andreas Demleitner
Language: in German
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Introduction to Mathematics Education
Mo, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
Teacher: Katharina Böcherer-Linder
Language: in German
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.
Required: Analysis~I, Linear Algebra~I
(Introduction to) Mathematics Education (2HfB21, MEH21, MEB21)
Introduction to Mathematics Education (MEdual24)
Mathematics Education ‒ Functions and Analysis
Seminar: Mi, 14-17h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Jürgen Kury
Language: in German
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.
Required: Introduction to Mathematics Education, Knowledge about analysis and numerics
Mathematics Education for Specific Areas of Mathematics (MEd18, MEH21, MEB21)
Mathematics Education ‒ Probability Theory and Algebra
Seminar: Mi, 11-14h, SR 403, Ernst-Zermelo-Str. 1
Attention: Change of time and room!
Teacher: Frank Reinhold
Language: in German
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.
Required: Introduction to Mathematics Education, knowledge from stochastics and algebra.
Mathematics Education for Specific Areas of Mathematics (MEd18, MEH21, MEB21)
Mathematics education seminar: High School Maths = University Maths ± x
Seminar: Fr, 8-11h, Seminar für Ausbildung und Fortbildung der Lehrkräfte Freiburg, Oltmannstr. 22
Teacher: Holger Dietz
Language: in German
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.
Basic lectures
Supplementary Module in Mathematics Education (MEd18, MEH21, MEB21)
Mathematics education seminars at Freiburg University of Education
Teacher: Lecturers of the University of Education Freiburg
Language: in German
Supplementary Module in Mathematics Education (MEd18, MEH21, MEB21)
Module "Research in Mathematics Education"
Part 1: Seminar 'Development Research in Mathematics Education ‒ Selected Topics': Mo, 14-16h, Mensa 3 / Zwischendeck SR 032, PH Freiburg, 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
Dates and rooms can be found in the course catalogue of the PH Freiburg
Teacher: Lecturers of the University of Education Freiburg, Anselm Strohmaier
Language: in German
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.
Research in Mathematics Education (MEd18, MEH21, MEB21)
Organisation: Susanne Knies
Language: in German
What characterizes a good tutorial? This question will be discussed in the first workshop and tips and suggestions will be given. Experiences will be shared in the second workshop.
Elective (Option Area) (2HfB21)
Elective (BSc21)
Elective (MSc14)
Elective (MScData24)
Introduction to Programming for Science Students
Lecture: Mo, 16-18h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Teacher: Ludwig Striet
Language: in German
none
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
BOK course (BSc21)
Supplementary Module in Mathematics (MEd18)
Computer exercises in Numerics
Teacher: Sören Bartels
Assistant: Vera Jackisch
Language: in German
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Numerics (BSc21)
Supplementary Module in Mathematics (MEd18)
Computer exercises in Statistics
Mo, 14-16h, PC-Pool Raum 201, Hermann-Herder-Str. 10
Teacher: Sebastian Stroppel
Language: in German
This computer exercise course is aimed at students who have already attended the lectures Elementary Probability Theory I and II or are attending the second part this semester. Computer-based methods will be discussed to deepen the understanding of the lecture material and demonstrate further application examples. For this purpose, the programming language python is used. After an introduction to python, methods of descriptive statistics and graphical analysis of data will be considered, the numerical generation of random numbers will be explained and parametric and non-parametric tests and linear regression methods will be discussed. Previous knowledge of python and/or programming skills are not required.
Analysis I+II, Linear Algebra I+II, Elementary Probability Theory I+II (part II can be followed in parallel).
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Supplementary Module in Mathematics (MEd18)
Elective (MScData24)
Do, 14-16h, PC-Pool Raum -100, Hermann-Herder-Str. 10
Teacher: Carola Heinzel
Assistant: Samuel Adeosun
Language: in English
This course introduces the foundational concepts and practical skills necessary for understanding and implementing machine learning models, with a particular focus on deep learning and neural networks. Students will progress from basic programming skills in Python , with a focus on the PyTorch library, to advanced topics such as training multi-layer perceptrons, optimization techniques, and transformer architectures. By the end of the course, participants will have the ability to implement and analyze neural networks, apply optimization strategies, and understand modern transformer-based models for tasks such as text generation and time series analysis.
Basic knowledge in programming and basic knowledge in stochastics.
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)
Di, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Peter Pfaffelhuber
Assistant: Sebastian Stroppel
Language: in English
Lean4 is both, a programming language and an interactive theorem prover. By the latter, we mean software that is able to check mathematical proofs. It is interactive since the software tells you what remains to be proven after every line of code. The course is an introduction to this technique, with examples from various fields of mathematics. Lean4 is special since researchers all over the world are currently building a library of mathematical theories, which contains at the moment around 1.5 million lines of code. I aim to cover basics from calculus, algebra, topology and measure theory in Lean4.
Analysis 1, 2, Linear algebra 1
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)
Undergraduate seminar: One-Dimensional Maximum Principle
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 05.02., 16:00, SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Guofang Wang
Assistant: Xuwen Zhang
Language: in German
Analysis I and II
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Seminar: Do, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Preregistration: until 30.01. to Vivien Vogelmann
Preliminary Meeting 04.02., 12:00, SR 318, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Susanne Knies
Assistant: Vivien Vogelmann
Language: in German
The seminar deals with statements that are known from finite-dimensional vector spaces but no longer apply in the infinite-dimensional case. What are the consequences of this? What applies instead? With which additional conditions can one possibly save oneself?
For more detailed information see the webpage!
Analysis I, II and Linear Algebra I, II
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Undergraduate seminar: Lattice Theory
Seminar: Mo, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Preregistration: until 31.01. to Markus Junker
Preliminary Meeting 07.02., 11:15, SR 318, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Markus Junker
Language: in German
Linear Algebra I and II, Analysis I
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Undergraduate seminar: Counter-Examples in Probability Theory
Teacher: David Criens
Assistant: Andreas Demleitner
It is not only theorems, proofs or illustrative examples, but also counterexamples that show the depth and beauty of a theory. Natural questions are: (a) are the requirements of a theorem necessary and not only sufficient; (b) are the requirements sufficient and not just necessary; (c) is an implication an equivalence, i.e. does the implication in the other direction also hold.
In this undergraduate seminar we deal with counter-examples from probability theory. Possible topics range from classic questions such as measurability, independence of random variables, expectations or conditional probabilities, to more advanced topics such as limit value rates, martingals or Markov processes. A suitable topic can be found for any interested student.
Elementary Probability Theory I (topics from probability theory I–III can also be assigned)
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Seminar: Mo, 12-14h, online, -
Preregistration: by e-mail to Diyora Salimova
Preliminary Meeting 14.04., 15:00, via zoom (please write the lecturer in case the time slot does not fit you)
Preparation meetings for talks: Dates by arrangement
Teacher: Diyora Salimova
Language: Talk/participation possible in German and English
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 including, in particular, certain types of PDE solutions.
Basics of functional analysis, numerics of differential equations, and probability theory
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)
Seminar: Do, 10-12h, SR 403, Ernst-Zermelo-Str. 1
Preregistration: by e-mail to Wolfgang Soergel
Preliminary Meeting 28.01., 14:15, SR 127, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Language: Talk/participation possible in German and English
This seminar is intended to introduce to the theory of linear algebraic groups. Linear algebraic groups are generalizations of the matrix groups known from linear algebra.
I imagine a format in which I or Sercombe lecture and in between the seminar participants give talks. The seminar is a reasonable addition to the commutative algebra lecture. Reference to that lecture increase in the course of the seminar.
Algebra and Number Theory (where the details of Galois theory and field theory are less relevant than the general theory of groups and rings) and Linear Algebra.
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 04.02., 12:15, SR 218, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Ernst Kuwert
Analysis I–III
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: Di, 12-14h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 04.02., 10:00, SR 318, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Nadine Große
Assistant: Maximilian Stegemeyer
Language: Talk/participation possible in German and English
Differential Geometry I
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: Di, 16-18h, SR 403, Ernst-Zermelo-Str. 1
Preliminary Meeting 29.01., 13:15, Raum 313, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Heike Mildenberger
Assistant: Maxwell Levine
Language: Talk/participation possible in German and English
Set Theory
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Teacher: Harald Binder
Language: Talk/participation possible in German and English
To answer complex biomedical questions from large amounts of data, a wide range of analysis tools is often necessary, e.g. deep learning or general machine learning techniques, which is often summarized under the term ``Medical Data Science''. Statistical approaches play an important rôle as the basis for this. A selection of approaches is to be presented in the seminar lectures that are based on recent original work. The exact thematic orientation is still to be determined.
Good knowledge of probability theory and mathematical statistics.
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)
Seminar: Numerics of Partial Differential Equations
Seminar: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 04.02., 12:00, Raum 209, Hermann-Herder-Str. 10, Or registration by e-mail to Sören Bartels.
Teacher: Sören Bartels
Assistant: Vera Jackisch, Tatjana Schreiber
Language: Talk/participation possible in German and English
The seminar will cover advanced topics in the theory and numerics of partial differential equations. This includes the iterative solution of the resulting linear systems of equations with multigrid and domain decomposition methods, the adaptive refinement of finite element grids, the derivation of an approximation theory with explicit constants, and the solution of nonlinear problems.
Introduction to Theory and Numerics of Partial Differential Equations
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)
Seminar on p-adic Geometry
Seminar: Mo, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Preliminary Meeting 13.02., 14:30, SR 404, Ernst-Zermelo-Str. 1, Please email Abhisehk Oswal, and Ben Snodgrass if you are interested in the seminar but cannot make it to the preliminary meeting.
Teacher: Abhishek Oswal
Assistant: Ben Snodgrass
Language: in English
It has become clear over the last several decades that \(p\)-adic techniques play an indispensable role in arithmetic geometry. At an elementary level, \(p\)-adic numbers provide a compact and convenient language to talk about congruences between integers. Concretely, just as the field of real numbers \(\mathbb R\) arise as the completion of the field \(\mathbb Q\) of rational numbers with respect to the usual notion of distance on \(\mathbb Q\), the field \(\mathbb Q_p\) of \(p\)-adic numbers arise as the completion of \(\mathbb Q\) with respect to an equally natural \(p\)-adic metric. Roughly, in the \(p\)-adic metric, an integer \(n\) is closer to \(0\), the larger the power of the prime number \(p\) that divides it. A general philosophy in number theory is then to treat all these completions \(\mathbb R\), \(\mathbb Q_p\) of the field \(\mathbb Q\) on an equal footing. As we shall see in this course, familiar concepts from real analysis (i.e. notions like analytic functions, derivatives, measures, integrals, Fourier analysis, real and complex manifolds, Lie groups...), have completely parallel notions over the \(p\)-adic numbers.
While the Euclidean topology of \(\mathbb R^n\) is rather well-behaved (so one may talk meaningfully about paths, fundamental groups, analytic continuation, ...), the \(p\)-adic field \(\mathbb Q_p\) on the other hand is totally disconnected. This makes the task of developing a well-behaved notion of global \(p\)-adic analytic manifolds/spaces rather difficult. In the 1970s, John Tate’s introduction of the concept of rigid analytic spaces, solved these problemsand paved the way for several key future developments in \(p\)-adic geometry.
The broad goal of this course will be to introduce ourselves to this world of \(p\)-adic analysis and rigid analytic geometry (due to Tate). Along the way, we shall see a couple of surprising applications of this circle of ideas to geometry and arithmetic. Specifically, we plan to learn Dwork’s proof of the fact that the zeta function of an algebraic variety over a finite field is a rational function.
Field theory, Galois theory and Commutative algebra.
Some willingness to accept unfamiliar concepts as black boxes. Prior experience with algebraic number theory, or algebraic geometry will be beneficial but not necessary.
Elective (Option Area) (2HfB21)
Mathematical Seminar (BSc21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Mathematical Seminar (MSc14)
Elective (MSc14)
Elective (MScData24)
Seminar: The Wiener Chaos Decomposition and (Non-)Central Limit Theorems
Teacher: Angelika Rohde
Language: Talk/participation possible in German and English
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)
Note: Only for the degree programme "Mathematics in Data and Technology"
Teacher: Nadine Binder
Language: Talk/participation possible in German and English
Imagine being able to use routine data such as diagnoses, lab results, and medication plans to answer medical questions in innovative ways and improve patient care. In this seminar, we will learn to identify relevant data, understand suitable analysis methods, and what to consider when applying them in practice. Together, we will analyze scientific studies on routine data and discuss clinical questions, the methods used, and their feasibility for implementation.
What makes this seminar special: Medical and mathematics students collaborate to understand scientific studies from both perspectives. When possible, you will work in pairs (or individually if no pair can be formed) to analyze a study from your respective viewpoints and prepare related presentations. You may test available programming code or develop your own approaches to replicate the methods and apply them to your own questions. The pairs can be formed during the preliminary meeting.
necessary: Basics in Appiled Mathematics
useful: Probability Theory I
Mathematical Seminar (MScData24)
Elective in Data (MScData24)
Graduate Student Speaker Series
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Organisation: Sören Bartels, Ernst August v. Hammerstein
Language: in English
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.
Graduate Student Speaker Series (MScData24)
Within the EUCOR cooperation, you can attend courses at the partner universities. If you click on the universities, you will find links to their course catalogues.
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
Details: please click on the title and follow the link!
Computational Economics
Lecture: Mi, 14-16h, Paulussaal, Pauluskirche
Exercise session: Mi, 8-10h, HS 1098, KG I
Course offered by the Institute for Economics
Teacher: Dirk Neumann
Elective in Data (MScData24)
Foundations of Artificial Intelligence
Lecture: Mi, 14-16h, HS 00-026, Georges-Köhler-Allee 101
Exercise session: Fr, 10-12h, verschiedene Räume, -
Course offered by the Faculty of Engineering
Teacher: Joschka Boedecker, Abhinav Valada
Elective in Data (MScData24)
Image Processing and Computer Graphics
Lecture (3 hours): Di, 14-16h, HS 00-036, Georges-Köhler-Allee 101, Mi, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Tutorial (1 hour): Mi, 10-12h, verschiedene Räume, -
Course offered by the Faculty of Engineering
Teacher: Thomas Brox, Matthias Teschner
Elective in Data (MScData24)
Course offered by the Institute for Economics
Teacher: Ekaterina Kazak
Elective in Data (MScData24)
Further courses can be admitted as Elective in Data or as Elective after consultation with the Examination Board.
Service Teaching is specifically for students of subjects other than mathematics and not intended for the mathematics degree programmes.
Lecture: Mo, Mi, 10-12h, HS 00-026, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates
Teacher: Ernst August v. Hammerstein
Assistant: Damian Sercombe
Mathematics I for Engineering Students
Lecture: Mo, Mi, 16-18h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Ernst Kuwert
Assistant: Florian Johne
Mathematics II for Science Students
Lecture: Di, Do, 10-12h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Susanne Knies
Assistant: Sören Andres
Probability Theory for Computer Science Students
Lecture: Mo, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates
Teacher: Thorsten Schmidt
Working group seminar: Applied Analysis
Mo, 14-16h, Bibliotheksraum 216, Hermann-Herder-Str. 10
Teacher: Patrick Dondl
Working group seminar: Geometrical Analysis
Di, 16-18h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Ernst Kuwert, Guofang Wang
Working group seminar: Non-Newtonian Fluids
Fr, 10-12h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Michael Růžička
Research seminar: Algebra, Number Theory, and Algebraic Geometry
Fr, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Organisation: Stefan Kebekus, Abhishek Oswal, Wolfgang Soergel
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.
Research seminar: Applied Mathematics
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Organisation: Sören Bartels, Patrick Dondl, Michael Růžička, Diyora Salimova
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.
Research seminar: Differential Geometry
Mo, 16-18h, SR 404, Ernst-Zermelo-Str. 1
Organisation: Nadine Große
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.
Di, 14: 30-16h, SR 404, Ernst-Zermelo-Str. 1
Organisation: Amador Martín Pizarro, Heike Mildenberger
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.
Research seminar: Medical Statistics
Do, 13-14h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Organisation: Harald Binder
Research seminar: Probability Theory
Mi, 16-17h, SR 226, Hermann-Herder-Str. 10
Organisation: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
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.
Mathematics Education Colloquium
Di, 18: 30-20h, HS II, Albertstr. 23b
Organisation: Katharina Böcherer-Linder, Ernst Kuwert
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.
Mathematical Colloquium
Do, 15-16h, HS II, Albertstr. 23b
Organisation: Nadine Große, Amador Martín Pizarro
Colloquium for Mathematics Students
Do, 14-15h, HS II, Albertstr. 23b
Organisation: Markus Junker, Amador Martín Pizarro
In the ‘Mathematical Colloquium for Students’, topics from the various fields of work are presented in a ‘mathematically understandable’ way. The lectures are aimed at advanced Bachelor's students, Master's students of all specialisations, as well as doctoral students. Afterwards, there will be an opportunity for questions, discussion and dialogue over coffee and tea.
Seminar on Data Analysis and Modelling
Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1
Organisation: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer
Current, interdisciplinary research is presented here, in which mathematical models enable the understanding of natural and social science issues.