Preliminary course catalogue - changes and additions are likely.
Click on the course title for more information!
Further Chapters in Analysis
Lecture: Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
Teacher: Ernst August v. Hammerstein
Language: in German
\textit{Multiple integration:} Jordan content in \(\mathbb R^n\), Fubini's theorem, transformation theorem, divergence and rotation of vector fields, path and surface integrals in \(\mathbb R^3\), Gauss' theorem, Stokes' theorem.\ \textit{Complex analysis:} Introduction to the theory of holomorphic functions, Cauchy's integral theorem, Cauchy's integral formula and applications.
Required: Analysis~I and II, Linear Algebra~I and II
Further Chapters in Analysis
Algebraic Topology
Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Maximilian Stegemeyer
Language: in German
Mathematical Concentration
Analysis III
Lecture: Mo, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced
Teacher: Michael Růžička
Language: in German
Lebesgue measure and measure theory, Lebesgue integral on measure spaces and Fubini's theorem, Fourier series and Fourier transform, Hilbert spaces. Differential forms, their integration and outer derivative. Stokes' theorem and Gauss' theorem.
Required: Analysis I and II, Linear Algebra I
Mathematical Concentration
Complex Analysis
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Stefan Kebekus
Language: in German
Complex analysis deals with functions \(f : \mathbb C \to \mathbb C\) , which map complex numbers to complex numbers. Many concepts of Analysis~I can be directly transferred to this case, e.\,g. the definition of differentiability. One might expect that this would lead to a theory analogous to Analysis~I but much more is true: in many respects you get a more elegant and simpler theory. For example, complex differentiability on an open set implies that a function is even infinitely often differentiable, and this is further consistent with analyticity. For real functions, all these notions are different. However, some new ideas are also necessary: For real numbers \(a\), \(b\) one integrates for \[\int_a^b f(x) \mathrm dx\] over the elements of the interval \([a, b]\) or \([b, a]\). However, if \(a\), \(b\) are complex numbers, it is no longer so clear clear how such an integral is to be calculated. One could, for example, in the complex numbers along the line that connects \(a, b \in \mathbb C\), or along another curve that leads from \(a\) to \(b\). Does this lead to a well-defined integral term or does such a curve integral depend on the choice of the curve?
Required: Analysis I+II, Linear Algebra I
Mathematical Concentration
Introduction to Theory and Numerics of Partial Differential Equations
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Patrick Dondl
Language: in English
The aim of this course is to give an introduction into theory of linear partial differential equations and their finite difference as well as finite element approximations. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensable tool in science and technology. We provide an introduction to the construction, analysis, and implementation of finite element methods for different model problems. We will address elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.
Required: Analysis~I and II, Linear Algebra~I and II as well as knowledge about higher-dimensional integration (e.g. from Analysis~III or Extensions of Analysis) \ Recommended: Numerics for differential equations, Functional analysis
Mathematical Concentration
Calculus of Variations
Lecture: Mo, Mi, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Guofang Wang
Assistant: Florian Johne
Language: in German
Mathematical Concentration
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
Futures and Options
Lecture: Mo, 10-12h, -, -
Exercise session: Di, 8-10h, -, -
Teacher: Eva Lütkebohmert-Holtz
Language: in English
This course covers an introduction to financial markets and products. Besides futures and standard put and call options of European and American type we also discuss interest-rate sensitive instruments such as swaps.
For the valuation of financial derivatives we first introduce financial models in discrete time as the Cox--Ross--Rubinstein model and explain basic principles of risk-neutral valuation. Finally, we will discuss the famous Black--Scholes model which represents a continuous time model for option pricing.
Required: Elementary Probability Theory~I
Supplementary Module in Mathematics
Machine Learning and Mathematical Logic
Lecture: Do, 14-16h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Maxwell Levine
Language: in English
Supplementary Module in Mathematics
Markov Chains
Lecture: Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: David Criens
Language: in English
The class of Markov chains is an important class of (discrete-time) stochastic processes that are used frequently to model for example the spread of infections, queuing systems or switches of economic scenarios. Their main characteristic is the Markov property, which roughly means that the future depends on the past only through the current state. In this lecture we provide the mathematical foundation of the theory of Markov chains. In particular, we learn about path properties, such as recurrence and transience, state classifications and discuss convergence to the equilibrium. We also study extensions to continuous time. On the way we discuss applications to biology, queuing systems and resource management. If the time allows, we also take a look at Markov chains with random transition probabilities, so-called random walks in random environment, which is a prominent model in the field of random media.
Required: Elementary Probability Theory~I \ Recommended: Analysis~III, Probability Theory~I
Supplementary Module in Mathematics
Mathematical Introduction to Deep Neural Networks
Lecture: Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Diyora Salimova
Language: in English
Supplementary Module in Mathematics
Numerical Optimal Control
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Teacher: Moritz Diehl
Language: in English
The aim of the course is to give an introduction to numerical methods for the solution of optimal control problems in science and engineering. The focus is on both discrete time and continuous time optimal control in continuous state spaces. It is intended for a mixed audience of students from mathematics, engineering and computer science.
The course covers the following topics:
The lecture is accompanied by intensive weekly computer exercises offered both in MATLAB and Python (6~ECTS) and an optional project (3~ECTS). The project consists in the formulation and implementation of a self-chosen optimal control problem and numerical solution method, resulting in documented computer code, a project report, and a public presentation.
Required: Analysis~I and II, Linear Algebra~I and II \ Recommended: Numerics I, Ordinary Differential Equations, Numerical Optimization
Supplementary Module in Mathematics
Theory and Numerics for Partial Differential Equations – ??
Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Sören Bartels
Language: in English
Supplementary Module in Mathematics
Mathematics Education ‒ Functions and Analysis
Do, 9-12h, SR 226, Hermann-Herder-Str. 10
Teacher: Katharina Böcherer-Linder
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
Mathematics Education ‒ Probability Theory and Algebra
Mi, 11-14h, SR 404, Ernst-Zermelo-Str. 1
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
Mathematics education seminar: Media Use in Teaching Mathematics
Seminar: Mi, 15-18h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Jürgen Kury
The use of teaching media in mathematics lessons wins both at the level of lesson planning and lesson realization in importance. Against the background of constructivist learning theories shows that the reflective use of computer programs, among other things mathematical concept formation in the long term. For example experimenting with computer programs allows mathematical structures to be discovered, without this being overshadowed by individual routine operations (such as term transformation) would be covered up. This has far-reaching consequences for mathematics lessons. For this reason, this seminar aims to provide students the necessary decision-making and action skills to prepare future mathematics teachers for their professional activities. Starting from initial considerations about lesson planning, computers and tablets with regard to their respective didactic potential and tested with learners during a classroom visit. The exemplary systems presented are:
The students should develop teaching sequences, which will then be tested and reflected on with pupils (where this will be possible).
Recommended: Basic courses in mathematics
Supplementary Module in Mathematics Education
Mathematics education seminars at Freiburg University of Education
Teacher: Lecturers of the University of Education Freiburg
Language: in German
Supplementary Module in Mathematics Education
Module "Research in Mathematics Education"
Part 1: Seminar 'Development Research in Mathematics Education ‒ Selected Topics': Mo, 14-16h, Raum noch nicht bekannt, PH Freiburg
Part 2: Seminar 'Research Methods in Mathematics Education': Mo, 16-19h, Raum noch nicht bekannt, PH Freiburg
Part 3: Master's thesis seminar: Development and Optimisation of a Research Project in Mathematics Education
Registration: see course descriptions
Teacher: Lecturers of the University of Education Freiburg
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
Learning by Teaching
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.
Supplementary Module in Mathematics
SAALA
Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Katharina Böcherer-Linder, Markus Junker
Supplementary Module in Mathematics
Computer exercises for 'Introduction to Theory and Numerics of Partial Differential Equations'
Teacher: Patrick Dondl
Language: in English
Supplementary Module in Mathematics
Computer exercises in Numerics
Teacher: Patrick Dondl
Language: in German
Supplementary Module in Mathematics
Computer exercises for 'Theory and Numerics of Partial Differential Equations'
Please note the registration modalities for the individual proseminars published in the comments to the course catalog: As a rule, places are allocated after pre-registration by e-mail at the preliminary meeting at the end of the lecture period of the summer semester. You must then register online for the examination; the registration period runs from August 1, 2025 to October 8, 2025; if you would like to attend a proseminar but have not been allocated a place, please contact the degree program coordinator immediately.
Seminar
Please note the registration modalities for the individual seminars published in the comments to the course catalog: As a rule, places are allocated after pre-registration by e-mail at the preliminary meeting at the end of the lecture period of the summer semester. You must then register online for the exam; the registration period runs from August 1, 2025 to October 8, 2025.
M.Ed.-Seminar (nach Praxissemester)
Seminar: Computational PDEs
Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Sören Bartels
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
Supplementary Module in Mathematics
Seminar: Medical Data Science
Seminar: Mi, 10:15-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary Meeting 17.07., HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
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.
Supplementary Module in Mathematics
Seminar: Minimal Surfaces
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Guofang Wang
Supplementary Module in Mathematics
Seminar
Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Supplementary Module in Mathematics
Seminar
Seminar: Mo, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Angelika Rohde
Supplementary Module in Mathematics