Lecturer: Peter Pfaffelhuber
Assistant: Samuel Ayomide Adeosun
Language: in German

29.09.–02.10.; begins on 29.09. at 10h15 in HS Physiologie.

Content

Optional offer for first-year students of mathematics: The pre-course gives a taste of studying mathematics and is intended to make it easier to get started, but it is not a prerequisite for the degree programme.

Lecturer: Susanne Knies
Language: in German

02.10.–05.10.2024, begins at 9h in HS Rundbau.

Lecturer: Fachschaft
Language: in German

Lecturer: Fachschaft
Language: in German

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

Time and place

Lecture: Di, Mi, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sit-in exam 24.02., 14:00-17:00, HS Rundbau, Albertstr. 21, HS Weismann-Haus, Albertstr. 21a
Sit-in exam (resit) 16.04., 09:00-12:00, HS Rundbau, Albertstr. 21

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

Analysis I is one of the two basic lectures in the mathematics course. It deals with concepts based on the notion of limit. The central topics are: induction, real and complex numbers, convergence of sequences and series, completeness, exponential function and trigonometric functions, continuity, derivation of functions of one variable and regulated integrals.

Previous knowledge

Required: High school mathematics. \
Attendance of the preliminary course (for students in mathematics) is recommended.

Usability

Analysis (2HfB21, BSc21, MEH21, MEB21)
Analysis I (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: Mo, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sit-in exam 17.02., 10:00-12:00
Sit-in exam (resit) 28.05., 10:00-12:00

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

Linear Algebra I is one of the two introductory lectures in the mathematics degree program that form the basis for further courses. Topics covered include: fundamental concepts (in particular fundamental concepts of set theory and equivalence relations), groups, fields, vector spaces over arbitrary fields, basis and dimension, linear mappings and transformation matrix, matrix calculus, linear systems of equations, Gaussian elimination, linear forms, dual space, quotient vector spaces and homomorphism theorem, determinant, eigenvalues, polynomials, characteristic polynomial, diagonalizability, affine spaces. The background to the mathematical content is explained in terms of ideas and the history of mathematics.

Previous knowledge

Required: High school mathematics. \
Attendance of the preliminary course (for students in mathematics) is recommended.

Usability

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

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 Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours fortnightly, various dates
Sit-in exam (resit) 23.10., 09:00-11:00, SR 226, Hermann-Herder-Str. 10

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

Numerics is a sub-discipline of mathematics that deals with the practical solution of mathematical problems. As a rule, problems are not solved exactly but approximately, for which a sensible compromise between accuracy and computational effort must be found. The first part of the two-semester course focuses on questions of linear algebra such as solving linear systems of equations and determining the eigenvalues of a matrix. Attendance at the accompanying practical exercises ({\em Praktische Übung zur Numerik}) is recommended. These take place every 14 days, alternating with the lecture's tutorial.

Previous knowledge

Required: Linear Algebra~I \
Recommended: Linear Algebra~II and Analysis~I (required for Numerics~II)

Usability

Numerics (BSc21)
Numerics (2HfB21, MEH21)
Numerics I (MEB21)

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 14.03.
Sit-in exam (resit) 06.08., 10:00-12:00

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

Stochastic is, to put it loosely, the “mathematics of chance”, about which---possibly contrary to first impressions---many precise and not at all random statements can be formulated and proven. The aim of the lecture is to give an introduction to stochastic modeling, to explain some basic concepts and results of Stochastic and to illustrate them with examples. It is also intended as a motivating preparation for the lecture “Probability Theory” in the summer semester, especially for students in the B.Sc. in Mathematics. Topics covered include: Discrete and continuous random variables, probability spaces and measures, combinatorics, expected value, variance, correlation, generating functions, conditional probability, independence, weak law of large numbers, central limit theorem. The lecture Elementary Probability Theory~II in the summer semester will mainly be devoted to statistical topics. If you are interested in a practical, computer-supported implementation of individual lecture contents, participation in the regularly offered practical excercise “Praktischen Übung Stochastik" is also recommended (in parallel or subsequently).

Previous knowledge

Required: Linear Algebra I, Analysis I and II. \
Note that Linear Algebra I can be attended in parallel.

Usability

Elementary Probabilty Theory (2HfB21, MEH21)
Elementary Probability Theory I (BSc21, MEB21, MEdual24)

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

Lecture: Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 19.02., 14:00-17:00, HS Anatomie, Albertstr. 17
Sit-in exam (resit) 15.04., 10:00-13:00, HS Weismann-Haus, Albertstr. 21a

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

This compulsory lecture for teacher training students in the M.Ed. builds on the basic lectures Analysis I and II and supplements them with the following two main topics:

\textit{Multidimensional integration:} The one-dimensional Riemann integral known from Analysis I is generalized to real-valued functions of several variables, for which a suitable instrument for measuring the content/volume of multidimensional sets is first introduced with the Jordan content. Then the classical integral theorems (transformation theorem, Fubini's theorem) are derived, and path and surface integrals are considered. With the help of the divergence and rotation of vector fields, the two aforementioned integral types can be related to each other using the integral theorems of Gauß and Stokes, which considerably simplifies the calculations in practical applications.

\textit{Complex Analysis:} In contrast to Analysis I, here the (complex) differentiability of functions of a complex variable is examined. As will be shown, complex differentiable, so-called holomorphic functions are subject to much stricter rules and laws than their real-valued counterparts, which leads to both beautiful and surprising results. To this end, we will prove Cauchy's intergal theorem and Cauchy's integral formula and take a closer look at applications and conclusions from these.

Previous knowledge

Analysis~I and II, Linear Algebra~I and II

Usability

Further Chapters in Analysis (MEd18, MEH21, MEdual24)

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

Lecturer: Sören Bartels, Moritz Diehl, Thorsten Schmidt
Assistant: Alen Kushova, Simone Pavarana
Language: in English

Time and place

Lecture: Di, Do, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Exercise session: Do, 10-12h, HS II, Albertstr. 23b
Programming exercise: 2 hours, date to be determined

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

This course provides an introduction into the basic concepts, notions, definitions and results in probability theory, numerics and optimization, accompanied with programming projects in Python. Besides deepen mathematical skills in principle, the course lays the foundation of further classes in these three areas.

Previous knowledge

None that go beyond admission to the degree programme.

Usability

Basics in Applied Mathematics (MScData24)

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: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 26.02.
Sit-in exam (resit) 15.04., 09:00-12:00

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

This lecture continues the linear algebra courses. It treats groups, rings, fields and applications in the number theory and geometry. The highlights of the lecture are the classification of finite fields, the impossibility of the trisection of angles with circle and ruler, the non-existence of a solution formula for the general equations of fifth degree and the quadratic reciprocity law.

Previous knowledge

Linear Algebra I and II

Usability

Algebra and Number Theory (2HfB21, MEH21)
Compulsory Elective in Mathematics (BSc21)
Introduction to Algebra and Number Theory (MEB21)
Algebra and Number Theory (MEdual24)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)

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

Lecturer: Maximilian Stegemeyer
Language: in German

Time and place

Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Exercise session: Mi, 14-16h, SR 403, Ernst-Zermelo-Str. 1
Oral exam 11.03.

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

Algebraic topology studies topological spaces by assigning algebraic objects, e.g. groups, vector spaces or rings, to them in a particular way. This assignment is usually done in a way which is invariant under homotopy equivalences. Therefore one often speaks of homotopy invariants and algebraic topology can be seen as the study of the construction and the properties of homotopy invariants.

In this lecture we will first recall the notion of the fundamental group of a space and study its connection to covering spaces. Then we will introduce the singular homology of a topological space and study it extensively. In the end, we will consider cohomology and homotopy groups and explore their relation to singular homology. We will also consider various applications of these invariants to topological and geometric problems.

Previous knowledge

Topology

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
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: Michael Růžička
Assistant: Luciano Sciaraffia
Language: in German

Time and place

Lecture: Mo, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 16.02., 13:00-15:00
Sit-in exam (resit) 08.04., 09:00-11:00, HS Weismann-Haus, Albertstr. 21a

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

The Analysis III lecture deals with measure and integration theory, with particular emphasis on the Lebesgue measure. These theories are of particular importance for many further lectures in analysis, applied mathematics, stochastics, probability theory and geometry, as well as physics. Main topics are measures and integrals in \(\mathbb R^n\), Lebesgue spaces, convergence theorems, the transformation theorem, surface integrals and Gauss' integral theorem.

Previous knowledge

Required: Analysis I and II, Linear Algebra I \
Useful: Linear Algebra II

Usability

Elective (Option Area) (2HfB21)
Analysis III (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Elective in Data (MScData24)

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

Lecturer: Yuchen Bi
Language: in English

Time and place

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

Content

This course offers an introduction to differential geometry with a focus on the structure of smooth manifolds. Key topics include the construction and properties of vector fields, differential forms, and their applications. The course will also include an introduction to Riemannian metrics if time permits, though the treatment will remain at an introductory level.

Previous knowledge

Required: Analysis~I–III, Lineare Algebra~I and II \ Prior exposure to curves and surfaces (“Kurven und Flächen”) and topology is beneficial.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
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: Stefan Kebekus
Assistant: Xier Ren
Language: 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
Sit-in exam 09.02., 08:00-12:00
Sit-in exam (resit) 20.07., 08:00-12:00

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

This lecture deals with the theory of complex differentiable complex-valued functions in one complex variable. You will learn that these are much more rigid than the differentiable real-valued functions in one real variable and that their properties are more similar to those of polynomial functions. Complex analysis is fundamental to the study of large parts of mathematics, in particular number theory and algebraic geometry, and its applications extend to probability theory, functional analysis, and mathematical physics.

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: Patrick Dondl
Assistant: Ludwig Striet, Oliver Suchan
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

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

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.

Previous knowledge

Required: Analysis~I and II, Linear Algebra~I and II as well as knowledge about higher-dimensional integration (e.g. from Analysis~III or from Further Chapters in Analysis) \
Recommended: Numerics for differential equations, Functional analysis

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (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 August v. Hammerstein
Assistant: Sebastian Hahn
Language: in English

Time and place

Lecture: Di, Do, 14-16h, SR 404, 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

The lecture builds on basic knowledge about Probability Theory. The fundamental problem of statistics is to infer from a sample of observations as precise as possible statements about the data-generating process or the underlying distributions of the data. For this purpose, the most important methods from statistical decision theory such as test and estimation methods are introduced in the lecture.

Key words hereto include Bayes estimators and tests, Neyman-Pearson test theory, maximum likelihood estimators, UMVU estimators, exponential families, linear models. Other topics include ordering principles for reducing the complexity of models (sufficiency and invariance).

Statistical methods and procedures are used not only in the natural sciences and medicine, but in almost all areas in which data is collected and analyzed This includes, for example, economics (“econometrics”) and the social sciences (especially psychology). However, in the context of this lecture, we will focus less on applications, but---as the name suggests---more on the mathematical justification of the methods.

Previous knowledge

Probability Theory (in particular measure theory and conditional probabilities/expectations)

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: Amador Martín Pizarro
Assistant: Charlotte Bartnick
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
Oral exam

The lecture will probably be held in English.

Content

In this course the basics of geometric model theory will be discussed and concepts such as quantifier elimination and categoricity will be introduced. A theory has quantifier elimination if every formula is equivalent to a quantifier-free formula. For the theory of algebraically closed fields of fixed characteristic, this is equivalent to requiring that the projection of a Zariski-constructible set is again Zariski-constructible. A theory is called \(\aleph_1\)-categorical if all the models of cardinality \(\aleph_1\) are isomorphic. A typical example is the theory of non-trivial \(\mathbb Q\)-vector spaces. The goal of the course is to understand the theorems of Baldwin-Lachlan and of Morley to characterize \(\aleph_1\)-categorical theories.

Previous knowledge

necessary: Mathematical Logic \
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: Giuseppe Genovese
Assistant: Roger Bader
Language: in English

Time and place

Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Exercise session: Do, 16-18h, SR 218, Ernst-Zermelo-Str. 1

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

The goal of the course is to provide a mathematical treatment of deep neural networks and energy models, that are the building blocks of many modern machine learning architectures. About neural networks we will study the basics of statistical learning theory, the back-propagation algorithm and stochastic gradient descent, the benefits of depth. About energy models we will cover some of the most used learning and sampling algorithms. In the exercise classes, besides solving theoretical problems, there will be some Python programming sessions to implement the models introduced in the lectures.

Previous knowledge

Probability Theory I \
Basic knowledge of Markov chains is useful for some part of the course.

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: Angelika Rohde
Assistant: Johannes Brutsche
Language: in English

Time and place

Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
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

A stochastic process \((X_t)_{t\in T}\) is a family of random variables, where mostly the situation \(T = \mathbb{N}\) or \(T = [0, 1]\) is studied. Basic examples include stationary time series, the Poisson process and Brownian motion as well as processes derived from those. The lecture includes ergodic theory and its applications, Brownian motion and especially the study of its path properties, the elegant concept of weak convergence on Polish spaces as well as functional limit theorems. Finally, we introduce stochastic integration with respect to local martingales, based on the continuous time version of the martingale transform.

Previous knowledge

Probability Theory I

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: Guofang Wang
Assistant: Florian Johne
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

Die Anforderungen an Studien- und Prüfungsleistungen werden in den aktuellen Ergänzungen der Modulhandbücher beschrieben, die ab Ende Oktober 2025 als Teil des Kommentierten Vorlesungsverzeichnisses veröffentlicht werden.

Content

The aim of the calculus of variations is to minimise or maximise certain mathematically treatable quantities. More precisely, we consider \(\Omega \subset {\mathbb R}^n\) functionals or variation integrals of the form \[F (u) = \int_\Omega f(x,u (x ),Du (x))dx, \quad \hbox{ f\"ur } u : \Omega\to {\mathbb R}\] on \(\Omega \subset {\mathbb R}^n\).

Examples are arc length and area, as well as energies of fields in physics. The central question is the existence of minimisers. After a brief introduction to the functional analysis tools, we will first familiarise ourselves with some necessary and sufficient conditions for the existence of minimisers. We will see that compactness plays a very important role. We will then introduce some techniques that help us to get by without compactness in special cases: The so-called compensated compactness and the concentrated compactness.

Previous knowledge

necessary: Functional Analysis \
useful: PDE, numerical PDE

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
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: All professors and 'Privatdozenten' of the Mathematical Institute
Language: Talk/participation possible in German and English

Time and place

Dates by arrangement

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 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: Eva Lütkebohmert-Holtz
Language: in English

Time and place

Lecture: Mo, 10-12h, HS 1015, KG I
Exercise session: Di, 8-10h, HS 1098, KG I
Sit-in exam 13.02., 09:00-12:00

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

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.

Previous knowledge

Elementary Probability Theory I

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: Abhishek Oswal
Assistant: Damian Sercombe
Language: in English

Time and place

Lecture: Mo, 14-16h, SR 125, 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

There is no information available yet.

Previous knowledge

There is no information available yet.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
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: Maxwell Levine
Language: in English

Time and place

Lecture: Do, 14-16h, SR 226, Hermann-Herder-Str. 10
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

Developments in artificial intelligence have boomed in recent years, holding the potential to reshape not just our daily routines but also society at large. Many bold claims have been made regarding the power and reach of AI. From a mathematical perspective, one is led to ask: What are its limitations? To what extent does our knowledge of reasoning systems in general apply to AI?

This course is intended to provide some applications of mathematical logic to the field of machine learning, a field within artificial intelligence. The goal of the course is to present a breadth of approachable examples.

The course will include a gentle introduction to machine learning in a somewhat abstract setting, including the notions of PAC learning and VC dimension. Connections to set theory and computability theory will be explored through statements in machine learning that are provably undecidable. We will also study some applications of model theory to machine learning.

The literature indicated in the announcement is representative but tentative. A continuously written PDF of course notes will be the main resource for students.

Previous knowledge

Background in basic mathematical logic is strongly recommended. Students should be familiar with the following notions: ordinals, cardinals, transfinite induction, the axioms of ZFC, the notion of a computable function, computable and computably enumerable sets (a.k.a. recursive and recursively enumerable sets), the notions of languages and theories and structures as understood in model theory, atomic diagrams, elementarity, and types. The concepts will be reviewed briefly in the lectures. Students are not expected to be familiar with the notion of forcing in set theory.

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Pure 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: David Criens
Assistant: Dario Kieffer
Language: in English

Time and place

Lecture: Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
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

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.

Previous knowledge

Required: Elementary Probability Theory I \
Recommended: Analysis III, Probability Theory I

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: 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

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

The course will provide an introduction to deep learning algorithms with a focus on the mathematical understanding of the objects and methods used. Essential components of deep learning algorithms will be reviewed, including different neural network architectures and optimization algorithms. The course will cover theoretical aspects of deep learning algorithms, including their approximation capabilities, optimization theory, and error analysis.

Previous knowledge

Analysis I and II, Lineare Algebra I and II

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: Rainer Dahlhaus
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

From a narrow perspective, time series analysis is the statistical study of the properties of stochastic processes in discrete time. In this lecture, we will take a broader view: First we will examine the important probabilistic properties of stationary processes, including strong laws of large numbers (based on the Ergodic theorem) and various versions of the central limit theorem (for processes with strong dependence, even the rate of convergence can change). Another exciting topic is the relation between stationary processes and Fourier analysis based on the Cramér-representation, in which a stationary process is represented as a Fourier-integral of a stochastic process in continuous time (such as the Brownian motion). This later leads, on the statistical side, to a quasi-maximum likelihood method in the frequency domain. Furthermore, we investigate linear and nonlinear time series models, the prediction of time series, linear filters, linear state space models, model selection, maximum likelihood and quasi maximum likelihood methods, the Toeplitz-theory for quadratic forms of stationary processes. Finally, we provide an outlook on locally stationary processes, where the process can be locally apprximated by stationary processes.

Previous knowledge

Elementary Probability Theory I (Stochastik I) and Probability Theory (Wahrscheinlichkeitstheorie)

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: Peter Pfaffelhuber
Assistant: Samuel Ayomide Adeosun
Language: in English

Time and place

Exercise session: Do, 12-14h, SR 218, Ernst-Zermelo-Str. 1, first appointment is on October 15.
Lecture: asynchronous (videos)

• The first in person activity of this lecture are the exercises on Wednesday, 15.10. at 10 h.
• 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

Measure Theory is the foundation of advanced probability theory. In this course, we build on knowledge in analysis and provide all necessary results for later classes in statistics, probabilistic machine learning and stochastic processes. It contains set systems, constructions of measures using outer measures, the integral, and product measures.

Previous knowledge

Basic courses in analysis, and an understanding of mathematical proofs.

Usability

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
Lecture: asynchronous (videos)
Sit-in exam 18.03., 14:00

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

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:

• Introduction to Dynamic Systems and Optimization
• Rehearsal of Newton-type methods and Numerical Optimization
• Algorithmic Differentiation
• Discrete Time Optimal Control
• Dynamic Programming
• Continuous Time Optimal Control
• Numerical Simulation Methods
• Hamilton–Jacobi–Bellmann Equation
• Pontryagin and the Indirect Approach
• Direct Optimal Control
• Real-Time Optimization for Model Predictive Control

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.

Previous knowledge

Required: Analysis I and II, Linear Algebra I and II \
Recommended: Numerics I, Ordinary Differential Equations, Numerical Optimization

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
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

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

The lecture addresses the development and analysis of numerical methods for the approximation of certain nonlinear partial differential equations. The considered model problems include harmonic maps into spheres and total-variation regularized minimization problems. For each of the problems, a suitable finite element discretization is devised, its convergence is analyzed and iterative solution procedures are developed. The lecture is complemented by theoretical and practical lab tutorials in which the results are deepened and experimentally tested.

Previous knowledge

'Introduction to Theory and Numerics for PDEs' or 'Introduction to PDEs'

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: Eric Trébuchon
Language: in English

Time and place

Lecture: Mo, 12-14h, SR 404, 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

This course provides an introduction to analytical methods in mathematical physics, with a particular emphasis on many-body quantum mechanics. A central focus is the rigorous proof of the stability of matter for Coulomb systems, such as atoms and molecules. The key question - why macroscopic objects made of charged particles do not collapse under electromagnetic forces - remained unresolved in classical physics and lacked even a heuristic explanation in early quantum theory. Remarkably, the proof of stability of matter marked the first time that mathematics offered a definitive answer to a fundamental physical and stands as one of the early triumphs of quantum mechanics.

Content:

• Mathematical background: \(L^p\) and Sobolev spaces; Fourier transform; \\
  
• Introduction to quantum mechanics and prototypical examples; \\
  
• Many-body quantum mechanics; \\
  
• Hamilton operator and its properties; Lieb-Thierring inequalities, electrostatic inequalities, Coulomb energy; \\
  
• Proof of Stability of Matter.

Previous knowledge

Analysis III and Linear Algebra are required. \
No prior knowledge of physics is assumed; all relevant physical concepts will be introduced from scratch.

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: Mikhail Tëmkin
Language: in English

Time and place

Lecture: Mo, 10-12h, SR 404, 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

Real-world data is often given as a finite set of points in \(\mathbb R^n\), called a point cloud. Topological data analysis aims to extract features of a point cloud algorithmically. At its core, it is a pipeline of tools from pure mathematics. These tools are of fundamental theoretical importance, and many have practical applications of their own (which the course will briefly discuss). The tools span geometry (convex sets, Delaunay triangulation), topology (simplicial and chain complexes, homology), and algebra (quivers). The course provides a thorough introduction to them and culminates by assembling them into persistent homology, the main object of study in topological data analysis. Although targeted at students in the “Mathematics in Data and Technology” program, it may also interest pure mathematicians because of the close interplay between the two areas.

Previous knowledge

Linear Algebra

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Pure 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: Fr, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Sit-in exam 09.02., 12:00-14:00, HS Weismann-Haus, Albertstr. 21a

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

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: Basics lectures (Analysis, Linear Algebra)

The course ‘Introduction to Mathematics Education’ is therefore recommended from the 4th semester at the earliest.

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: Katharina Böcherer-Linder
Language: in German

Time and place

Do, 9-12h, SR 226, Hermann-Herder-Str. 10

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

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

Introduction to Mathematics Education \
Knowledge about analysis and numerics

Usability

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

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

Lecturer: Frank Reinhold
Language: in German

Time and place

Mi, 11-14h, SR 404, Ernst-Zermelo-Str. 1

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

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

Introduction to Mathematics Education \ knowledge from stochastics and algebra

Usability

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

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, 15-18h, SR 404, Ernst-Zermelo-Str. 1

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.

Previous knowledge

Recommended: Basic courses in mathematics

GeoGebra Account (can be created in the seminar)

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, 301, KG 4, 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, 010, Pavillon 3, PH Freiburg, starting on 22 December 2025 – 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: please e-mail to Anselm Strohmaier

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: Susanne Knies
Language: in German

Time and place

15.10., Raum 232, Ernst-Zermelo-Str. 1, (1st workshop)
Date to be determined (2nd workshop)

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

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.

Usability

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

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

Lecturer: Katharina Böcherer-Linder, Markus Junker
Language: in German

Time and place

Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1

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

This newly designed course will address topics from lectures on analysis and linear algebra (such as limits, continuity, geometric mappings) and examine how these topics are covered in secondary school and to what extent a university-level understanding of mathematics helps in understanding secondary school mathematics.

The event is planned as an interactive seminar in which participants prepare case studies that are then discussed together. Assessment will be based on regular attendance and the presentations and elaborations of the case studies.

Previous knowledge

Introductory lectures in Analysis and Linear Algebra

Usability

Supplementary Module in Mathematics (MEd18)
High-school Oriented Aspects of Analysis and Linear Algebra (MEdual24)

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

Lecturer: Patrick Dondl
Assistant: Ludwig Striet, Oliver Suchan
Language: in English

Time and place

Programming exercise: 2 hours, date to be determined

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

The computer tutorial accompanies the lecture with programming exercises.

Previous knowledge

See the lecture – additionally: programming knowledge.

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: Patrick Dondl
Assistant: Alen Kushova
Language: in German

Time and place

Programming exercise: 2 hours, various dates

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 computer tutorial accompanying the Numerics (first term) lecture the algorithms developed and analyzed in the lecture are put into practice and and tested experimentally. The implementation is carried out in the programming languages Matlab, C++ and Python. Elementary programming knowledge is assumed.

Previous knowledge

See the lecture {\em Numerics I} (which should be attended in parallel or should already have been completed). \ Additionally: 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: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English

Time and place

Programming exercise: 2 hours, date to be determined

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 practical exercises accompanying the lecture 'Theory and Numerics for Partial Differential Equations – Selected Nonlinear Problems', the algorithms developed and analyzed in the lecture are implemented and tested experimentally. The implementation can be carried out in the programming languages Matlab, C++ or Python. Elementary programming knowledge is assumed.

Previous knowledge

see lecture

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: Sebastian Stroppel
Language: in English

Time and place

Do, 10-12h, PC-Pool Raum -100, Hermann-Herder-Str. 10

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 matplotlob, 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: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer
Language: in German

Time and place

Seminar: Mi, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Preregistration: Entry in list with Mr Backenhofer, room 437
Preliminary seminar meeting 24.07., 13:00, SR 404, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Students training to become teachers are given priority.

Content

Number theory is concerned with questions about the properties of integers. Many of them can be easily formulated but their solutions require heavy mathematical machinery. In this proseminar we want to get to know number-theoretic problems that have elementary solutions. Topics include divisibility properties of integers, continued fractions and transcendental numbers.

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: 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: until 10 July 2025 per email to Diyora Salimova
Preliminary seminar meeting 15.07., 11:00, SR 226, Hermann-Herder-Str. 10
Individual preparation meetings for the talks: Dates by arrangement

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

Content

In this proseminar we will explore several aspects of Ordinary Differential Equations (ODEs), a fundamental area of mathematics with widespread applications across natural sciences, engineering, economics, and beyond. Students will engage actively by presenting and discussing various topics, including existence and uniqueness theorems, stability analysis, linear systems, nonlinear dynamics, and numerical methods for solving ODEs. Participants will enhance their analytical skills and deepen their theoretical understanding by studying classical problems and contemporary research directions.

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: Heike Mildenberger
Assistant: Stefan Ludwig
Language: in German

Time and place

Seminar: Di, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Preregistration: no preregistration
Preliminary seminar meeting 23.07., 12:15, Fakultätssitzungsraum 427, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

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

Content

The topics are: Finite and infinite graphs, Eulerian paths, connectivity properties, colourings, spanning trees, random graphs. If desired, more advanced subjects, such as the Rado graph and 0-1 laws or probabilistic methods, can also be presented.

Previous knowledge

Linear Algebra I and II, Analysis 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: Susanne Knies
Assistant: Jonah Reuß
Language: in German

Time and place

Block seminar after the school practical semester 18–20 February 2026

Remaining places in the M.Ed. seminar after the school practical semester can be allocated as undergraduate seminar places. For more information see there!

Usability

Introductory Student Seminar (2HfB21, BSc21, MEH21, MEB21)
Supplementary Module in Mathematics (MEd18)

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

Lecturer: Susanne Knies
Assistant: Jonah Reuß
Language: in German

Time and place

Block seminar after the school practical semester 18–20 February 2026
Preregistration: until 20 July 2025 per email to Jonah Reuss
Preliminary seminar meeting 22.07., Raum 232, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

The seminar is preferably intended for M.Ed. students. Remaining places can be allocated as undergraduate seminar places.

Usability

Introductory Student Seminar (2HfB21, BSc21, MEH21, MEB21)
Supplementary Module in Mathematics (MEd18)

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

Lecturer: Sören Bartels
Language: Talk/participation possible in German and English

Time and place

Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preliminary seminar meeting 15.07., 12:30, Raum 209, Hermann-Herder-Str. 10
Individual preparation meetings for the talks: Dates by arrangement

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

Content

The seminar will be devoted to the development of reliable and efficient discretizations of time stepping methods for parabolic evolution problems. The considered model problems either result from minimization problems or dynamical systems and are typically constrained or nondifferentiable. Criteria that allow to adjust the step sizes and strategies that lead to an acceleration of the convergence to stationary configurations will be addressed in the seminar. Specific topics and literature will be assigned in 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: Wolfgang Soergel
Assistant: Niklas Müller
Language: Talk/participation possible in German and English

Time and place

Seminar: Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Preregistration: In case of interest, please email to Wolfgang Soergel
Preliminary seminar meeting 17.07., 12:15, SR 403, Ernst-Zermelo-Str. 1

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

Content

Structure of noncommutative rings with applications to representations of finite groups.

Previous knowledge

necessary: Linear Algebra I and 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: Harald Binder
Language: Talk/participation possible in German and English

Time and place

Seminar: Mi, 10:15-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary seminar meeting 23.07., 10:15, 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: 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 30.07., SR 125, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

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

Content

Minimal surfaces are surfaces in space with a ‘minimal’ area and can be described using holomorphic functions. They appear, for example, in the investigation of soap skins and the construction of stable objects (e.g. in architecture). Elegant methods from various mathematical fields such as complex analysis, calculus of variations, differential geometry, and partial differential equations are used to analyse minimal surfaces.

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: Johannes Brutsche
Language: Talk/participation possible in German and English

Time and place

Seminar: Mo, 16-18h, SR 127, Ernst-Zermelo-Str. 1
Preregistration: If your are interested in the seminar, please write an email to Johannes Brutsche listing your prerequisites in probability and note if you plan to attend the Probability Theory II.
Preliminary seminar meeting 22.07., 14:00, Raum 232, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

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

Content

Random walks are stochastic processes (in discrete time) formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. Many results that are part of this seminar also carry over to Brownian motion and related processes in continuous time. In particular, the theory for random walks contains many central and elegant proof ideas which can be extended to various other settings. We start the theory at the very beginning but quickly move on to proving local central limit theorems, study Green's function and recurrence properties, hitting times and the Gambler's ruin estimate. Further topics may include a dyadic coupling with Brownian motion, Dirichlet problems, random walks that are not indexed in \(\mathbb{N}\) but the lattice \(\mathbb{Z}^d\), and intersection probabilities for multidimensional random walks (which are processes \(X:\mathbb{N}\rightarrow\mathbb{R}^d\)). Here, we will see that in dimension \(d=1,2,3\) two paths hit each other with positive probability, while for \(d\geq 4\) they avoid each other almost surely.

Previous knowledge

Probability Theory I \
Some talks only require knowledge of Stochastics I, so if you are interested in the seminar and have not taken part in the probability theory I class, do not hesitate to reach out to us regarding a suitable topic.

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 The specific date of the seminar has not yet been fixed and will be determined after consultation with the participants.
Preliminary seminar meeting 22.07., 13:00, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preliminary seminar meeting 30.09., 16:30, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26

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

Content

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.

Previous knowledge

necessary: Basics in Applied Mathematics \
useful: Probability Theory I

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

Seminar: Mi, 14-16h, SR 127, 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: Thomas Brox

Time and place

Lecture: Mo, 10-12h, SR 01-016/18, Georges-Köhler-Allee 101
Exercise session: Mo, 16-18h, 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: Jasper Peter Rennspies

Time and place

Lecture: Di, 10:30-12h, HS 3042, KG III
Exercise session: Di, 14-16h, HS 3043, KG III

Lectures and exercises take place in blocks in individual semester weeks; the exact dates are listed on the course website.

Usability

Elective in Data (MScData24)

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

Lecturer: Abhinav Valada

Time and place

Lecture: Di, 14-16h, HS 00-026, Georges-Köhler-Allee 101
Exercise session: Fr, 10-12h, HS 00-006, Georges-Köhler-Allee 082
Sit-in exam (resit) 15.09.

Course offered by the Faculty of Engineering. 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: Roxana Halbleib

Time and place

Lecture: Mo, 12:30-14h, HS 1199, KG I, Do, 8:30-10h, HS 1010, KG I
Tutorial: 2 hours, various dates

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

Usability

Elective in Data (MScData24)

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

Lecturer: Abhinav Valada

Time and place

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

Time and place

Lecture: Mo, Mi, 8-10h, HS 00-026, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates

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, Moritz Diehl, Sebastien Gros

Time and place

Block course with tutorial 06.10. bis 10.10., 09:00-17:30, HS 1199, KG I

Course offered by the Faculty of Engineering. For contents, prerequisites, and requirements see the course website.
Registration for this event is done using a separate registration form!

Usability

Elective in Data (MScData24)

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

Lecturer: Joschka Bödecker

Time and place

Lecture: Fr, 8-10h, HS 00-026, Georges-Köhler-Allee 101
Exercise session: Mo, 16-18h, 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: Heike Mildenberger
Assistant: Simon Klemm
Language: in German

Time and place

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

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

Time and place

Lecture: Mi, 10-12h, HS 3043, KG III
Tutorial: 2 hours, various dates

Lecturer: Ernst August v. Hammerstein
Language: in English

Time and place

Lecture: Di, 10-12h, HS 1221, KG I
Exercise session: Fr, 10-12h, HS 1098, KG I

Lecturer: Peter Pfaffelhuber
Assistant: Niklas Müller
Language: in German

Time and place

Lecture: Mo, Di, 12-14h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

Lecturer: Susanne Knies
Assistant: Ben Snodgrass
Language: in German

Time and place

Lecture: Mo, 14-16h, HS Rundbau, Albertstr. 21, Fr, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

Lecturer: Ernst Kuwert, Guofang Wang
Language: Talk/participation possible in German and English

Time and place

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

Lecturer: Michael Růžička
Language: Talk/participation possible in German and English

Time and place

Fr, 10-12h, SR 127, Ernst-Zermelo-Str. 1

Lecturer: Wolfgang Soergel

Time and place

Mi, 10-12h, SR 403, Ernst-Zermelo-Str. 1

Previous knowledge

Knowledge about semi-simple Lie-algebras.

Organisation: Annette Huber-Klawitter, Stefan Kebekus, Abhishek Oswal, Wolfgang Soergel
Language: Talk/participation possible in German and English

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, Michael Růžička, Diyora Salimova
Language: Talk/participation possible in German and English

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
Language: Talk/participation possible in German and English

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
Language: Talk/participation possible in German and English

Time and place

Di, 14-16h, SR 125, 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
Language: Talk/participation possible in German and English

Time and place

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

Organisation: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
Language: Talk/participation possible in German and English

Time and place

Mi, 16-17h, 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.

Lecturer: Various speakers
Organisation: Katharina Böcherer-Linder, Ernst Kuwert
Language: in German

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.

Lecturer: Various speakers
Organisation: Amador Martín Pizarro
Language: Talk/participation possible in German and English

Time and place

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

Lecturer: Various speakers
Organisation: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer
Language: Talk/participation possible in German and English

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.