Lecturer: Sebastian Goette
Assistant: Chloe Grey Suchan
Language: in German

Time and place

05.10. bis 09.10., 11:00-13:00, HS Weismann-Haus, Albertstr. 21a

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
Assistant: Riccardo Tosi
Language: in German

Time and place

05.10. bis 09.10., 10:00-12:00, HS Rundbau, Albertstr. 21

5 October 2026 - 9 October 2026, 10.00–12.00 am each day in the HS Rundbau

Content

An optional course for first-year students of various sciences and engineering disciplines. The pre-course refreshes school-level knowledge relevant to the maths lectures and provides an initial insight into what to expect in the lectures.

Language: in German

Language: in German

Lecturer: Guofang Wang
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: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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 pre-course (for students in mathematics) is recommended.

Usability

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

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

Time and place

Lecture: Mo, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sit-in exam: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

Linear Algebra I is one of the two introductory lectures in the mathematics degree programme 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 pre-course (for students in mathematics) is recommended.

Usability

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

Lecturer: Sören Bartels
Assistant: Jonathan Brugger
Language: in German

Time and place

Lecture: Mi, 14-16h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours fortnightly, various dates

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

Numerics is a sub-discipline of mathematics that deals with the practical solution of mathematical problems. In most cases, 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.

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)

Lecturer: Ernst August v. Hammerstein
Assistant: Sebastian Stroppel
Language: in German

Time and place

Lecture: Do, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours fortnightly, various dates
Sit-in exam 23.02.

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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 term will mainly be devoted to statistical topics.

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)

Lecturer: Peter Pfaffelhuber, Diyora Salimova
Assistant: Samuel Ayomide Adeosun
Language: in English

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

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

Time and place

Lecture: Do, 14-16h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 22.02., 10:00-12:00
Sit-in exam (resit) 23.04., 14:00-16:00

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

This compulsory lecture for students of teacher education 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{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.

Previous knowledge

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

Usability

Further Chapters in Analysis (MEd18, MEH21, MEdual24)

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

Time and place

Mi, 13-15h, SR 404, Ernst-Zermelo-Str. 1

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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 student 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)

Lecturer: Abhishek Oswal
Assistant: Ben Snodgrass
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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

Short description of topics: Number fields, Prime decomposition in Dedekind domains, Ideal class groups, Unit groups, Dirichlet's unit theorem, local fields, valuations, decomposition and inertia groups, introduction to class field theory.

Previous knowledge

Required: Algebra and Number Theory

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)

This course is worth 9 credits as an elective module.

Lecturer: Stefan Kebekus
Assistant: Riccardo Tosi
Language: in German

Time and place

Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

This course is worth 9 credits as an elective module.

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

Time and place

Lecture: Mo, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

This lecture provides an introduction to Lebesgue’s theory of multidimensional measures and integration. The focus is on general measures and integrals, convergence theorems, integration in \({\mathbb R}^n\), the transformation theorem and Gauss’s theorem, and possibly also differential forms.

The lecture is relevant for further study in analysis, applied mathematics, stochastics, probability theory and geometry, as well as in physics.

Previous knowledge

Analysis I and II, Linear Algebra I and II

Usability

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

This course is worth 9 credits as an elective module in the optional area or as Elective in Data.

Lecturer: Nadine Große
Assistant: Jonah Reuß
Language: in English

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

Differential geometry investigates geometric properties of curved spaces using methods of differential calculus. It has applications in other areas of mathematics and in physics, such as theoretical mechanics and the theory of relativity.

This lecture provides an introduction to (semi-)Riemannian geometry. In particular, it will focus on geodesics and the Riemannian curvature tensor.

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)

This course is worth 9 credits as an elective module.

Lecturer: Ernst August v. Hammerstein
Language: in German

Time and place

Lecture: Mo, Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

Complex Analysis is a classical branch of advanced mathematics that was largely established during the 19th century through the pioneering work of Cauchy, Riemann, and Weierstraß. It extends the concepts of differentiability and integrability, familiar from analysis, to complex-valued functions \(f:\mathbb{C}\to \mathbb{C}\) and examines the resulting consequences, which are far richer than one might initially assume and lead to a theory that is often more elegant and sometimes even simpler. This theory is fundamental to many advanced areas of mathematics, particularly number theory and algebraic geometry, and its applications extend to probability theory, functional analysis, and mathematical physics.

The starting point for all these considerations is that complex numbers can be identified with points in \(\mathbb{R}^2\) (the complex or Gaussian plane), and thus complex differentiable functions can be identified with real-valued functions \(g:\mathbb{R}^2\to\mathbb{R}^2\) that satisfy the so-called Cauchy–Riemann differential equations. The surprising results of complex analysis can ultimately be traced back to the particularly elegant properties of these differential equations. Some of these properties state, for example, that complex-differentiable functions are continuously differentiable infinitely often, they can be represented locally as power series, and their values within a circular disc are already determined by those on its boundary.

Central topics of the lecture will include, among others, the Cauchy–Riemann differential equations, Cauchy’s integral theorem, Cauchy’s integral formula, the maximum principle, Laurent series, the residue theorem, and Riemann’s mapping theorem. Depending on students' interest and remaining time, more advanced topics such as Picard’s theorems, doubly periodic functions, or applications in number theory may also be covered.

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)

This course is worth 9 credits as an elective module.

Lecturer: Michael Růžička
Assistant: Alen Kushova
Language: in English

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

This lecture is the first in a series of sequential lectures on the theory and numeric of partial differential equations.

Partial differential equations often serve as models for physical processes, e.g., in determining a temperature distribution, in describing vibrations of membranes, or fluid flows.

In this lecture, we will focus on elliptic differential equations. We will cover both the classical existence theory and the modern theory of solvability for such equations. Even if one has explicit solution formulas for simple problems, these can rarely be computed in practice. Therefore, it is important to compute numerically approximate solutions and to verify that they converge appropriately toward the exact solution. To this end, the lecture will present the corresponding theory of finite elements.

Programming exercises will be offered in parallel with the lecture (see the comments on the programming exercises).

Previous knowledge

Required: Analysis~I to III, Linear Algebra~I and II \ Recommended: 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)

This course is worth 9 credits as an elective module and 11 credits as Elective in Data.

Language: in English

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

This course is worth 9 credits as an elective module and 11 credits as Elective in Data.

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

Time and place

Lecture: Di, Fr, 12-14h, SR 127, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, various dates
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 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)

This course is worth 9 credits as an elective module andd 11 credits as Elective in Data.

Lecturer: David Criens
Language: in English

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

This course is worth 9 credits as an elective module and 11 credits as Elective in Data.

Lecturer: Angelika Rohde
Assistant: Johannes Brutsche
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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Previous knowledge

required: Probability Theory II \ helpful: Probability Theory III

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)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

This course is worth 9 credits as an elective module and 11 credits as Elective in Data.

Lecturer: Heike Mildenberger
Language: in English

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

How does one show that something cannot be proved? More precisely: how does one show that a statement does not follow from certain axioms?
The lecture begins with a brief introduction to the most common axiomatic systems in mathematics: the Zermelo–Fraenkel system with the Axiom of Choice (ZFC) and the axiomatic system of von Neumann, Bernays and Gödel (NBG). The axioms shape our understanding of the possible definable – or perhaps less constructively given – mathematical objects. However, they do not paint a complete picture of a single mathematical universe. The list of derivable mathematical statements is incomplete: for some \(\varphi\) , neither \(\varphi\) nor its negation can be proven from ZFC. We say that ‘\(\varphi\) is independent of ZFC’. The best-known statement independent of ZFC is the Continuum Hypothesis, which states that there are exactly \(\aleph_1\) real numbers.

This lecture introduces the technique of independence proofs. After starting with simple forcing techniques for cardinal number exponentiation, we will explore ZF-models without the Axiom of Choice and iterated forcing (e.g. to prove the relative consistency of Martin’s Axiom). Lecture notes are available.

Previous knowledge

Prerequisites: Introductory lectures \ Useful background knowledge: Mathematical logic

Usability

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

This course is worth 9 credits as an elective module.

Lecturer: Amador Martín Pizarro
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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

We obtain the field \(\mathbb R\) of real numbers as the completion of \(\mathbb Q\) with respect to the standard absolute value, by adding the limit of every Cauchy sequence to that sequence. For a prime number \(p\), we define the \(p\)-adic absolute value of a non-zero rational number \(q\) as \[|q|_p = e^{-\mathrm{ord}_p(q)}\] where \(\mathrm{ord}_p(q) = n\) if \(q = p^n \cdot \frac{a}{b}\) such that \(p\) divides neither \(a\) nor \(b\). The \(p\)-adic absolute value satisfies a stronger form of the triangle inequality, and every integer has a \(p\)-adic absolute value of at most 1. The completion of \(\mathbb Q\) with respect to \(| · |_p\) is the field \(\mathbb Q_p\) of \(p\)-adic numbers. Thus, amongst other things, we obtain an element in \(\mathbb Q_p\) as the limit of the partial series \[s_n = \sum_{k \leqslant n} p^k.\] In this lecture, we shall investigate properties of the \(p\)-adic absolute value and its valuation \(\mathrm{ord}_p\). The aim of the lecture is to give a (nearly) positive answer to a conjecture by Emil Artin: Artin claimed that every non-trivial polynomial over \(\mathbb Q_p\) of degree \(d\) in more than \(d^2 + 1\) variables has a non-trivial zero.

Previous knowledge

Course '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)

This course is worth 9 credits as an elective module.

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

Time and place

Dates by arrangement

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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 catalogue. 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. programmes).

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)

This course is worth 9 credits as an elective module.

Lecturer: Damian Sercombe
Language: in English

Time and place

Lecture: Di, 10-12h, SR 127, Ernst-Zermelo-Str. 1

The lecture is supplemented by tutorials and a more extensive self-study component than usual. The lecture therefore counts as a four-hour lecture.

Content

Schemes represent the generalization of varieties to arbitrary base rings. Master’s and doctoral students specializing in algebraic or arithmetic geometry cannot avoid this theory. Traditionally, students master the material through independent study; this course aims to support that process. We will rely on Hartshorne’s established text (Chapter II and parts of Chapter III), covering topics such as sheaves, schemes, separated and proper morphisms, projective morphisms, differentials, flat and smooth morphisms, line bundles and divisors, and sheaf cohomology.

The lectures will present the key aspects of each topic, while students are expected to work through the details via independent study of the literature. One tutorial session will provide an opportunity to discuss the reading material, while a second session will be dedicated to answering questions and discussing exercises. The scope and workload will correspond to a four-hour lecture course. The course will be conducted in English.

Previous knowledge

Commutative Algebra

Usability

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

This course is worth 9 credits as an elective module.

Lecturer: Eva Lütkebohmert-Holtz
Language: in English

Time and place

Lecture: Mo, 10-12h, -, -, Termin noch unklar
Exercise session: Di, 8-10h, -, -, Termin noch unklar
Sit-in exam: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

This course is worth 6 credits as an elective module.

Lecturer: Chiara Saffirio
Assistant: Phillip Pflaum
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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

Topics on Fourier series (convergence in norm; multipliers and almost everywhere convergence; applications to geometry and PDEs, applications to number theory and ergodic theory)

Previous knowledge

Analysis I and II; Measure and Integration 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 (MScData24)

This course is worth 6 credits as an elective module.

Lecturer: Stefan Tappe
Language: in English

Time and place

Lecture: Do, 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

Insurance Mathematics has become an indispensable tool for insurance companies. It deals with the mathematical modeling of insured risks, the calculation of fair premiums for taking over such risks, and the computation of the required reserves.

In this lecture, we will start with life insurance mathematics, where we analyze several types of life insurance polices. Afterwards, we will proceed with risk theory, also known as non-life insurance mathematics. Here we consider portfolios of insured risks, where the number of claims and the claim sizes may be random.

Previous knowledge

Stochastik I, Probability Theory

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)

This course is worth 3 credits as an elective module.

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

Time and place

Lecture: Mo, 16-18h, HS II, Albertstr. 23b
Exercise session: Mi, 16-18h, HS II, Albertstr. 23b

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Previous knowledge

Analysis, Linear Algebra

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)

This course is worth 6 credits as an elective module, with project 9 credits.

Lecturer: Dario Kieffer
Language: in English

Time and place

Lecture: Di, 14-16h, 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

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)

This course is worth 6 credits as an elective module.

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

Time and place

Lecture: asynchronous (videos)
Tutorial: 2 hours, date to be determined and announced in class

• The first in-person session for this lecture is the tutorial on Wednesday, 15.10. at 10 h (to be updated!).
• The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

This course is worth 6 credits as an elective module.

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: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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 programming 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)

This course is worth 6 credits as an elective module, with project 9 credits.

Lecturer: Sören Bartels, Luciano Sciaraffia
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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

This course is worth 6 credits as an elective module.

Lecturer: Maximilian Stegemeyer
Language: in English

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

Fiber bundles are an important concept in topology and geometry as they show up naturally in many situations. Fiber bundles are certain maps between spaces that behave 'nice' locally. Global properties can therefore be understood by patching together local constructions. Next to their omnipresence in topology and geometry, the importance of fiber bundles is due to the fact that isomorphism classes of fiber bundles with a given fiber are a homotopy invariant of the underlying base space. Understanding these isomorphism classes is therefore a key task of algebraic topology. In this course we will introduce fiber bundles with a particular focus on vector bundles and principal fiber bundles. The main goal of the course is the classification of vector bundles. We shall further see some basics of K-theory and introduce characteristic classes of vector bundles. On the way we shall also get to know some concepts of homotopy theory.

Previous knowledge

Algebraic Topology \ Basic knowledge in differential geometry is helpful, but not necessary.

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)

This course is worth 6 credits as an elective module.

Lecturer: Katharina Böcherer-Linder
Language: in German

Time and place

Mo, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, various dates
Sit-in exam: date to be announced

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

Lecturer: Katharina Böcherer-Linder
Language: in German

Time and place

Do, 9-12h, SR 404, Ernst-Zermelo-Str. 1

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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 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)

Lecturer: Anika Dreher
Language: in German

Time and place

Fr, 9-12h, SR 404, Ernst-Zermelo-Str. 1

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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 application for the content areas of stochastics 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)

Lecturer: Jürgen Kury
Language: in German

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

The use of teaching resources in mathematics lessons is becoming increasingly important, both in terms of lesson planning and lesson delivery. Against the backdrop of constructivist learning theories, it is evident that the thoughtful use of modular mathematics systems in the classroom enhances the long-term effectiveness of teaching. Particular emphasis is placed on giving greater weight to deep structures. These include cognitive activation, constructive support for learning and the consolidation of learning processes. Digital media can be used specifically here to deepen mathematical understanding, stimulate thinking processes and promote sustainable learning.

Artificial intelligence (AI) is increasingly being incorporated into mathematics teaching. This student seminar explores how AI-based systems – such as automated diagnostic tools, adaptive learning aids and intelligent tutoring systems – can support teachers. The aim is to reflect on the opportunities and challenges of using AI, and to test and evaluate specific ways in which it can be used in the classroom.

The student seminar aims to equip students with the necessary decision-making and practical skills to prepare future mathematics teachers for their professional careers. Starting with initial considerations regarding lesson planning, computers and tablets are then examined in terms of their respective educational potential and tested during a classroom visit with pupils.

Students are expected to develop lesson sequences, which are then tested with pupils and reflected upon.

Previous knowledge

Recommended: Basic courses in mathematics

GeoGebra Account (can be created in the student seminar)

Usability

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

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)

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 a 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 student seminar for the Master thesis.

The main objectives of the module are the ability to receive mathematics didactic research in order 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)

Organisation: Susanne Knies
Language: in German

Time and place

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

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

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)

This course is worth 3 credits as an elective module.

Lecturer: Alen Kushova, Michael Růžička
Language: in English

Time and place

Programming exercise: 2 hours, date to be determined

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

The objective of the programming exercises is the development of a small finite element software library in a programming language of the student’s choice (e.g. MATLAB, Python, Julia, C/C++). The sessions are organized as a sequence of key implementation including numerical integration on simplicial meshes, assembly of mass and stiffness matrices, treatment of boundary conditions and error estimation.

Students who plan to write an admission thesis, master's thesis, or diploma thesis in Applied Mathematics are encouraged to participate in the practical exercises. Basic programming experience (e.g. MATLAB, Python, Julia, C/C++) is required.

Previous knowledge

See the lecture – additionally: programming knowledge.

Usability

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

This course is worth 3 credits as an elective module

Lecturer: Sören Bartels
Assistant: Jonathan Brugger
Language: in German

Time and place

Programming exercise: 2 hours, various dates

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

In the programming exercise accompanying the Numerics I (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)

This course is worth 3 credits as an elective module in the Option Area.

Lecturer: Sören Bartels
Assistant: Luciano Sciaraffia
Language: in English

Time and place

Programming exercise: 2 hours, date to be determined

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Content

In the programming 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.

Usability

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

This course is worth 3 credits as an elective module

Lecturer: Sebastian Stroppel
Language: in English

Time and place

Programming exercise: 2 hours, various dates: Do, 14-16h, PC-Pool Raum -113, 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)

This course is worth 3 credits as an elective module.

Lecturer: Annette Huber-Klawitter
Assistant: Riccardo Tosi
Language: in German

Remaining places on the M.Ed. student seminar may be allocated as introductory student seminar; for further details, see ‘Student seminars’, in particular the pre-registration procedures and the preliminary meeting date!

Usability

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

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

Time and place

Seminar: Di, 12-14h, SR 226, Hermann-Herder-Str. 10
Preregistration: by 19 July 2026 by email to Diyora Salimova
Preliminary seminar meeting 22.07., 11:00-12:00, SR 226, Hermann-Herder-Str. 10
Individual preparation meetings for the talks: Dates by arrangement

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

Content

In this introductory student seminar 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)

Lecturer: Heike Mildenberger
Language: in German

Time and place

Seminar: Di, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 20.07., 13:00-14:00, Raum 313, Ernst-Zermelo-Str. 1, No prior registration necessary. If you are unable to attend yourself, you are welcome to send a representative.
Individual preparation meetings for the talks: Dates by arrangement

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

Content

In the 1930s, Turing, Church, Kleene and others clarified what we now understand as a computable set of words (also known as a computable language). Computable sets are Turing-computable sets and are also referred to as recursive sets. There is also a simple description in terms of number theory. In 1956, Noam Chomsky published a seminal paper on computability theory, in which he introduced more precise concepts of computability. These are known as regular, context-free and context-sensitive grammars. The general Chomsky grammar coincides with the class of recursively enumerable sets.

Later, correspondences were found between certain computational powers of automata and the levels of grammar. Following theorems by Myhill and Nerode in 1957 and Rabin and Scott in 1958, the paper [1] by Bar-Hillel, Perles and Shamir, containing the pumping lemma from 1961, is regarded as a further important milestone.

In this introductory student seminar, we will study the relationships between the writing power of a Turing machine and the various automata on the one hand, and the grammar hierarchy on the other. Those who are interested may consult the original literature. We will mainly be working with the Springer textbook by Erk and Priese [2], which is available online via the University Library and in which all correspondences are shown. The classic textbook by Hopcroft, Motwani and Ullman, Introduction to Automata Theory, Formal Languages and Complexity Theory [3], is also very suitable. However, context-sensitive grammars (which constitute \(L_1\) in the Chomsky hierarchy of \(L_3\), \(L_2\), \(L_1\), \(L_0\) – where a lower index denotes a larger class) are scarcely covered in that text.

Previous knowledge

Proofs by induction

Usability

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

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

Time and place

Seminar: Mi, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 16.07., 13:00-14:00, SR 125, Ernst-Zermelo-Str. 1, no prior registration required
Individual preparation meetings for the talks: Dates by arrangement

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

Content

In everyday life, mathematics helps us to describe, understand and, often, solve problems in a wide variety of fields. Examples include cryptography (e.g. RSA codes), coding (e.g. audio digitalisation or QR codes), and technical devices (e.g. calculators, navigation systems). Mathematics also plays a role in the social sciences, for example in game theory within economics.

In this introductory student seminar, we aim, on the one hand, to familiarise ourselves with these applications and their connection to mathematics. On the other hand, we aim to describe the problems as accurately as possible using mathematical methods and, ideally, to solve them as well.

The recommended reading list is intended only as a starting point; participants are expected to find further sources themselves.

Previous knowledge

Analysis I, II, Linear Algebra I, II. Further prior knowledge may be required for individual lectures; this is indicated in the programme.

Usability

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

Lecturer: Annette Huber-Klawitter
Assistant: Riccardo Tosi
Language: in German

Time and place

Block seminar after the school practical semester The seminar will take place during the week of 15–19 February 2027.
Preregistration: List available from Ms Frei, Room 421, Ludmilla Frei
Preliminary seminar meeting 13.07., 12:30-13:30, SR 404, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

The student seminar is preferably intended for M.Ed. students. Remaining places can be allocated as introductory student seminar places. It will be held as a block seminar in February 2027.

Content

Each lecture in this student seminar will introduce a mathematician whose results have proved fundamental to the development of mathematics. The aim of this course is therefore not only to explain important theorems that have shaped the course of this discipline, but also to get to know the people behind the proofs. Following an overview of the life of the mathematician in question and, where relevant, the historical context, one of their key results will be explained, together with the corresponding proof. Examples of the topics covered in the student seminar include analysis (Fourier), algebra (Noether), mathematical physics (Kowalewskaja), set theory (Cantor, Zermelo) and number theory (Lindemann, Germain).

Previous knowledge

A basic knowledge of Linear Algebra and Analysis.

Usability

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

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

Time and place

Seminar: Do, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preregistration: by e-mail to Wolfgang Soergel
Preliminary seminar meeting 15.07., 15:15, SR 414, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

Content

This student seminar will focus on irreducible representations of non-compact Lie groups and, in particular, on the transition to the so-called Harish-Chandra modules and the significance of the category \(\mathcal O\). The student seminar builds on the lecture on Lie groups and the student seminar on semi-simple Lie algebras from the summer term.

Previous knowledge

Lecture on Lie groups or the student seminar on semi-simple Lie algebra.

Usability

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

This seminar is worth 6 credits as an elective module.

Lecturer: Guofang Wang
Assistant: Xuwen Zhang
Language: Talk/participation possible in German and English

Time and place

Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 22.07., 16:15, SR 125, Ernst-Zermelo-Str. 1, no prior registration necessary!
Individual preparation meetings for the talks: Dates by arrangement

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

Content

Eigenvalues play an important role to understand an operator. In this student seminar, we learn basic knowledge about eigenvalues of the Laplace operator with certain boundary condition and compute its eigenvalues and also eigenfunctions for special domains.

Previous knowledge

Analysis III, Functional analysis

Usability

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

This seminar is worth 6 credits as an elective module.

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: by email to Olga Sieber
Preliminary seminar meeting 22.07., 13:30-15:30, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

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 role as the basis for this. A selection of approaches is to be presented in the student 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)

This seminar is worth 6 credits as an elective module.

Lecturer: Patrick Dondl
Assistant: Oliver Suchan
Language: in English

Time and place

Seminar: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Preliminary seminar meeting 16.07., 12:00, Bibliotheksraum 216, Hermann-Herder-Str. 10, no prior registration necessary!
Individual preparation meetings for the talks: Dates by arrangement

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

Content

Optimal transport concerns the problem, going back to Monge (1781), of moving one distribution of mass onto another at minimal cost. Kantorovich's relaxation recasts this as a linear problem with a rich duality theory and equips the space of probability measures with the Wasserstein distances. In this student seminar we develop the theory from the Monge–Kantorovich problem and Kantorovich duality through Brenier's theorem on the existence and structure of optimal maps and its link to the Monge–Ampère equation, geodesics and displacement convexity in Wasserstein space, up to the connection with gradient flows (Otto calculus, JKO scheme). Time permitting, we also treat the computational side (entropic regularization, Sinkhorn's algorithm). Optimal transport has become a central tool in the analysis of nonlinear PDE, in geometry and probability, and increasingly in imaging and data science.

Previous knowledge

Functional Analysis

Usability

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

This seminar is worth 6 credits as an elective module.

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

Time and place

Seminar: Mo, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 20.07., 13:00-14:00, SR 127, Ernst-Zermelo-Str. 1, no prior regristration necessary!
Individual preparation meetings for the talks: Dates by arrangement

No course enrolment via HISinOne, but exam registration until 14 October 2026 necessary!

Content

In this student seminar, we will generalise the theory of Lebesgue spaces \(L^p(\Omega)\) to Orlicz spaces \(L^\phi(\Omega)\). These spaces play a major role in the theory and numerical analysis of nonlinear partial differential equations.

Previous knowledge

Analysis I–III, and some Functional Analysis

Usability

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

This seminar is worth 6 credits as an elective module.

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

Time and place

Seminar: Do, 16:30-18h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26, or by appointment
Preregistration: by email to PD Dr. Nadine Binder
Preliminary seminar meeting 23.07., 13:00, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preliminary seminar meeting 06.10., 16:30, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26

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

Content

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

Previous knowledge

None that go beyond admission to the degree programme.

Usability

Mathematical Seminar (MScData24)
Elective in Data (MScData24)

This seminar is worth 6 credits as an Elective in Data.

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

Time and place

Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10

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)

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: Amador Martín Pizarro
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

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

Lecturer: Markus Junker
Language: in German

Time and place

Lecture: Mi, 10-12h, -, -
Tutorial: 2 hours, various dates

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

Lecturer: Ernst August v. Hammerstein
Language: in English

Time and place

Lecture: Fr, 10-12h, -, -
Exercise session: Mo, 16-18h, -, -

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

Lecturer: Patrick Dondl
Assistant: Mikhail Tëmkin
Language: in German

Time and place

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

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

Lecturer: Susanne Knies
Assistant: Leon Blattmann
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

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

Content

The lecture covers the fundamentals of various sub-fields of mathematics.

• Basic mathematical notation
• Written formulation of mathematical statements
• Elementary combinatorics and permutations
• Sequences and series, in particular finite and infinite geometric series
• Elementary functions (polynomials and rational functions, general exponential and logarithmic functions, trigonometric functions)
• Differential and integral calculus and its rules (e.g. the chain rule, integration by parts, substitution); Taylor series
• Basic concepts of probability theory: binomial distribution, Poisson distribution, normal distribution, exponential distribution, expected value, variance, standard deviation

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

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

Time and place

Fr, 10-12h, HS II, Albertstr. 23b

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 404, Ernst-Zermelo-Str. 1

Content

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

Organisation: Harald Binder
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
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, Heike Mildenberger
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: Nadine Große, 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, Jens Timmer
Language: Talk/participation possible in German and English

Time and place

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