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

30.09.–02.10. and 04.10.; begins on 30.09. at 9h15 in HS Rundbau.

Lecturer: Mirjam Hoferichter, 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: Michael Růžička
Assistant: Alexei Gazca
Language: in German

Time and place

Lecture: Di, Mi, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sit-in exam 11.02., 09:00-12:00, HS Rundbau, Albertstr. 21, HS Weismann-Haus, Albertstr. 21a, GHS Physik, Hermann-Herder-Str. 3a, GHS Biologie, Schänzlestr. 1
Sit-in exam (resit) 15.04., 09:00-12:00, HS Rundbau, Albertstr. 21, HS Weismann-Haus, Albertstr. 21a

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: Stefan Kebekus
Assistant: Marius Amann
Language: in German

Time and place

Lecture: Mo, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sit-in exam 27.02., 09:00-12:00, HS Rundbau, Albertstr. 21, GHS Physik, Hermann-Herder-Str. 3a, GHS Biologie, Schänzlestr. 1
Sit-in exam (resit) 26.04., 09:00-13:00, HS Rundbau, Albertstr. 21

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: Sören Bartels
Assistant: Tatjana Schreiber
Language: in German

Time and place

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

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: Angelika Rohde
Assistant: Johannes Brutsche
Language: in German

Time and place

Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours fortnightly, various dates
Sit-in exam 07.03., 09:00-10:00
Sit-in exam (resit) 05.09., 10:00-12:00, HS Rundbau, Albertstr. 21, GHS Physik, Hermann-Herder-Str. 3a

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: Nadine Große
Assistant: Jonah Reuß
Language: in German

Time and place

Lecture: Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 12.02., 08:30-11:30, GHS Chemie (HS -1028), Flachbau Chemie, Albertstr. 21
Sit-in exam (resit) 09.04., 08:30-11:30, HS II, Albertstr. 23b

Content

\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)

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

Lecturer: Moritz Diehl, Patrick Dondl, Angelika Rohde
Assistant: Ben Deitmar, Coffi Aristide Hounkpe
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
Programming exercise: 2 hours, date to be determined

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 25.02., 13:00-16:00, HS Rundbau, Albertstr. 21
Sit-in exam (resit) 09.04., 09:00-12:00

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

Required: 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: Abhishek Oswal
Assistant: Andreas Demleitner
Language: in English

Time and place

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

Content

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)

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

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

Time and place

Lecture: Mo, 12-14h, HS Rundbau, Albertstr. 21, Mi, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sit-in exam 19.02., 10:15-11:45, HS Rundbau, Albertstr. 21
Sit-in exam (resit) 28.04., 10:00-11:30, SR 226, Hermann-Herder-Str. 10

Content

Lebesgue measure and measure theory, Lebesgue integral on measure spaces and Fubini's theorem, Fourier series and Fourier transform, Hilbert spaces. Differential forms, their integration and outer derivative. Stokes' theorem and Gauss' theorem.

Previous knowledge

Required: Analysis I and II, Linear Algebra I

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: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: in German

Time and place

Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class

Content

Differential geometry, especially Riemannian geometry, deals with the geometric properties of curved spaces. Such spaces also occur in other areas of mathematics and physics, for example in geometric analysis, theoretical mechanics and the general theory of relativity.

Previous knowledge

Required: Analysis~I–III, Lineare Algebra~I and II \ Recommended: Analysis of Curves and Surfaces ("Kurven und Flächen"), 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: Guofang Wang
Assistant: Christine Schmidt, Xuwen Zhang
Language: in German

Time and place

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

Content

A large number of different problems from the natural sciences and geometry lead to partial differential equations. Consequently, there can be no talk of an all-encompassing theory. Nevertheless, there is a clear picture for linear equations, which is based on three prototypes: the potential equation \(-\Delta u = f\), the heat equation \(u_t - \Delta u = f\) and the wave equation \(u_{tt} - \Delta u = f\), which we will examine in the lecture.

Previous knowledge

Required: Analysis III \ Recommended: Complex Analysis ({\em Funktionentheorie})

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: Sören Bartels
Assistant: Vera Jackisch
Language: in English

Time and place

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

Content

The aim of this course is to 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 Extensions of 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: David Criens
Assistant: Eric Trébuchon
Language: in German

Time and place

Lecture: Di, Mi, 16-18h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam 24.02., 14:00-16:00, HS II, Albertstr. 23b
Sit-in exam (resit) 12.08.

Content

Complex analysis deals with functions \(f : \mathbb C \to \mathbb C\) , which map complex numbers to complex numbers. Many concepts of Analysis~I can be directly transferred to this case, e.\,g. the definition of differentiability. One might expect that this would lead to a theory analogous to Analysis~I but much more is true: in many respects you get a more elegant and simpler theory. For example, complex differentiability on an open set implies that a function is even infinitely often differentiable, and this is further consistent with analyticity. For real functions, all these notions are different. However, some new ideas are also necessary: For real numbers \(a\), \(b\) one integrates for \[\int_a^b f(x) \mathrm dx\] over the elements of the interval \([a, b]\) or \([b, a]\). However, if \(a\), \(b\) are complex numbers, it is no longer so clear clear how such an integral is to be calculated. One could, for example, in the complex numbers along the line that connects \(a, b \in \mathbb C\), or along another curve that leads from \(a\) to \(b\). Does this lead to a well-defined integral term or does such a curve integral depend on the choice of the curve?

Previous knowledge

Required: Analysis I+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: Ernst August v. Hammerstein
Assistant: Sebastian Stroppel
Language: in English

Time and place

Lecture: Mo, Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Exercise session: Di, 16-18h, SR 127, Ernst-Zermelo-Str. 1

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

Required: 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: Maxwell Levine
Assistant: Hannes Jakob
Language: in English

Time and place

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

Content

How does one prove that something cannot be proved? More precisely, how does one prove that a particular statement does not follow from a particular collection of axioms?

These questions are often asked with respect to the axioms most commonly used by mathematicians: the axioms of Zermelo-Fraenkel set theory, or ZFC for short. In this course, we will develop the conceptual tools needed to understand independence proofs with respect to ZFC. On the way we will develop the theory of ordinal and cardinal numbers, the basics of inner model theory, and the method of forcing. In particular, we will show that Cantor's continuum hypothesis, the statement that \(2^{\aleph_0}=\aleph_1\), is independent of ZFC.

Previous knowledge

Required: Mathematical Logic

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: Annette Huber-Klawitter, Amador Martín Pizarro
Assistant: Christoph Brackenhofer
Language: in German

Time and place

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

Content

Semi-algebraic geometry is about properties of subsets of \(**R**^n\), which are given by inequalities of the form [ f(x1, \dots, xn)\geq 0] for polynomials \(f\in**R**[X_1,\dots,X_n]\).

The theory has many different facets. On the one hand, it can be seen as a version of algebraic geometry over \(\mathbf{R}\) (or even more generally over so-called real closed fields). On the other hand, the properties of these fields are a central tool for the model-theoretic proof of Tarski-Seidenberg's theorem on quantifier elimination in real closed fields. Geometrically, this is interpreted as a projection theorem.

From this theorem, a proof of Hilbert's 17th problem easily follows, which was solved by Artin in 1926.

\textit{Is every real polynomial \(P \in \mathbf{R}[x_1, \dots, x_n]\), which takes a non-negative value for every \(n\)-tuple in \(\mathbf{R}^n\), a sum of squares of rational functions (i.e., quotients of polynomials)?}

In the lecture, we will explore both aspects. Necessary tools from commutative algebra or model theory will be discussed according to the prior knowledge of the audience.

Previous knowledge

Required: Algebra and Number Theory \ Recommended: Knowledge in commutative algebra and algebraic geometry (cf. Kommutative Algebra und Einführung in die algebraische Geometrie), model 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)

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

Lecturer: Sören Bartels, Patrick Dondl
Language: in English

Time and place

Lecture
Tutorial: 2 hours, date to be determined and announced in class

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, total-variation regularized minimization problems, and nonlinear bending models. 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

Required: Introduction to Theory and Numerics for PDEs or Introduction to PDEs

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
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: Peter Pfaffelhuber
Assistant: Samuel Ayomide Adeosun
Language: in English

Time and place

Q&A sesssion / flipped classroom: Mo, 10-12h, HS II, Albertstr. 23b
Exercise session: Mi, 12-14h, SR 127, Ernst-Zermelo-Str. 1
Lecture: asynchronous (videos)

Content

A stochastic process \((X_t)_{t\in I}\) is nothing more than a family of random variables, where \(I\) is some index set modeling time. Simple examples are random walks, Markov chains, Brownian motion and derived processes. The latter play a particularly important role in the modeling of financial mathematics or questions from the sciences. We will first deal with martingales, which describe fair games. After constructing the Poisson process and Brownian motion, we will focus on properties of Brownian motion. Infinitesimal characteristics of a Markov process are described by generators, which allows a connection to the theory of partial differential equations. Finally, a generalization of the law of large numbers is discussed with the ergodic theorem for stationary stochastic processes. Furthermore, insights are given into a few areas of application, such as biomathematics or random graphs.

Previous knowledge

Required: 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: Thorsten Schmidt
Assistant: Moritz Ritter
Language: in English

Time and place

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

Content

This lecture marks the culmination of our series on probability theory, achieving the ultimate goal of this series: the combination of stochastic analysis and financial mathematics---a field that has yielded an amazing wealth of fascinating results since the 1990s. The core is certainly the application of semimartingale theory to financial markets culminating in the fundamental theorem of asset pricing. This results is used everywhere in financial markets for arbitrage-free pricing.

After this we look into modern forms of stochastic analysis covering neural SDEs, signature methods, uncertainty and term structure models. The lecture will conclude with an examination of the latest applications of machine learning in financial markets and the reciprocal influence of stochastic analysis on machine learning.

Previous knowledge

Required: Probability Theory II (Stochastic Processes)

Usability

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

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

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

Time and place

Dates by arrangement

Content

In a reading course, the material of a four-hour lecture is studied in supervised self-study. In rare cases, this may take place as part of a course; however, reading courses are not usually listed in the course catalog. If you are interested, please contact a professor or a private lecturer before the start of the course; typically, this will be the supervisor of your Master's thesis, as the reading course ideally serves as preparation for the Master's thesis (both in the M.Sc. and the M.Ed. programs).

The content of the reading course, the specific details, and the coursework requirements will be determined by the supervisor at the beginning of the lecture period. The workload should be equivalent to that of a four-hour lecture with exercises.

Usability

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

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

Lecturer: Xuwen Zhang
Language: in English

Time and place

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

Content

We will study functions of bounded variation, which are functions whose weak first partial derivatives are Radon measures. This is essentially the weakest definition of a function to be differentiable in the measure-theoretic sense. After discussing the basic properties of them, we move on to the study of sets of finite perimeter, which are Lebesgue measurable sets in the Euclidean space whose indicator functions are BV functions. Sets of finite perimeter are fundamental in the modern Calculus of Variations as they generalize in a natural measure-theoretic way the notion of sets with regular boundaries and possess nice compactness, thus appearing in many Geometric Variational problems. If time permits, we will discuss the (capillary) sessile drop problem as one important application.

Previous knowledge

Required: Basic knowledge in measure theory and analysis is required.

Usability

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

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

Lecturer: Eva Lütkebohmert-Holtz
Assistant: Hongyi Shen
Language: in English

Time and place

Lecture: Mo, 10-12h, HS 3042, KG III
Exercise session: Di, 8-10h, HS 1015, KG I
Sit-in exam (resit) 14.08., 15:00-18:00

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

Required: 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: Maximilian Stegemeyer
Language: in English

Time and place

Lecture: Do, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Exercise session: Di, 8-10h, SR 127, Ernst-Zermelo-Str. 1

Content

Lie groups and operations of Lie groups play a central role in geometry and topology. They can be used to describe continuous symmetries, one of the most important concepts of mathematics and physics. Exploiting symmetries, e.g. when describing homogeneous spaces, makes it easier to solve many specific problems and often provides a deeper insight into the structures examined. In addition, the geometry and topology of Lie groups and homogeneous spaces is of great interest.

In this lecture, we start with introducing the basic theory of Lie groups and Lie algebras, especially with insights into the structure theory of Lie algebras. In the second part we will look at homogeneous spaces with a special focus on Riemannian symmetric spaces. The latter form an important class of examples of Riemannian manifolds. In addition to the Lie-theoretical aspects, a special focus will always be on the homogeneous Riemannian metrics of the respective spaces.

Previous knowledge

Required: Differential geometry~I

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: David Criens
Assistant: Dario Kieffer
Language: in English

Time and place

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

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

Time and place

Oral exam 28.02.

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

Required: 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: Wolfgang Soergel
Language: in German

Time and place

Lecture: Di, 16-18h, SR 403, Ernst-Zermelo-Str. 1

Content

Introduction to classic mechanics from the point of view of mathematics. We start with the mathematical modelling of space and time. Then we discuss Newton's equations of movement, physical systems with compulsory conditions, the D'Alembert principle, the Hamilton formalism and its derivation from the Newton's equations and applications of Hamilton formalism.

Previous knowledge

Required: Analysis III

Usability

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

Students in the B.Sc. Mathematics programme can choose to give a talk, in which case the course counts as a seminar. Usability and requirements as for the seminar ‘Theory of Non-Commutative Algebras’.

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: Di, Fr, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
Programming exercise: 2 hours, date to be determined
Oral exam 06.12.

This course takes only place in the first half of the semester, until end of November.

Content

The aim of this course is to enable the students to carry out simulations and their mathematical analysis for stochastic models originating from applications such as mathematical finance and physics. For this, the course teaches a decent knowledge on stochastic differential equations (SDEs) and their solutions. Furthermore, different numerical methods for SDEs, their underlying ideas, convergence properties, and implementation issues are studied.

Previous knowledge

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

Usability

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

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

Lecturer: Moritz Diehl
Assistant: Florian Messerer
Language: in English

Time and place

Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b

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: Katharina Böcherer-Linder
Language: in German

Time and place

Mo, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, choose one: Fr, 8-10h, SR 127, Ernst-Zermelo-Str. 1, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Sit-in exam 10.02., 08:15-10:00

Content

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

Previous knowledge

Required: Analysis~I, Linear Algebra~I

Usability

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

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

Lecturer: Katharina Böcherer-Linder
Language: in German

Time and place

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

Content

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

Previous knowledge

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

Usability

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

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

Lecturer: Anika Dreher
Language: in German

Time and place

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

Content

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

Previous knowledge

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

Usability

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

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 127, Ernst-Zermelo-Str. 1

Content

The use of teaching media in mathematics lessons wins both at the level of lesson planning and lesson realization in importance. Against the background of constructivist learning theories shows that the reflective use of computer programs, among other things mathematical concept formation in the long term. For example experimenting with computer programs allows mathematical structures to be discovered, without this being overshadowed by individual routine operations (such as term transformation) would be covered up. This has far-reaching consequences for mathematics lessons. For this reason, this seminar aims to provide students the necessary decision-making and action skills to prepare future mathematics teachers for their professional activities. Starting from initial considerations about lesson planning, computers and tablets with regard to their respective didactic potential and tested with learners during a classroom visit. The exemplary systems presented are:

• dynamic geometry Software: Geogebra
• Spreadsheets: Excel
• Apps for Smartphones and tablets

The students should develop teaching sequences, which will then be tested and reflected on with pupils (where this will be possible).

Previous knowledge

Recommended: Basic courses in mathematics

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, Frank Reinhold
Language: in German

Time and place

Part 1: Seminar 'Development Research in Mathematics Education ‒ Selected Topics': Mo, 14-16h, Raum noch nicht bekannt, PH Freiburg
Part 2: Seminar 'Research Methods in Mathematics Education': Mo, 16-19h, Raum noch nicht bekannt, PH Freiburg
Part 3: Master's thesis seminar: Development and Optimisation of a Research Project in Mathematics Education

Registration: see course descriptions

Content

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

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

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

Usability

Research in Mathematics Education (MEd18, MEH21, MEB21)

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

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

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)

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

Lecturer: Sören Bartels
Assistant: Vera Jackisch
Language: in English

Time and place

Programming exercise: 2 hours, date to be determined

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: Sören Bartels
Assistant: Tatjana Schreiber
Language: in German

Time and place

Programming exercise: 2 hours fortnightly, various dates

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: Susanne Knies, Ludwig Striet
Language: in German

Time and place

Seminar: Do, 12-14h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 15.07., 13:00, SR 403, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

Numerous dynamic processes in the natural sciences can be modeled by ordinary differential equations. In this proseminar we will deal with explicit solution methods for differential equations as well as the application situations (reaction kinetics, predator-prey models, mathematical pendulum, different growth processes, . . . ) which can be described by them.

Previous knowledge

Analysis~I and II, Lineare 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: Angelika Rohde
Assistant: Johannes Brutsche
Language: in German

Time and place

Seminar: Mi, 12-14h, SR 125, Ernst-Zermelo-Str. 1, Fr, 13-15h, SR 404, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary seminar meeting 16.07., 10:15, Raum 232, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

Paul Erd\H{o}s liked to talk about the BOOK in which God keeps the \textit{perfect} proofs of mathematical theorems, according to the famous quote by G. H. Hardy that "there is no permanent place for ugly mathematics" ([1], Preface). In an attempt at a best approximation to this BOOK, Aigner and Ziegler have published a large number of sentences with elegant, sophisticated, and sometimes surprising evidence. In this proseminar, a selection of these results will be presented. The spectrum of topics covers all different areas of mathematics, from number theory, geometry, analysis, and combinatorics to graph theory and includes well-known results, such as Littlewood and Offord's lemma, the Dinitz problem, Hilbert's third problem (of his 23 problems presented at the International Congress of Mathematicians in Paris in 1900), the Borsuk conjecture, and many more.

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: Wolfgang Soergel
Assistant: Damian Sercombe
Language: in German

Time and place

Seminar: Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Preregistration:
Individual preparation meetings for the talks: Dates by arrangement

Content

In this proseminar we will discuss topics that are found in various textbooks and scripts for basic lectures in linear algebra but which are not part of the standard material. The lectures build on each other only slightly.

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: Ernst August v. Hammerstein
Language: in German

Time and place

Seminar
Preregistration:
Preliminary seminar meeting 19.07., 16:00, Raum 232, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

A knot can be mathematically defined relatively simply as a closed curve in the three-dimensional space \(\mathbb{R}^3\). From everyday life, one is certainly already familiar with different types of knots, e.g, surgeons knot, sailors knots, and many more. The aim of mathematical knot theory is to find characteristic quantities for the description and classification of knots and thus possibly also to be able to decide whether two knots are equivalent, i.e., if they can be transformed into one another through certain operations. Ropes, cords or wires can be used to illustrate knots as well as interlacings. Prospective teachers can use these not only in this seminar, but perhaps also later in the classroom to display different results in a very practical way.

Previous knowledge

Required: Basic Mathematics courses. \ Possibly a little knowledge in topology in addition.

Usability

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

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

Lecturer: Thorsten Schmidt
Assistant: Moritz Ritter
Language: Talk/participation possible in German and English

Time and place

Seminar: Fr, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary seminar meeting 18.10.
Individual preparation meetings for the talks: Dates by arrangement

Content

This seminar will focus on theoretical machine learning results, including modern universal approximation theorems, approximation of filtering methods through transformes, application of machine learning methods in financial markets and possibly other related topics. Moreover, we will cover topics in stochastic analysis, like fractional Ito calculus, uncertainty, filtering and optimal transport. You are also invited to suggest related topics.

Previous knowledge

Required: Basic Probability and either Machine Learning or Probability Theory II (Stochastic Processes).

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: Sören Bartels
Assistant: Tatjana Schreiber
Language: Talk/participation possible in German and English

Time and place

Seminar
Preregistration:
Preliminary seminar meeting 08.07., 12:30, Raum 209, Hermann-Herder-Str. 10
Individual preparation meetings for the talks: Dates by arrangement

Content

Machine-learning methods have recently been used to approximate solutions of partial differential equations. While in some cases they lead to advantages over classical approaches, their general superiority is widely open. In the seminar we will review the main concepts and recent developments.

Previous knowledge

Introduction to Theory and Numerics for PDEs

Usability

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

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

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

Time and place

Seminar: Mi, 10-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary seminar meeting 17.07., HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26

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: 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 17.07., 16:00
Individual preparation meetings for the talks: Dates by arrangement

Content

Minimal surfaces are surfaces in space with a “minimal” area and can be described using holomorphic functions. They occur, for example in the investigation of soap skins and the construction of stable objects (e.g. in architecture). In the investigation of minimal surfaces elegant methods from various mathematical fields such as function theory, calculus of variations, differential geometry and partial differential equations. are applied.

Previous knowledge

Required: Analysis III or knowledge about multidimensional integration and complex analysis. \ Recommended: Elementary knowledge about differential geometry.

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: Sebastian Goette
Assistant: Mikhail Tëmkin
Language: Talk/participation possible in German and English

Time and place

Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Preliminary seminar meeting 16.07., SR 125, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

We will discuss advanced topics in algebraic topology. Depending on the interest of the participants we could work on one of the following topics---if you have other topic suggestions, please contact the lecturer.

• The Steenrod algebra. An additional structure on the cohomology modulo \(p\) allows finer statements on the existence of continuous mappings, such as the existence of of linearly independent vector fields on spheres. The Wu formulas provide a connection to characteristic classes of manifolds.
• Structured spectra. In order to represent multiplicative (co-)homology functors by spectra, one needs a closed monoidal category of spectra, for example a category of spectra, for example symmetric or orthogonal spectra. In this context we also get to know model structures better.
• \(K\)-theory and index theory. Elliptic differential operators on compact manifolds are manifolds are Fredholm operators. Their index can be defined by the theorem of Atiyah--Singer topologically. We prove this theorem using (mainly) topological methods and give some geometric applications.

Previous knowledge

Algebraic Topology~I and II

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: Annette Huber-Klawitter
Assistant: Xier Ren
Language: Talk/participation possible in German and English

Time and place

Seminar: Fr, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary seminar meeting 15.07., 11:00, SR 318, Ernst-Zermelo-Str. 1
Individual preparation meetings for the talks: Dates by arrangement

Content

In this seminar, we are going to study finite dimensional (unital, possibly non-commutative) algebras over a (commutative) field \(k\). Prototypes are the rings of square matrices over \(k\), finite field extensions, or the algebra \(k^n\) with diagonal multiplication.

We will concentrate on path algebras of finite quivers (German: Köcher). Modules over them are equivalently described as representations of the quiver. Many algebraic properties can be directly understood from properties of the quiver.

Previous knowledge

Required: Linear Algebra \ Recommended: Algebra and Number Theory, Commutative Algebra and Introduction to Algebraic Geometry

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.

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
Language: in English

Time and place

Lecture: Mo, 10-12h, 01-009/13, Georges-Köhler-Allee 101
Exercise session: Mo, 16-18h, 01-009/13, Georges-Köhler-Allee 101

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

Usability

Elective in Data (MScData24)

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

Lecturer: Abhinav Valada
Language: in English

Time and place

Lecture: Di, 10-12h, HS 00-006, Georges-Köhler-Allee 082
Exercise session: Fr, 10-12h, HS 00-006, Georges-Köhler-Allee 082

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: Ekaterina Kazak
Language: in English

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: Roxana Halbleib
Language: in English

Time and place

Lecture: Mo, 12:30-14h, HS 1098, KG I, Di, 12:30-14h, HS 1199, 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. Economics.

Usability

Elective in Data (MScData24)

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

Lecturer: Joschka Bödecker
Language: in English

Time and place

Lecture: Fr, 8-10h, HS 00-026, Georges-Köhler-Allee 101

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

Usability

Elective in Data (MScData24)

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

Lecturer: Moritz Diehl
Language: in English

Time and place

Lecture: Mo, 8:30-10h, HS 00-026, Georges-Köhler-Allee 101, Mi, 8:30-10h, HS 00-036, 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: Markus Junker
Assistant: Charlotte Bartnick
Language: in German

Time and place

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

Lecturer: Amador Martín Pizarro
Assistant: Stefan Ludwig
Language: in German

Time and place

Lecture: Mi, 10-12h, HS 3117, KG III
Tutorial: 2 hours, various dates

Lecturer: Ernst August v. Hammerstein
Assistant: Hongyi Shen
Language: in English

Time and place

Lecture: Di, 10-12h, HS 1098, KG I
Exercise session: Fr, 10-12h, HS 1199, KG I

Lecturer: Ernst Kuwert
Assistant: Florian Johne
Language: in German

Time and place

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

Lecturer: Susanne Knies
Assistant: Sören Andres
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 125, 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, 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, Nadine Große
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: Markus Junker, Amador Martín Pizarro
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, 11:30-13h, 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: 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: Annette Huber-Klawitter, Markus Junker, Amador Martín Pizarro
Language: Talk/participation possible in German and English

Time and place

Do, 14-15h, HS II, Albertstr. 23b

Content

In the ‘Mathematical Colloquium for Students’, topics from the various fields of work are presented in a ‘mathematically understandable’ way. The lectures are aimed at advanced Bachelor's students, Master's students of all specialisations, as well as doctoral students. Afterwards, there will be an opportunity for questions, discussion and dialogue over coffee and tea.

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.