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!

Teaching

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

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)

Time and place

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

Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.

Teaching

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

Content

The aim of this course is to give an introduction into theory of linear partial differential equations and their finite difference as well as finite element approximations. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensable tool in science and technology. We provide an introduction to the construction, analysis, and implementation of finite element methods for different model problems. We will address elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.

Previous knowledge

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

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Specialisation (MEd18, MEH21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Advanced Lecture in Numerics (MScData24)
Elective in Data (MScData24)

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

Time and place

Programming exercise: 2 hours, date to be determined

Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.

Teaching

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

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.

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

Teaching

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

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.

Time and place

Di, 16-18h, SR 226, Hermann-Herder-Str. 10

Teaching

Teacher: Patrick Dondl
Assistant: Simone Hermann, Oliver Suchan

Time and place

Di, 16-18h, SR 226, Hermann-Herder-Str. 10

Teaching

Teacher: Patrick Dondl
Assistant: Simone Hermann, Oliver Suchan

Usability

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Lecture: Mi, 14-16h, HS Rundbau, Albertstr. 21
Sit-in exam 04.08., 09:00-12:00
Sit-in exam (resit) 21.10., 10:00-13:00

Teaching

Teacher: Sören Bartels, Guofang Wang
Assistant: Oliver Suchan
general: ,

Teaching

Teacher: Sören Bartels, Steve Wolff-Vorbeck
Assistant: Oliver Suchan
general:

Usability

Computer Exercise (2HfB21, MEH21, MEB21)
Supplementary Module in Mathematics (MEd18)

Time and place

Lecture: Mi, 14-16h, HS Rundbau, Albertstr. 21

Teaching

Teacher: Diyora Salimova
Assistant: Oliver Suchan
general: ,

Usability

Numerics I (MEB21)

Teaching

Teacher: Diyora Salimova
Assistant: Coffi Aristide Hounkpe, Jakob Rotter, Oliver Suchan
general:

Usability

Computer Exercise (2HfB21, MEH21, MEB21)
Supplementary Module in Mathematics (MEd18)