Numerics I
Lecture: Mi, 14-16h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours fortnightly, various dates
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
Teacher: Patrick Dondl
Assistant: Jonathan Brugger
Language: in German
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.
Required: Linear Algebra~I \
Recommended: Linear Algebra~II and Analysis~I (required for Numerics~II)
Numerics (BSc21)
Numerics (2HfB21, MEH21)
Numerics I (MEB21)
Basics in Applied Mathematics
Lecture: Di, Do, 8-10h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
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.
Teacher: Sören Bartels, Moritz Diehl, Thorsten Schmidt
Language: in English
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.
None that go beyond admission to the degree programme.
Basics in Applied Mathematics (MScData24)
Introduction to Theory and Numerics of Partial Differential Equations
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
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.
Teacher: Patrick Dondl
Assistant: Ludwig Striet, Oliver Suchan
Language: in English
The aim of this course is to give an introduction into theory of linear partial differential equations and their finite difference as well as finite element approximations. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensable tool in science and technology. We provide an introduction to the construction, analysis, and implementation of finite element methods for different model problems. We will address elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.
Required: Analysis~I and II, Linear Algebra~I and II as well as knowledge about higher-dimensional integration (e.g. from Analysis~III or from Further Chapters in Analysis) \
Recommended: Numerics for differential equations, Functional analysis
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Advanced Lecture in Numerics (MScData24)
Elective in Data (MScData24)
Mathematical Introduction to Deep Neural Networks
Lecture: Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 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.
Teacher: Diyora Salimova
Assistant: Ilkhom Mukhammadiev
Language: in English
The course will provide an introduction to deep learning algorithms with a focus on the mathematical understanding of the objects and methods used. Essential components of deep learning algorithms will be reviewed, including different neural network architectures and optimization algorithms. The course will cover theoretical aspects of deep learning algorithms, including their approximation capabilities, optimization theory, and error analysis.
Analysis I and II, Lineare Algebra I and II
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Theory and Numerics for Partial Differential Equations – Selected Nonlinear Problems
Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 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.
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English
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.
'Introduction to Theory and Numerics for PDEs' or 'Introduction to PDEs'
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Computer exercises for 'Introduction to Theory and Numerics of Partial Differential Equations'
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.
Teacher: Patrick Dondl
Assistant: Ludwig Striet, Oliver Suchan
Language: in English
The computer tutorial accompanies the lecture with programming exercises.
See the lecture – additionally: programming knowledge.
Elective (Option Area) (2HfB21)
Elective (BSc21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)
Computer exercises in Numerics
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.
Teacher: Patrick Dondl
Assistant: Jonathan Brugger
Language: in German
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.
See the lecture {\em Numerics I} (which should be attended in parallel or should already have been completed). \ Additionally: Elementary programming knowledge.
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Numerics (BSc21)
Supplementary Module in Mathematics (MEd18)
Computer exercises for 'Theory and Numerics of Partial Differential Equations – Selected Nonlinear Problems'
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.
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English
In the practical exercises accompanying the lecture 'Theory and Numerics for Partial Differential Equations – Selected Nonlinear Problems', the algorithms developed and analyzed in the lecture are implemented and tested experimentally. The implementation can be carried out in the programming languages Matlab, C++ or Python. Elementary programming knowledge is assumed.
see lecture
Elective (Option Area) (2HfB21)
Elective (BSc21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)
Undergraduate seminar: Ordinary Differential Equations
Seminar: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration: until 10 July 2025 per email to Diyora Salimova
Preliminary Meeting 15.07., 11:00, SR 226, Hermann-Herder-Str. 10
Preparation meetings for talks: Dates by arrangement
In HISinOne: no course registration, but exam registration until 8 October 2025.
Teacher: Diyora Salimova
Language: Talk/participation possible in German and English
In this proseminar we will explore several aspects of Ordinary Differential Equations (ODEs), a fundamental area of mathematics with widespread applications across natural sciences, engineering, economics, and beyond. Students will engage actively by presenting and discussing various topics, including existence and uniqueness theorems, stability analysis, linear systems, nonlinear dynamics, and numerical methods for solving ODEs. Participants will enhance their analytical skills and deepen their theoretical understanding by studying classical problems and contemporary research directions.
Analysis I and II, Linear Algebra I and II
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Seminar: Computational PDEs – Gradient Flows and Descent Methods
Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 15.07., 12:30, Raum 209, Hermann-Herder-Str. 10
Preparation meetings for talks: Dates by arrangement
In HISinOne: no course registration, but exam registration until 8 October 2025.
Teacher: Sören Bartels
Language: Talk/participation possible in German and English
The seminar will be devoted to the development of reliable and efficient discretizations of time stepping methods for parabolic evolution problems. The considered model problems either result from minimization problems or dynamical systems and are typically constrained or nondifferentiable. Criteria that allow to adjust the step sizes and strategies that lead to an acceleration of the convergence to stationary configurations will be addressed in the seminar. Specific topics and literature will be assigned in the preliminary meeting.
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)
Lecture: Mo, 12-14h, HS II, Albertstr. 23b, Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Sit-in exam 06.08., 14:00-16:00, HS Rundbau, Albertstr. 21
Attention: Change of time and room!
Teacher: Patrick Dondl
Assistant: Luciano Sciaraffia
Language: in English
Linear functional analysis, which is the subject of the lecture, uses concepts of linear algebra such as vector space, linear operator, dual space, scalar product, adjoint map, eigenvalue, spectrum to solve equations in infinite-dimensional function spaces, especially linear differential equations. The algebraic concepts have to be extended by topological concepts such as convergence, completeness and compactness.
This approach was developed at the beginning of the 20th century by Hilbert, among others, and is now part of the methodological foundation of analysis, numerics and mathematical physics, in particular quantum mechanics, and is also indispensable in other mathematical areas.
Linear Algebra I+II, Analysis I–III
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Lecture: Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
Language: in English
The lecture addresses algorithmic aspects in the practical realization of mathematical methods in big data analytics and machine learning. The first part will be devoted to the development of recommendation systems, clustering methods and sparse recovery techniques. The architecture and approximation properties as well as the training of neural networks are the subject of the second part. Convergence results for accelerated gradient descent methods for nonsmooth problems will be analyzed in the third part of the course. The lecture is accompanied by weekly tutorials which will involve both, practical and theoretical exercises.
Lectures "Numerik I, II" or lecture "Basics in Applied Mathematics"
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Lecture: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Patrick Dondl
Assistant: Eric Trébuchon
Language: in English
This course provides a comprehensive introduction to mathematical modeling. We will learn the systematic process of translating real-world problems into mathematical frameworks, analyzing them using appropriate mathematical tools, and interpreting the results in practical contexts. The course covers both discrete and continuous modeling approaches, with emphasis on differential equations, variational problems, and optimization techniques. Through case studies in physics, biology, engineering, and economics, students will develop skills in model formulation, validation, and refinement. Special attention is given to dimensional analysis, stability theory, and numerical methods necessary for implementing solutions with a focus on numerical methods for ordinary differential equations. The course combines theoretical foundations with hands-on experience in computational tools for model simulation and analysis.
Analysis I, II, Linear Algebra I, II, Numerics I, II
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Seminar: Mo, 12-14h, online, -
Preregistration: by e-mail to Diyora Salimova
Preliminary Meeting 14.04., 15:00, via zoom (please write the lecturer in case the time slot does not fit you)
Preparation meetings for talks: Dates by arrangement
Teacher: Diyora Salimova
Assistant: Ilkhom Mukhammadiev
Language: Talk/participation possible in German and English
In recent years, deep learning have been successfully employed for a multitude of computational problems including object and face recognition, natural language processing, fraud detection, computational advertisement, and numerical approximations of differential equations. Such simulations indicate that neural networks seem to admit the fundamental power to efficiently approximate high-dimensional functions appearing in these applications.
The seminar will review some classical and recent mathematical results on approximation properties of deep learning. We will focus on mathematical proof techniques to obtain approximation estimates on various classes of data including, in particular, certain types of PDE solutions.
Basics of functional analysis, numerics of differential equations, and probability theory
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)
Seminar: Numerics of Partial Differential Equations
Seminar: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Preliminary Meeting 04.02., 12:00, Raum 209, Hermann-Herder-Str. 10, Or registration by e-mail to Sören Bartels.
Teacher: Sören Bartels
Assistant: Vera Jackisch, Tatjana Schreiber
Language: Talk/participation possible in German and English
The seminar will cover advanced topics in the theory and numerics of partial differential equations. This includes the iterative solution of the resulting linear systems of equations with multigrid and domain decomposition methods, the adaptive refinement of finite element grids, the derivation of an approximation theory with explicit constants, and the solution of nonlinear problems.
Introduction to Theory and Numerics of Partial Differential Equations
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)
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Guofang Wang
Assistant: Christine Schmidt, Xuwen Zhang
Language: in German
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.
Required: Analysis III \ Recommended: Complex Analysis ({\em Funktionentheorie})
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 10-12h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Sören Bartels
Assistant: Vera Jackisch
Language: in English
The aim of this course is to give an introduction into theory of linear partial differential equations and their finite difference as well as finite element approximations. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensable tool in science and technology. We provide an introduction to the construction, analysis, and implementation of finite element methods for different model problems. We will address elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.
Required: Analysis~I and II, Linear Algebra~I and II as well as knowledge about higher-dimensional integration (e.g. from Analysis~III or Extensions of Analysis) \ Recommended: Numerics for differential equations, Functional analysis
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Advanced Lecture in Numerics (MScData24)
Elective in Data (MScData24)
Theory and Numerics for Partial Differential Equations – Nonlinear Problems
Teacher: Sören Bartels, Patrick Dondl
Language: in English
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.
Required: Introduction to Theory and Numerics for PDEs or Introduction to PDEs
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Advanced Lecture in Numerics (MScData24)
Elective in Data (MScData24)
Lecture: Di, Fr, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
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.
Teacher: Diyora Salimova
Assistant: Ilkhom Mukhammadiev
Language: in English
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.
Required: Probability and measure theory, basic numerical analysis and basics of MATLAB programming.
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)
Computer exercises for Introduction to Theory and Numerics of Partial Differential Equations
Teacher: Sören Bartels
Assistant: Vera Jackisch
Language: in English
The computer tutorial accompanies the lecture with programming exercises.
See the lecture – additionally: programming knowledge.
Elective (Option Area) (2HfB21)
Elective (BSc21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)
Seminar: Do, 12-14h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting 15.07., 13:00, SR 403, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
Teacher: Susanne Knies, Ludwig Striet
Language: in German
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.
Analysis~I and II, Lineare Algebra~I and II
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Machine-Learning Methods in the Approximation of PDEs
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
Language: Talk/participation possible in German and English
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.
Introduction to Theory and Numerics for PDEs
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)