Basics in Applied Mathematics
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Computer exercise: 2 hours, date to be determined
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)
Theory and Numerics for Partial Differential Equations – ??
Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined
Teacher: Sören Bartels
Language: in English
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 'Theory and Numerics of Partial Differential Equations'
Teacher: Sören Bartels
Language: in English
Elective (Option Area) (2HfB21)
Elective (BSc21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)
Seminar: Computational PDEs
Seminar: Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Sören Bartels
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: Mi, 14-16h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
31.07., 10:00-12:00
Sit-in exam (resit) 17.10., 10:00-13:00
Teacher: Sören Bartels
Assistant: Vera Jackisch
Language: in German
Numerics is a discipline of mathematics that deals with the practical solution of mathematical problems. As a rule, problems are not precisely solved but approximated, for which a sensible compromise of accuracy and computing effort has to be found. In the second part of the two -semester course, questions of the analysis such as the approximation of functions by polynomials, the approximately solution of non -linear equations and the practical calculation of integrals are treated. Attendance at the accompanying computer exercise sessions is recommended. These take place fortnightly, alternating with the tutorial for the lecture.
necessary: Linear Algebra I and Analysis I
useful: Linear Algebra II, Analysis II
Numerics (2HfB21, MEH21)
Numerics (BSc21)
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)
Computer exercises in Numerics
Teacher: Sören Bartels
Assistant: Vera Jackisch
Language: in German
In the practical exercises accompanying the Numerics II lecture, the algorithms developed and analysed in the lecture are implemented in practice and tested experimentally. The implementation is carried out in the programming languages Matlab, C++ and Python. Elementary programming skills are assumed.
See the lecture Numerics II.
In addition elementary programming knowledge.
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Numerics (BSc21)
Supplementary Module in Mathematics (MEd18)
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: Mi, 14-16h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
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)
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)
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)
Computer exercises in Numerics
Teacher: Sören Bartels
Assistant: Tatjana Schreiber
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)
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)
Seminar: Numerik partieller Differentialgleichungen
Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Vera Jackisch
Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)
Projektseminar: Numerische Analysis
Teacher: Sören Bartels
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels, Patrick Dondl, Michael Růžička, Diyora Salimova
Lecture: Mi, 14-16h, HS Rundbau, Albertstr. 21
04.08., 09:00-12:00
Sit-in exam (resit) 21.10., 10:00-13:00
Teacher: Sören Bartels, Guofang Wang
Assistant: Oliver Suchan
general: ,
Praktische Übung zu „Numerik“
Teacher: Sören Bartels, Steve Wolff-Vorbeck
Assistant: Oliver Suchan
general:
Computer Exercise (2HfB21, MEH21, MEB21)
Supplementary Module in Mathematics (MEd18)
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels, Michael Růžička, Diyora Salimova
Mathematik I für Studierende der Informatik und der Ingenieurwissenschaften
Lecture: Mo, 16-18h, Raum und Gebäude noch nicht bekannt, -, Mi, 16-18h, HS Rundbau, Albertstr. 21
Teacher: Sören Bartels
Assistant: Vera Jackisch
Proseminar: Numerische Algorithmen
Di, 16-18h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Jakob Rotter
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Projektseminar: Angewandte Analysis
Teacher: Patrick Dondl, Sören Bartels
Assistant: Vera Jackisch, Guofang Wang
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels, Patrick Dondl, Michael Růžička
Lecture: Mi, 14-16h, HS Rundbau, Albertstr. 21
04.08., 10:00-14:00
Sit-in exam (resit) 22.10., 00:00-00:00
Teacher: Sören Bartels
Assistant: Guofang Wang
general: ,
Praktische Übung zu „Numerik“
Teacher: Sören Bartels
Assistant: Guofang Wang
general:
Computer Exercise (2HfB21, MEH21, MEB21)
Supplementary Module in Mathematics (MEd18)
Seminar: Interpolations- und Projektionsoperatoren
Mi, 16-18h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Vera Jackisch
Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels, Patrick Dondl
Projektseminar: Angewandte Analysis
Teacher: Sören Bartels, Patrick Dondl
Assistant: Steve Wolff-Vorbeck
Teacher: Sören Bartels
Assistant: Jacob Keck
general: ,
Numerics (2HfB21, MEH21)
Numerics I (MEB21)
Teacher: Michael Růžička, Sören Bartels
Assistant: Vera Jackisch
general:
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Theorie und Numerik partieller Differentialgleichungen – nichtlineare partielle Differentialgleichungen
Lecture: Mi, Mo, 10-12h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Sören Bartels, Michael Růžička
Assistant: Alex Kaltenbach
general:
Compulsory Elective in Mathematics (BSc21)
Praktische Übung zu "Einführung in Theorie und Numerik partieller Differentialgleichungen"
Teacher: Michael Růžička, Sören Bartels
Assistant: Hedwig Keller, Vera Jackisch
Supplementary Module in Mathematics (MEd18)
Praktische Übung zu "Numerik"
Teacher: Sören Bartels
Assistant: Coffi Aristide Hounkpe, Jacob Keck
general:
Supplementary Module in Mathematics (MEd18)
Computer Exercise (2HfB21, MEH21, MEB21)
Praktische Übung zu "Theorie und Numerik partieller Differentialgleichungen – nicht-lineare partielle Differentialgleichungen"
Teacher: Sören Bartels, Michael Růžička
Assistant: Christian Palus, Philipp Tscherner
Projektseminar: Angewandte Analysis
Teacher: Sören Bartels, Patrick Dondl
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Patrick Dondl, Sören Bartels, Michael Růžička
Numerik für Differentialgleichungen
Teacher: Sören Bartels
Assistant: Jacob Keck, Janick Gerstenberger
general:
Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)
Praktische Übung zu „Numerik für Differentialgleichungen“
Teacher: Sören Bartels
Assistant: Jacob Keck, Janick Gerstenberger
general:
Seminar: Mathematische Bildverarbeitung
Mo, 14-16h, , online
Teacher: Sören Bartels
Assistant: Ludwig Striet, Vera Jakisch
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Oberseminar: Angewandte Mathematik
Di, 14-16h, bbb-Raum "Anderssen", online
Teacher: Sören Bartels, Patrick Dondl, Michael Růžička
Projektseminar: Angewandte Analysis
Teacher: Sören Bartels, Patrick Dondl
Assistant: Jakob Rotter
Teacher: Sören Bartels
Assistant: Pascal Weyer, Hedwig Keller
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Di, 16-18h, bbb-Raum "Topalov", online
Teacher: Sören Bartels
Assistant: Pascal Weyer, Hedwig Keller
Supplementary Module in Mathematics (MEd18)
Seminar: Numerische Mathematik
Mo, 14-16h, bbb-Raum "Sprechstunde Prof. Bartels", online
Teacher: Sören Bartels
Assistant: Jacob Keck, Philipp Tscherner, Jakob Rotter
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Projektseminar: Angewandte Analysis
Teacher: Sören Bartels, Patrick Dondl
Oberseminar: Angewandte Mathematik
Di, 14-16h, bbb-Raum "Lasker", online
Teacher: Sören Bartels, Patrick Dondl, Michael Růžička
Numerik II
Lecture: Mi, 14-16h, HS Rundbau, Albertstr. 21
04.08., 10:00-14:00
Sit-in exam (resit) 22.10., 00:00-00:00
Teacher: Sören Bartels
Assistant: Frank Meyer, Philipp Tscherner
Lecture: Mi, 16-18h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Jacob Keck, Pascal Weyer
general:
Supplementary Module in Mathematics (MEd18)
Compulsory Elective in Mathematics (BSc21)
Praktische Übung zu „Numerik für Differentialgleichungen“
Teacher: Sören Bartels
Assistant: Jacob Keck, Pascal Weyer
general:
Praktische Übung zu „Numerik“
Teacher: Sören Bartels
Assistant: Philipp Tscherner, Frank Meyer
general:
Supplementary Module in Mathematics (MEd18)
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels, Patrick Dondl, Michael Růžička
Projektseminar: Angewandte Analysis
Mo, 16-18h, SR 226, Hermann-Herder-Str. 10
Teacher: Patrick Dondl, Sören Bartels
Lecture: Mo, Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Christian Palus
general:
Compulsory Elective in Mathematics (BSc21)
Praktische Übung zu "Theorie und Numerik partieller Differentialgleichungen III" - Iterative Löser und Adaptivität
Do, 12-14h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Christian Palus
Seminar: Ausgewählte Themen der Theorie und Numerik partieller Differentialgleichungen
Mo, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Jacob Keck
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Projektseminar: Numerik partieller Differentialgleichungen
Mo, 16-18h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels, Patrick Dondl, Dietmar Kröner, Michael Růžička
Projektseminar: Numerik nichtlinearer partieller Differentialgleichungen
Teacher: Sören Bartels, Jacob Keck
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
14.02., 10:00-12:00
Sit-in exam (resit) 27.04., 00:00-00:00
Teacher: Sören Bartels
Assistant: Christian Palus
general: ,
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Theorie und Numerik partieller Differentialgleichungen – nicht-lineare partielle Differentialgleichungen
Lecture: Mo, Mi, 10-12h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: A. Papathanassopoulos
general:
Compulsory Elective in Mathematics (BSc21)
Praktische Übung zu "Einführung in Theorie und Numerik partieller Differentialgleichungen"
Do, 16-18h, PC-Pool Raum 201, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Christian Palus
general: ,
Supplementary Module in Mathematics (MEd18)
Praktische Übung zu "Theorie und Numerik partieller Differentialgleichungen II – nicht-lineare partielle Differentialgleichungen"
Mo, 14-16h, PC-Pool Raum 201, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: A. Papathanassopoulos, Jacob Keck
general:
Oberseminar: Angewandte Mathematik
Di, 14-16h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels, Patrick Dondl, Michael Růžička
Projektseminar: Numerik partieller Differentialgleichungen
Mo, 16-18h, SR 226, Hermann-Herder-Str. 10
Teacher: Sören Bartels
Assistant: Jacob Keck