Course Catalog

Study Program WiSe 2024/2025

Industrial Mathematics & Data Analysis, M.Sc.

Foundations (33 CP)

Module: Mathematical Methods for Data Analysis and Image Processing (9 CP)

Compulsory module in which you must attend the following lecture(s):
Course numberTitle of eventLecturer
03-M-MDAIP-1Mathematical Methods for Data Analysis and Image Processing (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 12:00 - 14:00 MZH 1470 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 1470 Lecture
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 6200 Exercise
Dirk Lorenz

Module: Modeling Project (15 CP)

Compulsory module in which you must attend the following lecture this semester:
Course numberTitle of eventLecturer
03-M-MP-2Modeling Project (Part 2) (in English)

Seminar (Teaching)
ECTS: 6

Dates:
weekly (starts in week: 1) Mon. 10:00 - 12:00 MZH 2340 Seminar
Peter Maaß

Module: Numerical Methods for Partial Differential Equations (9 CP)

Compulsory module in which you must attend the following lecture:
Course numberTitle of eventLecturer
03-M-NPDE-1Numerical Methods for Partial Differential Equations (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 2) Mon. 10:00 - 12:00 Companion Course (MZH 2490)
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 2340 Lecture
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 2340 Exercise
weekly (starts in week: 1) Thu. 12:00 - 14:00 MZH 2340 Lecture

The lecture deals with the discretisation of partial differential equations and the estimation of the error between continuous and discrete solution. The connection of theory, numerical analysis and implementation is particularly important. The numerical algorithms are to be implemented in programming tasks under guidance.

Alfred Schmidt

Area of Focus: Data Analysis (45 CP)

Area of Focus (27 CP)

The modules Special Topics Data Analysis A and Special Topics Data Analysis B (9 CP each) are mandatory. In addition, EITHER the module Special Topics Data Analysis C OR the module Advanced Communications Data Analysis (9 CP each) must be studied.

Module: Advanced Communications Data Analysis (2 x 4,5 CP = 9 CP)

Compulsory module in which you must attend a total of two seminars with 4,5 CP each. This semester you can choose from the following seminars:
Course numberTitle of eventLecturer
03-IMS-RTATRecent Trends in Algorithm Theory (in English)

Blockveranstaltung (Teaching)
ECTS: 3 (4,5 / 6)

Frequency: The seminar is planned as a block seminar, meaning that all talks will be at up to three days, most likely in the middle of December. We will discuss this in the first meeting. The first (organizational) meeting is planned as follows: Wednesday, October 16, at 14:00 pm in the room MZH 3150.

Learning Outcome:
Students learn how recent advances in algorithm theory can be used to improve state-of-the-art algorithms to obtain faster, better or new types of algorithms. They learn about relevant problems that are important and used in many applications. The main goals are to understand, design, and analyze algorithms for solving such problems.
Furthermore, the students will learn how to read and thoroughly understand original research papers. They learn how to prepare slides for these papers and give an oral presentation to other students who have no prior knowledge about the paper.

Contents: This seminar focuses on recent advances in algorithm theory. Most topics considered include important problems on graphs, typically related to optimization problems. These advances include faster running times of the algorithms, solutions with improved performance guarantees or new concepts in algorithm design, such as algorithms with machine-learned predictions.

Dr. Felix Christian Hommelsheim
03-M-AC-2High-Performance-Visualisierung
High-Performance Visualization
Ausgewählte Publikationen aus dem Bereich der Visualisierung großer wissenschaftlicher Datensätze

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1110 Seminar

Das Seminar beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Solche Daten fallen in unterschiedlichsten wissenschaftlichen Anwendungen an. Sie entstehen zum einen durch Simulationen auf Hochleistungsrechnern (z.\ B. zur Unterstützung der Klimaforschung oder für die Vorhersage von Umströmung von Flugzeugflügeln). Sie können aber auch durch Messungen, wie bspw. durch Erdbeobachtungsmissionen, erzeugt werden. Um überhaupt erst aussagekräftige Informationen für die Visualisierung zu erhalten, müssen diese enorm großen Rohdaten zunächst prozessiert werden. Für eine anschließende explorative Analyse werden echtzeitfähige, interaktive Methoden benötigt, die wiederum auf hochparallele und effiziente Verfahren beruhen. Das Seminar greift daher aktuelle Trends in der wissenschaftlichen Visualisierung auf. Zur Auswahl stehen herausragende Publikationen führender Wissenschaftler, die Themen von Multi-Resolution-Extraktion von Toplologiemerkmalen bis hin zu parallelen Beschleunigungsverfahren für das Volumenrendering in virtuellen Arbeitsumgebungen behandeln.

Prof. Dr. Andreas Gerndt
03-M-AC-5Mathematical Methods in Machine Learning (in English)

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Seminar
Peter Maaß
Dr. Matthias Beckmann
03-M-AC-29Challenges in Inverse Problems

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Mon. 16:00 - 18:00 Seminar online
Peter Maaß
03-M-AC-31Introduction to Robust Control (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 1450 Seminar
Dr. Chathura Wanigasekara

Modules: Special Topics Data Analysis (A, B, and C with 9 CP each)

Compulsory modules in which you must attend one lecture each. This semester you can choose from the following lectures:
Course numberTitle of eventLecturer
03-IMAT-AUAlgorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 5600 Kurs
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1470 Kurs

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI
https://lvb.informatik.uni-bremen.de/imat/03-imat-au.pdf


A key assumption of many powerful optimization methods is that all the data is fully accessible from the beginning.

However, from the point of view of many real-world applications (e.g., in logistics, production or project planning, cloud computing, etc.) this assumption is simply not true. Large data centers allocate resources to tasks without knowledge of exact execution times or energy requirements; transit times in networks are often uncertain; or, parameters such as bandwidth, demands or energy consumption are highly fluctuating. The current trend of data collection and data-driven applications often amplifies this phenomenon. As the amount of available data is increasing tremendously due to internet technology, cloud systems and sharing markets, modern algorithms are expected to be highly adaptive and learn and benefit from the dynamically changing mass of data.

In the above examples, our knowledge of the current data is only partial or based on historical estimates. The class ``Algorithms and Uncertainty'' will teach students about the most common models of such uncertain data and how to design and analyze efficient algorithms in these models.

Specifically, we will cover the theory of online optimization, where the input arrives without any prior information (such as network packets arriving to a router) and also needs to be processed immediately, before the next piece of input arrives. This model is best suited for analyzing critical networking and scheduling systems where devices and algorithms must perform well even in the worst-case scenario.

In the cases where previous history can be used to model the upcoming data, we often employ robust optimization or stochastic optimization. In robust optimization, the aim is to optimize the worst-case of all possible realizations of the input data. Hence, this model is rather conservative.
In stochastic optimization however, the algorithms work with the assumption that data is drawn from some probability distribution known ahead of time and typically the goal is to optimize the expected value.

Nowadays, another source of information is often available: machine learning algorithms can generate predictions which are accurate most of the time. However, there is no guarantee on the quality of the prediction, as the current instance may not be covered by the training set. This statement motivated a very recent research domain that will be covered in this course: how to use error-prone predictions in order to improve guaranteed algorithms.

Organization: The course will be taught in English in two sessions per week (4 SWS) including interactive exercise sessions.

Examination: The examination will be by individual oral exam. As admission to the oral exam it is mandatory to present solutions in the exercise session at least twice during the term.

Prerequisites: Having heard an introductory course to discrete algorithms and their mathematical analysis (e.g. Algorithmentheorie, Algorithmische Diskrete Mathematik) or graph theory is beneficial but not required.

Prof. Dr. Nicole Megow
03-M-SP-2Basics of Mathematical Statistics (Statistics I) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 External location: MZH 1100 Exercise

Die Veranstaltung findet zusammen mit 03-M-FTH-10 statt.

Prof. Dr. Werner Brannath
03-M-SP-26Algebraic Topology (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 7200 Exercise

Findet zusammen mit der LV 03-M-FTH-9 statt.

Prof. Dr. Dmitry Feichtner-Kozlov
03-M-SP-28Advanced Methods in Applied Statistics (Statistics III) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 10:00 - 12:00 MZH 7200 Exercise
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 7200 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 7200 Lecture

The quantitative assessment and the management of (extreme) risks are key tools for policy makers and stakeholders in many areas such as climate and environmental research, economics, or finance and insurance. In this course, we will get familiar with basic mathematical concepts of (quantitative) risk assessment and management.

Prof. Dr. Thorsten-Ingo Dickhaus
03-M-SP-38Finite Elements - Selected Chapters (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 2340 Exercise

The finite element method is used for the discretisation of partial differential equations in many different applications. In this course we will deepen existing knowledge in finite element methods with respect to different applications and learn new techniques to increase their computational speed.

Prof. Dr. Andreas Rademacher
03-M-SP-39Advanced Topics in Image Processing - The Beauty of Variational Calculus (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 14:00 - 16:00 MZH 2340 Exercise

This course focusses on two advanced tools in modern mathematical image processing, namely the direct method of variational calculus and the iterated soft thresholding algorithm.

Peter Maaß
Dr. Matthias Beckmann
Dr. rer. nat. Pascal Fernsel
03-M-SP-40Convex Analysis and Optimization (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Exercise
Dirk Lorenz

Extension (18 CP)

Module: Advanced Communications Industrial Mathematics (2 x 4,5 CP = 9 CP)

Compulsory module in which you must attend a total of two seminars with 4,5 CP each. This semester you can choose from the following seminars:
Course numberTitle of eventLecturer
03-IMS-RTATRecent Trends in Algorithm Theory (in English)

Blockveranstaltung (Teaching)
ECTS: 3 (4,5 / 6)

Frequency: The seminar is planned as a block seminar, meaning that all talks will be at up to three days, most likely in the middle of December. We will discuss this in the first meeting. The first (organizational) meeting is planned as follows: Wednesday, October 16, at 14:00 pm in the room MZH 3150.

Learning Outcome:
Students learn how recent advances in algorithm theory can be used to improve state-of-the-art algorithms to obtain faster, better or new types of algorithms. They learn about relevant problems that are important and used in many applications. The main goals are to understand, design, and analyze algorithms for solving such problems.
Furthermore, the students will learn how to read and thoroughly understand original research papers. They learn how to prepare slides for these papers and give an oral presentation to other students who have no prior knowledge about the paper.

Contents: This seminar focuses on recent advances in algorithm theory. Most topics considered include important problems on graphs, typically related to optimization problems. These advances include faster running times of the algorithms, solutions with improved performance guarantees or new concepts in algorithm design, such as algorithms with machine-learned predictions.

Dr. Felix Christian Hommelsheim
03-M-AC-2High-Performance-Visualisierung
High-Performance Visualization
Ausgewählte Publikationen aus dem Bereich der Visualisierung großer wissenschaftlicher Datensätze

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1110 Seminar

Das Seminar beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Solche Daten fallen in unterschiedlichsten wissenschaftlichen Anwendungen an. Sie entstehen zum einen durch Simulationen auf Hochleistungsrechnern (z.\ B. zur Unterstützung der Klimaforschung oder für die Vorhersage von Umströmung von Flugzeugflügeln). Sie können aber auch durch Messungen, wie bspw. durch Erdbeobachtungsmissionen, erzeugt werden. Um überhaupt erst aussagekräftige Informationen für die Visualisierung zu erhalten, müssen diese enorm großen Rohdaten zunächst prozessiert werden. Für eine anschließende explorative Analyse werden echtzeitfähige, interaktive Methoden benötigt, die wiederum auf hochparallele und effiziente Verfahren beruhen. Das Seminar greift daher aktuelle Trends in der wissenschaftlichen Visualisierung auf. Zur Auswahl stehen herausragende Publikationen führender Wissenschaftler, die Themen von Multi-Resolution-Extraktion von Toplologiemerkmalen bis hin zu parallelen Beschleunigungsverfahren für das Volumenrendering in virtuellen Arbeitsumgebungen behandeln.

Prof. Dr. Andreas Gerndt
03-M-AC-5Mathematical Methods in Machine Learning (in English)

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Seminar
Peter Maaß
Dr. Matthias Beckmann
03-M-AC-28Advanced Numerical Methods for Partial Differential Equations (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Mon. 16:00 - 18:00 MZH 2340 Seminar

This is a seminar with subjects from numerical methods for PDEs, expecially finite element methods, with applications to real world problems.

Alfred Schmidt
03-M-AC-29Challenges in Inverse Problems

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Mon. 16:00 - 18:00 Seminar online
Peter Maaß
03-M-AC-31Introduction to Robust Control (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 1450 Seminar
Dr. Chathura Wanigasekara

Module: Special Topics Industrial Mathematics A (9 CP)

Compulsory module in which you must attend one lecture. This semester you can choose from the following lectures:
Course numberTitle of eventLecturer
03-IMAT-AUAlgorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 5600 Kurs
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1470 Kurs

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI
https://lvb.informatik.uni-bremen.de/imat/03-imat-au.pdf


A key assumption of many powerful optimization methods is that all the data is fully accessible from the beginning.

However, from the point of view of many real-world applications (e.g., in logistics, production or project planning, cloud computing, etc.) this assumption is simply not true. Large data centers allocate resources to tasks without knowledge of exact execution times or energy requirements; transit times in networks are often uncertain; or, parameters such as bandwidth, demands or energy consumption are highly fluctuating. The current trend of data collection and data-driven applications often amplifies this phenomenon. As the amount of available data is increasing tremendously due to internet technology, cloud systems and sharing markets, modern algorithms are expected to be highly adaptive and learn and benefit from the dynamically changing mass of data.

In the above examples, our knowledge of the current data is only partial or based on historical estimates. The class ``Algorithms and Uncertainty'' will teach students about the most common models of such uncertain data and how to design and analyze efficient algorithms in these models.

Specifically, we will cover the theory of online optimization, where the input arrives without any prior information (such as network packets arriving to a router) and also needs to be processed immediately, before the next piece of input arrives. This model is best suited for analyzing critical networking and scheduling systems where devices and algorithms must perform well even in the worst-case scenario.

In the cases where previous history can be used to model the upcoming data, we often employ robust optimization or stochastic optimization. In robust optimization, the aim is to optimize the worst-case of all possible realizations of the input data. Hence, this model is rather conservative.
In stochastic optimization however, the algorithms work with the assumption that data is drawn from some probability distribution known ahead of time and typically the goal is to optimize the expected value.

Nowadays, another source of information is often available: machine learning algorithms can generate predictions which are accurate most of the time. However, there is no guarantee on the quality of the prediction, as the current instance may not be covered by the training set. This statement motivated a very recent research domain that will be covered in this course: how to use error-prone predictions in order to improve guaranteed algorithms.

Organization: The course will be taught in English in two sessions per week (4 SWS) including interactive exercise sessions.

Examination: The examination will be by individual oral exam. As admission to the oral exam it is mandatory to present solutions in the exercise session at least twice during the term.

Prerequisites: Having heard an introductory course to discrete algorithms and their mathematical analysis (e.g. Algorithmentheorie, Algorithmische Diskrete Mathematik) or graph theory is beneficial but not required.

Prof. Dr. Nicole Megow
03-M-SP-2Basics of Mathematical Statistics (Statistics I) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 External location: MZH 1100 Exercise

Die Veranstaltung findet zusammen mit 03-M-FTH-10 statt.

Prof. Dr. Werner Brannath
03-M-SP-26Algebraic Topology (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 7200 Exercise

Findet zusammen mit der LV 03-M-FTH-9 statt.

Prof. Dr. Dmitry Feichtner-Kozlov
03-M-SP-38Finite Elements - Selected Chapters (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 2340 Exercise

The finite element method is used for the discretisation of partial differential equations in many different applications. In this course we will deepen existing knowledge in finite element methods with respect to different applications and learn new techniques to increase their computational speed.

Prof. Dr. Andreas Rademacher
03-M-SP-39Advanced Topics in Image Processing - The Beauty of Variational Calculus (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 14:00 - 16:00 MZH 2340 Exercise

This course focusses on two advanced tools in modern mathematical image processing, namely the direct method of variational calculus and the iterated soft thresholding algorithm.

Peter Maaß
Dr. Matthias Beckmann
Dr. rer. nat. Pascal Fernsel
03-M-SP-40Convex Analysis and Optimization (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Exercise
Dirk Lorenz
04-M30-CP-SFT-3Trajectory Optimization (in English)

Lecture (Teaching)
ECTS: 4,5

Dates:
weekly (starts in week: 1) Mon. 14:00 - 18:00 FZB 0240
Prof. Dr. Christof Büskens
Matthias Knauer

Area of Focus: Industrial Mathematics (45 CP)

Area of Focus (27 CP)

The modules Special Topics Industrial Mathematics A and Special Topics Industrial Mathematics B (9 CP each) are mandatory. In addition, EITHER the module Special Topics Industrial Mathematics C OR the module Advanced Communications Industrial Mathematics (9 CP each) must be studied.

Module: Advanced Communications Industrial Mathematics (2 x 4,5 CP = 9 CP)

Compulsory module in which you must attend a total of two seminars with 4,5 CP each. This semester you can choose from the following seminars:
Course numberTitle of eventLecturer
03-IMS-RTATRecent Trends in Algorithm Theory (in English)

Blockveranstaltung (Teaching)
ECTS: 3 (4,5 / 6)

Frequency: The seminar is planned as a block seminar, meaning that all talks will be at up to three days, most likely in the middle of December. We will discuss this in the first meeting. The first (organizational) meeting is planned as follows: Wednesday, October 16, at 14:00 pm in the room MZH 3150.

Learning Outcome:
Students learn how recent advances in algorithm theory can be used to improve state-of-the-art algorithms to obtain faster, better or new types of algorithms. They learn about relevant problems that are important and used in many applications. The main goals are to understand, design, and analyze algorithms for solving such problems.
Furthermore, the students will learn how to read and thoroughly understand original research papers. They learn how to prepare slides for these papers and give an oral presentation to other students who have no prior knowledge about the paper.

Contents: This seminar focuses on recent advances in algorithm theory. Most topics considered include important problems on graphs, typically related to optimization problems. These advances include faster running times of the algorithms, solutions with improved performance guarantees or new concepts in algorithm design, such as algorithms with machine-learned predictions.

Dr. Felix Christian Hommelsheim
03-M-AC-2High-Performance-Visualisierung
High-Performance Visualization
Ausgewählte Publikationen aus dem Bereich der Visualisierung großer wissenschaftlicher Datensätze

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1110 Seminar

Das Seminar beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Solche Daten fallen in unterschiedlichsten wissenschaftlichen Anwendungen an. Sie entstehen zum einen durch Simulationen auf Hochleistungsrechnern (z.\ B. zur Unterstützung der Klimaforschung oder für die Vorhersage von Umströmung von Flugzeugflügeln). Sie können aber auch durch Messungen, wie bspw. durch Erdbeobachtungsmissionen, erzeugt werden. Um überhaupt erst aussagekräftige Informationen für die Visualisierung zu erhalten, müssen diese enorm großen Rohdaten zunächst prozessiert werden. Für eine anschließende explorative Analyse werden echtzeitfähige, interaktive Methoden benötigt, die wiederum auf hochparallele und effiziente Verfahren beruhen. Das Seminar greift daher aktuelle Trends in der wissenschaftlichen Visualisierung auf. Zur Auswahl stehen herausragende Publikationen führender Wissenschaftler, die Themen von Multi-Resolution-Extraktion von Toplologiemerkmalen bis hin zu parallelen Beschleunigungsverfahren für das Volumenrendering in virtuellen Arbeitsumgebungen behandeln.

Prof. Dr. Andreas Gerndt
03-M-AC-5Mathematical Methods in Machine Learning (in English)

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Seminar
Peter Maaß
Dr. Matthias Beckmann
03-M-AC-28Advanced Numerical Methods for Partial Differential Equations (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Mon. 16:00 - 18:00 MZH 2340 Seminar

This is a seminar with subjects from numerical methods for PDEs, expecially finite element methods, with applications to real world problems.

Alfred Schmidt
03-M-AC-29Challenges in Inverse Problems

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Mon. 16:00 - 18:00 Seminar online
Peter Maaß
03-M-AC-31Introduction to Robust Control (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 1450 Seminar
Dr. Chathura Wanigasekara

Modules: Special Topics Industrial Mathematics (A, B, and C with 9 CP each)

Compulsory modules in which you must attend one lecture each. This semester you can choose from the following lectures:
Course numberTitle of eventLecturer
03-IMAT-AUAlgorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 5600 Kurs
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1470 Kurs

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI
https://lvb.informatik.uni-bremen.de/imat/03-imat-au.pdf


A key assumption of many powerful optimization methods is that all the data is fully accessible from the beginning.

However, from the point of view of many real-world applications (e.g., in logistics, production or project planning, cloud computing, etc.) this assumption is simply not true. Large data centers allocate resources to tasks without knowledge of exact execution times or energy requirements; transit times in networks are often uncertain; or, parameters such as bandwidth, demands or energy consumption are highly fluctuating. The current trend of data collection and data-driven applications often amplifies this phenomenon. As the amount of available data is increasing tremendously due to internet technology, cloud systems and sharing markets, modern algorithms are expected to be highly adaptive and learn and benefit from the dynamically changing mass of data.

In the above examples, our knowledge of the current data is only partial or based on historical estimates. The class ``Algorithms and Uncertainty'' will teach students about the most common models of such uncertain data and how to design and analyze efficient algorithms in these models.

Specifically, we will cover the theory of online optimization, where the input arrives without any prior information (such as network packets arriving to a router) and also needs to be processed immediately, before the next piece of input arrives. This model is best suited for analyzing critical networking and scheduling systems where devices and algorithms must perform well even in the worst-case scenario.

In the cases where previous history can be used to model the upcoming data, we often employ robust optimization or stochastic optimization. In robust optimization, the aim is to optimize the worst-case of all possible realizations of the input data. Hence, this model is rather conservative.
In stochastic optimization however, the algorithms work with the assumption that data is drawn from some probability distribution known ahead of time and typically the goal is to optimize the expected value.

Nowadays, another source of information is often available: machine learning algorithms can generate predictions which are accurate most of the time. However, there is no guarantee on the quality of the prediction, as the current instance may not be covered by the training set. This statement motivated a very recent research domain that will be covered in this course: how to use error-prone predictions in order to improve guaranteed algorithms.

Organization: The course will be taught in English in two sessions per week (4 SWS) including interactive exercise sessions.

Examination: The examination will be by individual oral exam. As admission to the oral exam it is mandatory to present solutions in the exercise session at least twice during the term.

Prerequisites: Having heard an introductory course to discrete algorithms and their mathematical analysis (e.g. Algorithmentheorie, Algorithmische Diskrete Mathematik) or graph theory is beneficial but not required.

Prof. Dr. Nicole Megow
03-M-SP-2Basics of Mathematical Statistics (Statistics I) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 External location: MZH 1100 Exercise

Die Veranstaltung findet zusammen mit 03-M-FTH-10 statt.

Prof. Dr. Werner Brannath
03-M-SP-26Algebraic Topology (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 7200 Exercise

Findet zusammen mit der LV 03-M-FTH-9 statt.

Prof. Dr. Dmitry Feichtner-Kozlov
03-M-SP-38Finite Elements - Selected Chapters (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 2340 Exercise

The finite element method is used for the discretisation of partial differential equations in many different applications. In this course we will deepen existing knowledge in finite element methods with respect to different applications and learn new techniques to increase their computational speed.

Prof. Dr. Andreas Rademacher
03-M-SP-39Advanced Topics in Image Processing - The Beauty of Variational Calculus (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 14:00 - 16:00 MZH 2340 Exercise

This course focusses on two advanced tools in modern mathematical image processing, namely the direct method of variational calculus and the iterated soft thresholding algorithm.

Peter Maaß
Dr. Matthias Beckmann
Dr. rer. nat. Pascal Fernsel
03-M-SP-40Convex Analysis and Optimization (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Exercise
Dirk Lorenz
04-M30-CP-SFT-3Trajectory Optimization (in English)

Lecture (Teaching)
ECTS: 4,5

Dates:
weekly (starts in week: 1) Mon. 14:00 - 18:00 FZB 0240
Prof. Dr. Christof Büskens
Matthias Knauer

Extension (18 CP)

Module: Advanced Communications Data Analysis (2 x 4,5 CP = 9 CP)

Compulsory module in which you must attend a total of two seminars with 4,5 CP each. This semester you can choose from the following seminars:
Course numberTitle of eventLecturer
03-IMS-RTATRecent Trends in Algorithm Theory (in English)

Blockveranstaltung (Teaching)
ECTS: 3 (4,5 / 6)

Frequency: The seminar is planned as a block seminar, meaning that all talks will be at up to three days, most likely in the middle of December. We will discuss this in the first meeting. The first (organizational) meeting is planned as follows: Wednesday, October 16, at 14:00 pm in the room MZH 3150.

Learning Outcome:
Students learn how recent advances in algorithm theory can be used to improve state-of-the-art algorithms to obtain faster, better or new types of algorithms. They learn about relevant problems that are important and used in many applications. The main goals are to understand, design, and analyze algorithms for solving such problems.
Furthermore, the students will learn how to read and thoroughly understand original research papers. They learn how to prepare slides for these papers and give an oral presentation to other students who have no prior knowledge about the paper.

Contents: This seminar focuses on recent advances in algorithm theory. Most topics considered include important problems on graphs, typically related to optimization problems. These advances include faster running times of the algorithms, solutions with improved performance guarantees or new concepts in algorithm design, such as algorithms with machine-learned predictions.

Dr. Felix Christian Hommelsheim
03-M-AC-2High-Performance-Visualisierung
High-Performance Visualization
Ausgewählte Publikationen aus dem Bereich der Visualisierung großer wissenschaftlicher Datensätze

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1110 Seminar

Das Seminar beschäftigt sich mit den mathematischen Grundlagen der wissenschaftlichen Visualisierung und behandelt Methoden für das parallele Post-Processing großer wissenschaftlicher Datensätze. Solche Daten fallen in unterschiedlichsten wissenschaftlichen Anwendungen an. Sie entstehen zum einen durch Simulationen auf Hochleistungsrechnern (z.\ B. zur Unterstützung der Klimaforschung oder für die Vorhersage von Umströmung von Flugzeugflügeln). Sie können aber auch durch Messungen, wie bspw. durch Erdbeobachtungsmissionen, erzeugt werden. Um überhaupt erst aussagekräftige Informationen für die Visualisierung zu erhalten, müssen diese enorm großen Rohdaten zunächst prozessiert werden. Für eine anschließende explorative Analyse werden echtzeitfähige, interaktive Methoden benötigt, die wiederum auf hochparallele und effiziente Verfahren beruhen. Das Seminar greift daher aktuelle Trends in der wissenschaftlichen Visualisierung auf. Zur Auswahl stehen herausragende Publikationen führender Wissenschaftler, die Themen von Multi-Resolution-Extraktion von Toplologiemerkmalen bis hin zu parallelen Beschleunigungsverfahren für das Volumenrendering in virtuellen Arbeitsumgebungen behandeln.

Prof. Dr. Andreas Gerndt
03-M-AC-5Mathematical Methods in Machine Learning (in English)

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Seminar
Peter Maaß
Dr. Matthias Beckmann
03-M-AC-29Challenges in Inverse Problems

Seminar (Teaching)
ECTS: 4,5/ 6

Dates:
weekly (starts in week: 1) Mon. 16:00 - 18:00 Seminar online
Peter Maaß
03-M-AC-31Introduction to Robust Control (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 1450 Seminar
Dr. Chathura Wanigasekara

Module: Special Topics Data Analysis A (9 CP)

Compulsory module in which you must attend one lecture. This semester you can choose from the following lectures:
Course numberTitle of eventLecturer
03-IMAT-AUAlgorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 5600 Kurs
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1470 Kurs

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI
https://lvb.informatik.uni-bremen.de/imat/03-imat-au.pdf


A key assumption of many powerful optimization methods is that all the data is fully accessible from the beginning.

However, from the point of view of many real-world applications (e.g., in logistics, production or project planning, cloud computing, etc.) this assumption is simply not true. Large data centers allocate resources to tasks without knowledge of exact execution times or energy requirements; transit times in networks are often uncertain; or, parameters such as bandwidth, demands or energy consumption are highly fluctuating. The current trend of data collection and data-driven applications often amplifies this phenomenon. As the amount of available data is increasing tremendously due to internet technology, cloud systems and sharing markets, modern algorithms are expected to be highly adaptive and learn and benefit from the dynamically changing mass of data.

In the above examples, our knowledge of the current data is only partial or based on historical estimates. The class ``Algorithms and Uncertainty'' will teach students about the most common models of such uncertain data and how to design and analyze efficient algorithms in these models.

Specifically, we will cover the theory of online optimization, where the input arrives without any prior information (such as network packets arriving to a router) and also needs to be processed immediately, before the next piece of input arrives. This model is best suited for analyzing critical networking and scheduling systems where devices and algorithms must perform well even in the worst-case scenario.

In the cases where previous history can be used to model the upcoming data, we often employ robust optimization or stochastic optimization. In robust optimization, the aim is to optimize the worst-case of all possible realizations of the input data. Hence, this model is rather conservative.
In stochastic optimization however, the algorithms work with the assumption that data is drawn from some probability distribution known ahead of time and typically the goal is to optimize the expected value.

Nowadays, another source of information is often available: machine learning algorithms can generate predictions which are accurate most of the time. However, there is no guarantee on the quality of the prediction, as the current instance may not be covered by the training set. This statement motivated a very recent research domain that will be covered in this course: how to use error-prone predictions in order to improve guaranteed algorithms.

Organization: The course will be taught in English in two sessions per week (4 SWS) including interactive exercise sessions.

Examination: The examination will be by individual oral exam. As admission to the oral exam it is mandatory to present solutions in the exercise session at least twice during the term.

Prerequisites: Having heard an introductory course to discrete algorithms and their mathematical analysis (e.g. Algorithmentheorie, Algorithmische Diskrete Mathematik) or graph theory is beneficial but not required.

Prof. Dr. Nicole Megow
03-M-SP-2Basics of Mathematical Statistics (Statistics I) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 External location: LINZ4 4010 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 External location: MZH 1100 Exercise

Die Veranstaltung findet zusammen mit 03-M-FTH-10 statt.

Prof. Dr. Werner Brannath
03-M-SP-26Algebraic Topology (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 7200 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 7200 Exercise

Findet zusammen mit der LV 03-M-FTH-9 statt.

Prof. Dr. Dmitry Feichtner-Kozlov
03-M-SP-28Advanced Methods in Applied Statistics (Statistics III) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 10:00 - 12:00 MZH 7200 Exercise
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 7200 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 7200 Lecture

The quantitative assessment and the management of (extreme) risks are key tools for policy makers and stakeholders in many areas such as climate and environmental research, economics, or finance and insurance. In this course, we will get familiar with basic mathematical concepts of (quantitative) risk assessment and management.

Prof. Dr. Thorsten-Ingo Dickhaus
03-M-SP-38Finite Elements - Selected Chapters (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 2340 Exercise

The finite element method is used for the discretisation of partial differential equations in many different applications. In this course we will deepen existing knowledge in finite element methods with respect to different applications and learn new techniques to increase their computational speed.

Prof. Dr. Andreas Rademacher
03-M-SP-39Advanced Topics in Image Processing - The Beauty of Variational Calculus (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Fri. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 14:00 - 16:00 MZH 2340 Exercise

This course focusses on two advanced tools in modern mathematical image processing, namely the direct method of variational calculus and the iterated soft thresholding algorithm.

Peter Maaß
Dr. Matthias Beckmann
Dr. rer. nat. Pascal Fernsel
03-M-SP-40Convex Analysis and Optimization (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 12:00 - 14:00 MZH 2340 Lecture
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Exercise
Dirk Lorenz