Course Catalog

Study Program WiSe 2022/2023

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 Foundations of Data Analysis (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 08:00 - 10:00 MZH 4140 Lecture
weekly (starts in week: 1) Mon. 10:00 - 12:00 MZH 4140 Exercise
weekly (starts in week: 1) Wed. 08:00 - 10:00 MZH 1100 Lecture
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: 1) Mon. 12:00 - 14:00 MZH 2340 Exercise
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 2340 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 2340 Lecture
Prof. Dr. Andreas Rademacher

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-M-AC-2High-Performance-Visualisierung (in English)
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 1100 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-3Semiparametric Statistics (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 2340 Seminar

Statistical problems are described by statistical models. This means interpreting the data as realizations of random variables whose unconditional or conditional densities are described and estimated by statistical (regression) models. These models are usually identified by a set of parameters, which can be finite but also infinite dimensional. For this purpose, there are usually three types of possible models, depending on the structure of the data and the problem at hand: parametric, nonparametric, and semiparametric. A semiparametric model is characterized by the inclusion of both finite dimensional parametric and infinite dimensional nonparametric components. The main interest is usually in the finite dimensional parametric component, with the infinite dimensional component being co-estimated for the purpose of statistical inference and efficiency. In this seminar we will study the definition, properties, and applications of semiparametric models. Examples of semiparametric models include single-index models and Cox regression models for censored survival time data. We will also consider approaches to dealing with missing information in data sets. The use of semiparametric models plays a major role for medical studies, for example.

Prerequisites for participation in the seminar are basic knowledge of mathematical statistics (e.g. from Statistics 1) and of regression models (e.g. from Statistics 2). English speaking students are welcome.

In order to gain a good insight into the extensive theory of semi-parametric models, we will use the master thesis by Karel Vermeulen as our primary literature and study the chapters that are important for us in more detail, presenting the knowledge gained through the thesis in the form of individual presentations.

A list with the name of the thesis and further literature can be found below.

  • Master thesis of Karel Vermeulen. Semiparametric Efficiency
  • A. W. van der Vaart. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 1998.
  • A. W. van der Vaart. ”On Differentiable Functionals“. In: Ann. Statist. 19.1 (März 1991), S. 178–204.
  • Tsiatis, Anastasios. Semiparametric Theory and Missing Data. Vereinigtes Königreich, Springer New York, 2010.

Prof. Dr. Werner Brannath
03-M-AC-4Mathematical Modelling and Scientific Computing (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 6200 Seminar
Prof. Dr. Andreas Rademacher
03-M-AC-6Mathematical Foundations of AI (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 11:00 - 12:00 MZH 2340 Seminar
Sören Dittmer
03-M-AC-7Advanced Topics in Statistics (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Tue. 16:00 - 18:00 BIPS 1550 Seminar

regelmäßige Veranstaltung dienstags 14-16 im BIPS Raum 1550.

Prof. Dr. Vanessa Didelez

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-AU (03-ME-602.99c)Algorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 1470 Kurs Präsenz
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1470 Kurs Präsenz

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI

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
Dr. Felix Christian Hommelsheim
03-M-SP-1Inverse Problems (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 2340 Exercise
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Lecture
Peter Maaß
Dr. Matthias Beckmann
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 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1100 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 1450 Exercise
Prof. Dr. Werner Brannath
03-M-SP-3Mathematical Foundations of Deep Learning (in English)

Lecture (Teaching)
ECTS: 4,5

Dates:
weekly (starts in week: 9) Mon. 08:00 - 12:00 MZH 2340 Lecture/Exercise
weekly (starts in week: 8) Wed. 08:00 - 10:00 MZH 2340 Lecture / Exercise
Sören Dittmer
03-M-SP-5Theory of Nonparametric Tests (Statistics III) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Thu. 16:00 - 18:00 MZH 4140 Exercise
Prof. Dr. Thorsten-Ingo Dickhaus

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-M-AC-1Numerical 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
Alfred Schmidt
03-M-AC-3Semiparametric Statistics (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 2340 Seminar

Statistical problems are described by statistical models. This means interpreting the data as realizations of random variables whose unconditional or conditional densities are described and estimated by statistical (regression) models. These models are usually identified by a set of parameters, which can be finite but also infinite dimensional. For this purpose, there are usually three types of possible models, depending on the structure of the data and the problem at hand: parametric, nonparametric, and semiparametric. A semiparametric model is characterized by the inclusion of both finite dimensional parametric and infinite dimensional nonparametric components. The main interest is usually in the finite dimensional parametric component, with the infinite dimensional component being co-estimated for the purpose of statistical inference and efficiency. In this seminar we will study the definition, properties, and applications of semiparametric models. Examples of semiparametric models include single-index models and Cox regression models for censored survival time data. We will also consider approaches to dealing with missing information in data sets. The use of semiparametric models plays a major role for medical studies, for example.

Prerequisites for participation in the seminar are basic knowledge of mathematical statistics (e.g. from Statistics 1) and of regression models (e.g. from Statistics 2). English speaking students are welcome.

In order to gain a good insight into the extensive theory of semi-parametric models, we will use the master thesis by Karel Vermeulen as our primary literature and study the chapters that are important for us in more detail, presenting the knowledge gained through the thesis in the form of individual presentations.

A list with the name of the thesis and further literature can be found below.

  • Master thesis of Karel Vermeulen. Semiparametric Efficiency
  • A. W. van der Vaart. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 1998.
  • A. W. van der Vaart. ”On Differentiable Functionals“. In: Ann. Statist. 19.1 (März 1991), S. 178–204.
  • Tsiatis, Anastasios. Semiparametric Theory and Missing Data. Vereinigtes Königreich, Springer New York, 2010.

Prof. Dr. Werner Brannath
03-M-AC-4Mathematical Modelling and Scientific Computing (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 6200 Seminar
Prof. Dr. Andreas Rademacher
03-M-AC-6Mathematical Foundations of AI (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 11:00 - 12:00 MZH 2340 Seminar
Sören Dittmer
03-M-AC-8Combinatorial Optimization: Introduction and Algorithms (in English)
Application of Optimization and Optimal Control

Seminar (Teaching)
ECTS: 4,5 / 6

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

Die Veranstaltung findet im NEOS Gebäude statt.

Prof. Dr. Christof Büskens
Dr. Amin Mallek

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-AU (03-ME-602.99c)Algorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 1470 Kurs Präsenz
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1470 Kurs Präsenz

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI

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
Dr. Felix Christian Hommelsheim
03-M-SP-1Inverse Problems (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 2340 Exercise
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Lecture
Peter Maaß
Dr. Matthias Beckmann
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 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1100 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 1450 Exercise
Prof. Dr. Werner Brannath
03-M-SP-5Theory of Nonparametric Tests (Statistics III) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Thu. 16:00 - 18:00 MZH 4140 Exercise
Prof. Dr. Thorsten-Ingo Dickhaus
03-M-SP-6Algorithmic Game Theory (in English)

Lecture (Teaching)
ECTS: 9 (6)

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

Many every-day processes can seen as a game between autonomous interacting players, where each player acts stategically in order to pursue her own objectives. This lecture is an introduction to game-theoretic concepts and techniques, mainly with connections to applications. Use-cases are distributed systems, auctions, online-markets, resource allocation, traffic routing, and sports. The goal of the lecture is to provide an overview over state-of-the-art results in the area of algorithmic game theory. Main topics that we will cover in the course are games in normal form, efficiency of equilibria, auctions, truthfulness and VCG-mechanisms, social choice, cake cutting, and cooperative games.

The lectures and homework sheets will be in English language. If all participants agree, the exercise session could be held in German. If there is an oral exam, the language can be chosen by the candidate. In case of a written exam the questions will be in English, answering them in German or English is fine.

Prof. Dr. Daniel Schmand
03-M-SP-9Introduction to Nonlinear Optimization and Optimal Control (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 12:00 - 14:00 Lecture
weekly (starts in week: 1) Tue. 08:00 - 10:00 Lecture
weekly (starts in week: 1) Tue. 14:00 - 16:00 Exercise

Die Veranstaltung findet im NEOS Gebäude statt.

Prof. Dr. Christof Büskens
04-M30-CP-SFT-3Trajectory Optimization (in English)

Lecture (Teaching)
ECTS: 4,5

Dates:
weekly (starts in week: 1) Mon. 14:00 - 17:00 GW1 B0100
Matthias Knauer
Prof. Dr. Christof Büskens

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-M-AC-1Numerical 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
Alfred Schmidt
03-M-AC-3Semiparametric Statistics (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 2340 Seminar

Statistical problems are described by statistical models. This means interpreting the data as realizations of random variables whose unconditional or conditional densities are described and estimated by statistical (regression) models. These models are usually identified by a set of parameters, which can be finite but also infinite dimensional. For this purpose, there are usually three types of possible models, depending on the structure of the data and the problem at hand: parametric, nonparametric, and semiparametric. A semiparametric model is characterized by the inclusion of both finite dimensional parametric and infinite dimensional nonparametric components. The main interest is usually in the finite dimensional parametric component, with the infinite dimensional component being co-estimated for the purpose of statistical inference and efficiency. In this seminar we will study the definition, properties, and applications of semiparametric models. Examples of semiparametric models include single-index models and Cox regression models for censored survival time data. We will also consider approaches to dealing with missing information in data sets. The use of semiparametric models plays a major role for medical studies, for example.

Prerequisites for participation in the seminar are basic knowledge of mathematical statistics (e.g. from Statistics 1) and of regression models (e.g. from Statistics 2). English speaking students are welcome.

In order to gain a good insight into the extensive theory of semi-parametric models, we will use the master thesis by Karel Vermeulen as our primary literature and study the chapters that are important for us in more detail, presenting the knowledge gained through the thesis in the form of individual presentations.

A list with the name of the thesis and further literature can be found below.

  • Master thesis of Karel Vermeulen. Semiparametric Efficiency
  • A. W. van der Vaart. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 1998.
  • A. W. van der Vaart. ”On Differentiable Functionals“. In: Ann. Statist. 19.1 (März 1991), S. 178–204.
  • Tsiatis, Anastasios. Semiparametric Theory and Missing Data. Vereinigtes Königreich, Springer New York, 2010.

Prof. Dr. Werner Brannath
03-M-AC-4Mathematical Modelling and Scientific Computing (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 6200 Seminar
Prof. Dr. Andreas Rademacher
03-M-AC-6Mathematical Foundations of AI (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 11:00 - 12:00 MZH 2340 Seminar
Sören Dittmer
03-M-AC-8Combinatorial Optimization: Introduction and Algorithms (in English)
Application of Optimization and Optimal Control

Seminar (Teaching)
ECTS: 4,5 / 6

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

Die Veranstaltung findet im NEOS Gebäude statt.

Prof. Dr. Christof Büskens
Dr. Amin Mallek

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-AU (03-ME-602.99c)Algorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 1470 Kurs Präsenz
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1470 Kurs Präsenz

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI

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
Dr. Felix Christian Hommelsheim
03-M-SP-1Inverse Problems (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 2340 Exercise
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Lecture
Peter Maaß
Dr. Matthias Beckmann
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 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1100 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 1450 Exercise
Prof. Dr. Werner Brannath
03-M-SP-5Theory of Nonparametric Tests (Statistics III) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Thu. 16:00 - 18:00 MZH 4140 Exercise
Prof. Dr. Thorsten-Ingo Dickhaus
03-M-SP-6Algorithmic Game Theory (in English)

Lecture (Teaching)
ECTS: 9 (6)

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

Many every-day processes can seen as a game between autonomous interacting players, where each player acts stategically in order to pursue her own objectives. This lecture is an introduction to game-theoretic concepts and techniques, mainly with connections to applications. Use-cases are distributed systems, auctions, online-markets, resource allocation, traffic routing, and sports. The goal of the lecture is to provide an overview over state-of-the-art results in the area of algorithmic game theory. Main topics that we will cover in the course are games in normal form, efficiency of equilibria, auctions, truthfulness and VCG-mechanisms, social choice, cake cutting, and cooperative games.

The lectures and homework sheets will be in English language. If all participants agree, the exercise session could be held in German. If there is an oral exam, the language can be chosen by the candidate. In case of a written exam the questions will be in English, answering them in German or English is fine.

Prof. Dr. Daniel Schmand
03-M-SP-9Introduction to Nonlinear Optimization and Optimal Control (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Mon. 12:00 - 14:00 Lecture
weekly (starts in week: 1) Tue. 08:00 - 10:00 Lecture
weekly (starts in week: 1) Tue. 14:00 - 16:00 Exercise

Die Veranstaltung findet im NEOS Gebäude statt.

Prof. Dr. Christof Büskens
04-M30-CP-SFT-3Trajectory Optimization (in English)

Lecture (Teaching)
ECTS: 4,5

Dates:
weekly (starts in week: 1) Mon. 14:00 - 17:00 GW1 B0100
Matthias Knauer
Prof. Dr. Christof Büskens

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-M-AC-2High-Performance-Visualisierung (in English)
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 1100 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-3Semiparametric Statistics (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 2340 Seminar

Statistical problems are described by statistical models. This means interpreting the data as realizations of random variables whose unconditional or conditional densities are described and estimated by statistical (regression) models. These models are usually identified by a set of parameters, which can be finite but also infinite dimensional. For this purpose, there are usually three types of possible models, depending on the structure of the data and the problem at hand: parametric, nonparametric, and semiparametric. A semiparametric model is characterized by the inclusion of both finite dimensional parametric and infinite dimensional nonparametric components. The main interest is usually in the finite dimensional parametric component, with the infinite dimensional component being co-estimated for the purpose of statistical inference and efficiency. In this seminar we will study the definition, properties, and applications of semiparametric models. Examples of semiparametric models include single-index models and Cox regression models for censored survival time data. We will also consider approaches to dealing with missing information in data sets. The use of semiparametric models plays a major role for medical studies, for example.

Prerequisites for participation in the seminar are basic knowledge of mathematical statistics (e.g. from Statistics 1) and of regression models (e.g. from Statistics 2). English speaking students are welcome.

In order to gain a good insight into the extensive theory of semi-parametric models, we will use the master thesis by Karel Vermeulen as our primary literature and study the chapters that are important for us in more detail, presenting the knowledge gained through the thesis in the form of individual presentations.

A list with the name of the thesis and further literature can be found below.

  • Master thesis of Karel Vermeulen. Semiparametric Efficiency
  • A. W. van der Vaart. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 1998.
  • A. W. van der Vaart. ”On Differentiable Functionals“. In: Ann. Statist. 19.1 (März 1991), S. 178–204.
  • Tsiatis, Anastasios. Semiparametric Theory and Missing Data. Vereinigtes Königreich, Springer New York, 2010.

Prof. Dr. Werner Brannath
03-M-AC-4Mathematical Modelling and Scientific Computing (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 6200 Seminar
Prof. Dr. Andreas Rademacher
03-M-AC-6Mathematical Foundations of AI (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Wed. 11:00 - 12:00 MZH 2340 Seminar
Sören Dittmer
03-M-AC-7Advanced Topics in Statistics (in English)

Seminar (Teaching)
ECTS: 4,5 / 6

Dates:
weekly (starts in week: 1) Tue. 16:00 - 18:00 BIPS 1550 Seminar

regelmäßige Veranstaltung dienstags 14-16 im BIPS Raum 1550.

Prof. Dr. Vanessa Didelez

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-AU (03-ME-602.99c)Algorithms and Uncertainty (in English)

Kurs (Teaching)
ECTS: 6 (9)

Dates:
weekly (starts in week: 1) Tue. 12:00 - 14:00 MZH 1470 Kurs Präsenz
weekly (starts in week: 1) Thu. 14:00 - 16:00 MZH 1470 Kurs Präsenz

Profil: SQ
Schwerpunkt: IMA-SQ, IMA-AI

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
Dr. Felix Christian Hommelsheim
03-M-SP-1Inverse Problems (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Wed. 14:00 - 16:00 MZH 2340 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 2340 Exercise
weekly (starts in week: 1) Fri. 10:00 - 12:00 MZH 2340 Lecture
Peter Maaß
Dr. Matthias Beckmann
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 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 08:00 - 10:00 MZH 1100 Lecture
weekly (starts in week: 1) Fri. 08:00 - 10:00 MZH 1450 Exercise
Prof. Dr. Werner Brannath
03-M-SP-3Mathematical Foundations of Deep Learning (in English)

Lecture (Teaching)
ECTS: 4,5

Dates:
weekly (starts in week: 9) Mon. 08:00 - 12:00 MZH 2340 Lecture/Exercise
weekly (starts in week: 8) Wed. 08:00 - 10:00 MZH 2340 Lecture / Exercise
Sören Dittmer
03-M-SP-5Theory of Nonparametric Tests (Statistics III) (in English)

Lecture (Teaching)
ECTS: 9

Dates:
weekly (starts in week: 1) Tue. 10:00 - 12:00 MZH 1100 Lecture
weekly (starts in week: 1) Thu. 10:00 - 12:00 MZH 4140 Lecture
weekly (starts in week: 1) Thu. 16:00 - 18:00 MZH 4140 Exercise
Prof. Dr. Thorsten-Ingo Dickhaus