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# Lehrveranstaltungen WiSe 2021/2022

## Mathematik, B.Sc./M.Sc. (Studienbeginn vor 2022)

Veranstaltungen anzeigen: alle | in englischer Sprache | für ältere Erwachsene | mit Nachhaltigkeitszielen

## Master: Wahlpflichtveranstaltungen

### Vertiefungsrichtung Algebra

VAKTitel der VeranstaltungDozentIn
03-IMAT-AU (03-ME-602.99c)Algorithms and Uncertainty (in englischer Sprache)

Kurs
ECTS: 6

Termine:
wöchentlich Di 12:00 - 14:00 MZH 1450 Kurs Präsenz
wöchentlich Do 08:00 - 10:00 MZH 3150 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

### Vertiefungsrichtung Numerik

VAKTitel der VeranstaltungDozentIn
03-IMAT-AU (03-ME-602.99c)Algorithms and Uncertainty (in englischer Sprache)

Kurs
ECTS: 6

Termine:
wöchentlich Di 12:00 - 14:00 MZH 1450 Kurs Präsenz
wöchentlich Do 08:00 - 10:00 MZH 3150 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-IMVP-IMLInterpretable Machine Learning (in englischer Sprache)

Kurs
ECTS: 6 (optional +3)

Termine:
wöchentlich Mi 16:15 - 17:45 Kurs online
wöchentlich Do 08:15 - 09:45 Kurs online

Einzeltermine:
Di 01.03.22 10:00 - 15:00 Zoom
Mi 09.03.22 09:00 - 10:00 Zoom
Mi 16.03.22 - Do 17.03.22 (Mi, Do) 09:00 - 15:00 Zoom

Schwerpunkt: Ai

Prof. Dr. Marvin Nils Ole Wright
03-M-WP-28Algorithmic Game Theory (in englischer Sprache)

Vorlesung
ECTS: 9 (6)

Termine:
wöchentlich Di 14:00 - 16:00 MZH 2340 Vorlesung
wöchentlich Di 16:00 - 18:00 MZH 2340 Übung
wöchentlich Do 14:00 - 16:00 MZH 2340 Vorlesung

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
04-M30-CP-SFT-3Trajectory Optimization (in englischer Sprache)

Vorlesung
ECTS: 4,5

Termine:
wöchentlich Mo 14:00 - 16:00 HS 2010 (Großer Hörsaal)
Matthias Knauer
Prof. Dr. Christof Büskens

### Vertiefungsrichtung Stochastik & Statistik

VAKTitel der VeranstaltungDozentIn
03-M-WP-58Time Series Analysis, Univariate and Multivariate Methods (in englischer Sprache)

Vorlesung
ECTS: 4,5

Termine:
wöchentlich Di 12:00 - 14:00 Vorlesung online
zweiwöchentlich (Startwoche: 2) Mi 12:00 - 14:00 Übung Online

This course is as 2 hours lecture + 1 hour of exercise class = 3SWS = 4,5 CP , meaning ”a half module”. Both take place online via BigBlueButton and records (live broadcast) and the examination is a written exam. Also, there will be a follow-up course (again in the format of a ”half module”) in the next semester which is related to frequency domain analyses of univariate and multivariate time series (Chapters 11 to 20 of the reference book). The two courses can be combined to form one full 9 CP module.

Maryam Movahedifar

## Master: Seminare

### Vertiefungsrichtung Numerik

VAKTitel der VeranstaltungDozentIn
03-M-SEM-30Machine Learning in 3D and Mechanical Applications (in englischer Sprache)

Seminar
ECTS: 6

Termine:
wöchentlich Mo 10:00 - 12:00 MZH 4140 Seminar
David Erzmann

## Oberseminare

VAKTitel der VeranstaltungDozentIn
03-M-OS-7Oberseminar Mathematische Parameteridentifikation (in englischer Sprache)
Research Seminar - Mathematical Parameter Identification

Seminar

Termine:
wöchentlich Mi 12:00 - 14:00 MZH 2340

Daniel Otero Baguer

## General Studies

VAKTitel der VeranstaltungDozentIn
03-M-GS-3Grundlegende Methoden der angewandten Statistik (in englischer Sprache)
Basic Methods of Applied Statistics

Vorlesung
ECTS: 6

Termine:
wöchentlich Fr 08:00 - 10:00 SFG 0140 Vorlesung
wöchentlich Fr 10:00 - 12:00 SFG 0140 Übung 1
wöchentlich Fr 14:00 - 16:00 SFG 0140 Übung 2
Dr. Martin Scharpenberg
03-M-GS-5Statistische Beratung (in englischer Sprache)
Statistical Consulting

Seminar
ECTS: 3

Termine:
wöchentlich Fr 10:00 - 12:00 Seminar
Dr. Martin Scharpenberg
03-M-GS-6Data Science in Natural Sciences using R (in englischer Sprache)
a course on R programming and data science methods with practicals and projects

Vorlesung
ECTS: 3

Termine:
wöchentlich Mi 14:00 - 16:00 Externer Ort: MZH 0240 for Lecture and Work on Computers (2 SWS) Work on Computers in MZH-0240

The course provides an introductory level of programming skills in R.
Students are welcome to present own ideas, data and projects. I expect a project report or a method talk with demo on own data. Practicals in "R" will work also on synthetic data to illustrate methods features, limitations and differences.

Prof. Dr. Stephan Frickenhaus
03-M-GS-7Einführung in R (in englischer Sprache)
Introduction to R

Seminar
ECTS: 3

Termine:
wöchentlich Fr 13:00 - 16:00
Charlie Hillner
Prof. Dr. Werner Brannath