Seminare und Workshops

Termine für Seminare im Wintersemester 2021/22

Kalender blau: Grafik: Kathrin Ruf

Die Seminar- Anmeldung erfolgt für das Wintersemester 2021/22 wieder über das Matching-System.

Seminare, die für Studierende der TUM School of Education geeignet sind, enthalten einen entsprechenden Vermerk in der Seminarbeschreibung.

01. Juli 2021: Bekanntgabe des Angebots für das Wintersemester 2021/22

05. Juli (12 Uhr) - 12. Juli 2021 (12 Uhr): Anmeldung der Studierenden über das Matching-System

14. Juli - 21. Juli 2021: Auswahlrunde der Dozent*innen

26. Juli 2021: Die Ergebnisse werden im Matching-System veröffentlicht

 

Wie werden die Seminarplätze vergeben?

Die Aufteilung auf die angebotenen Workshops und Seminare erfolgt in zwei Stufen:
 

Sie melden sich über das Matching-System während des laufenden Semesters für eines der angebotenen Seminare bzw. einen der angebotenen Workshops des folgenden Semesters an. Die betreuenden Dozenten wählen aus der Bewerberliste aus. Sie können danach im Matching-System sehen, in welchem Seminar Sie einen Platz bekommen haben. Kurz vor Semesterbeginn werden Sie von uns zur Prüfung angemeldet und können dies dann in TUMonline unter Ihren "angemeldeten Prüfungen" sehen.

Falls Sie im Matching keinen Platz erhalten haben oder gerne an einem 2. Seminar teilnehmen möchten, klären Sie bitte mit der Seminarleitung eines Seminars mit Restplätzen, ob Sie noch teilnehmen können. Mailen Sie dann an bachelor (at) ma.tum.de oder master (at) ma.tum.de, um zum Bachelor- oder Master-Seminar angemeldet zu werden, und setzen Sie die Seminarleitung cc.

Seminare für Bachelor-Studierende

Bitte beachten Sie

Zu jedem Seminar, das wir für Bachelor- und Master-Studierende anbieten, erfolgt die Anmeldung über das Matching-System. Melden Sie sich bitte nur für Bachelor-Seminare an. Die Plätze in den Master-Seminaren vergeben wir bevorzugt an Master-Studierende, die in diesen Studiengängen bereits jetzt eingeschrieben sind.

Nach der Auswahlrunde können Sie sich auch auf freie Plätze in Master-Hauptseminaren anmelden. Bitte klären Sie direkt mit der jeweiligen Seminarleitung, ob Sie noch teilnehmen können. Bei einer Zustimmung mailen Sie bitte an master (at) ma.tum.de, um zum Master-Seminar angemeldet zu werden. Setzen Sie in Ihrer Mail die Seminarleitung bitte cc.

Angebotene Bachelor-Seminare im Wintersemester 2021/22

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Bachelor: 6
Studierende anderer Fakultäten: None

Inhalt

Das Seminar ist ein gemeinsamer Lektüre- und Diskussionskurs des Buches "Algorithms from the Book" von Kenneth Lange (SIAM, 2020). Es beschäftigt sich mit berühmten und erfolgreichen Algorithmen und ihren mathematischen Grundlagen. Kenneth Lange arbeitet derzeit an einer Neuauflage des Buches. Wir werden neue Kapitel zur preview benutzen dürfen.

Voraussetzungen

Solide Kenntnisse in Analysis, linearer Algebra und Numerik.

Literatur

Algorithms from the Book von Kenneth Lange, SIAM, 2020. Über die Bibliothek können Sie auf eine digitale Version des Buchs im Volltext zugreifen

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 5
Studierende anderer Fakultäten: 2

Inhalt

Functional inequalities provide a method to compare functions to each other in view of certain features. How symmetric is a function under certain operations? How wiggly is it? How close is it to a given set functions? Such questions play an important role in mathematical physics, differential geometry, PDE analysis and many more fields, and functional inequalities give an answer in terms of robust integral expression. In this seminar, we shall encounter several well-known functional inequalities, like rearrangement, Hardy-Littlewood-Sobolev, logarithmic Sobolev and Hausdorff-Young inequalities. The proofs will provide information on the optimal constants and the optimizers, which achieve equality. In each case, the method of proof rests on some deep insight and has an inherent beauty. Applications, for instance to the estimate on the rates of equilibration in particle systems or to bound the Ricci curvature of manifolds, will be discussed depending on the interest of the participants.

Voraussetzungen

Analysis, LADS and Maßtheorie are a must. Basic knowledge in functional analysis and/or PDEs is helpful for some topics, but is not at all necessary to enjoy the seminar.

Literatur

For the specific functional inequalities mentioned above, we follow E.Lieb und M.Loss: "Analysis" (GSM 14, AMS). For further inequalities and the mentioned applications, additional material will be provided.

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 2
Studierende anderer Fakultäten: None

Inhalt

Massive testing is an important ingredient to control infectious diseases such as the current COVID-19 pandemic. Group testing methodologies, where multiple different specimens are tested as a pool using a single test, can help increase the efficiency by reducing the number of required tests. In this seminar, we will study the extensive mathematical literature regarding the problem of determining appropriate designs of the group testing protocol. In particular, we aim to cover under which assumptions group testing makes sense at all, and if yes, which group size is optimal.

Voraussetzungen

MA5441 Fundamentals of Statistics

Literatur

Ding-Zhu Du, Frank Kwang Hwang. Combinatorial Group Testing and Its Applications, World Scientific, 1993 Ding-Zhu Du, Frank Kwang Hwang. Pooling Designs And Nonadaptive Group Testing: Important Tools For Dna Sequencing, World Scientific, 2006 Matthew Aldridge, Oliver Johnson, Jonathan Scarlett. Group testing: an information theory perspective Now Publishers, 2019 Further literature for each seminar topic will be provided to the participants in the form of research articles.

Informationen

The seminar will take place in blocks on 3-5 afternoons throughout the semester.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 4
Studierende anderer Fakultäten: None

Inhalt

In recent years, there has been an increasing interest in topics at the intersection of economics and computer science, as witnessed by the continued rapid rise of research areas such as algorithmic game theory and computational social choice. This development is due to the emergence of computational networks such as the Internet as well as the need to get a grip on algorithmic questions in economics. In this seminar, we will deal with both the theoretical foundations as well as their computational properties and possible applications.

Voraussetzungen

Experience in formally proving mathematical statements (standard proof techniques) Basic knowledge of complexity theory is useful (e.g., module IN0011)

Literatur

David C. Parkes and Sven Seuken: "Economics and Computation" (guest key published during overview meeting) Brandt et al.: "Handbook of Computational Social Choice" (freely available as PDF)

Informationen

All students have to apply for the seminar. Further information (including the application procedure) can be found on the course homepage: https://dss.in.tum.de/teaching/ws-21-22/49-teaching/semester/winter-semester-2021-22/256-seminar-on-markets-algorithms-incentives-and-networks-ws21-22.html Please attend the overview meeting if you are interested in participating.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 7
Studierende anderer Fakultäten: None

Inhalt

Can we estimate the time when humanity did leave Africa? Can we obtain, from genetic data only, size and history of a population? Population genetics allows to answer such questions, purely in looking into the signature of mutations. In this seminar, we will start with a review of the basis of population genetics (Kingman coalescent, measures for genetic diversity, site-frequency spectrum) to proceed thereafter to more advanced mathematical models that allow to analyze the evolution of so far neglected biological systems with generation overlap (bacteria, viruses, seeds of plants but also trees or long lived mammals). In the seminar course we aim to discuss the existing literature in this area with the objective of developing better suited mathematical models.

Voraussetzungen

Basic stochastics.

Literatur

Durrett, R. (2008). Probability Models for DNA Sequence Evolution (Springer). Original papers for the more specialized talks.

Informationen

Falls ein Termin Freitags 14:00 möglich wäre, so würden wir das begrüßen.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Bachelor: 10
Studierende anderer Fakultäten: None

Inhalt

Viele Probleme der Statistik können in algebraischer Sprache beschrieben werden und lassen sich deshalb mittels algebraischer Methoden lösen. Dieses Seminar bietet eine Einführung in die Welt der algebraischen Statistik. Am Anfang des Seminars präsentieren wir alle notwendige algebraische Begriffe, wie z.B. Polynome, Ideale und Gröbner-Basen. Parallel dazu lernen wir den Umgang mit Computeralgebrasystemen. Anschließend sehen wir ausgewählte Anwendungen in der Statistik, wie zum Beispiel Unabhängigkeit in Graphischen Modellen und Markow-Basen für Hierarchische Modelle.

Voraussetzungen

Einführung in die Wahrscheinlichkeitstheorie und Statistik.

Literatur

Wir betrachten ausgewählte Kapitel der folgenden Bücher: Cox D, Little J, and O'Shea D. 2007. Ideals, Varieties and Algorithms. Undergraduate Texts in Mathematics. Springer-Verlag. Sullivant S. 2018. Algebraic Statistics. Graduate Studies in Mathematics. American Mathematical Society.

Informationen

Eine Vorbesprechung findet Anfang Oktober statt. Vorträge können in deutscher oder englischer Sprache gehalten werden.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 5
Studierende anderer Fakultäten: None

Inhalt

Chains of infinite order, first introduced by Doblin and Fortet in 1937, are the generalization of k-step Markov chains when the parameter k approaches infinity. The study of those chains is of significance in a variety of fields, such as Probability Theory, Statistical Mechanics and Ergodic Theory. For further information, please visit the seminar's website https://www-m5.ma.tum.de/Allgemeines/CIO_2021W

Voraussetzungen

Introduction to Probability and Statistics, Markov Chains, Measure Theory

Literatur

We will read several old and new papers together. Please visit the website of the seminar https://www-m5.ma.tum.de/Allgemeines/CIO_2021W for a list of those papers.

Informationen

Sprache

englisch

Anzahl an Plätzen

Bachelor: 7
Studierende anderer Fakultäten: None

Inhalt

Linear algebraic groups are an important class of groups that come with the structure of an algebraic variety. Examples include the general linear group, the special linear group or the orthogonal group over a field. In this seminar, we will develop the foundations of the theory of linear algebraic groups. We will discuss the basic definitions, important subgroups such as tori and Borel subgroups, the relationship between a linear algebraic group and its Lie algebra, as well as the root datum of a linear algebraic group. The endpoint of the seminar will be a discussion of the classification of reductive groups. The most important tools for our course come from linear algebra and algebraic geometry. The necessary prerequisites from algebraic geometry will be explained in the seminar, with the level of detail depending on the participants' backgrounds. The theory of linear algebraic groups has a number of applications in algebraic geometry, finite group theory and many other subjects. Moreover, while the foundations are well-understood and accessible, open questions related to linear algebraic groups are ubiquitous in modern mathematical research.

Voraussetzungen

Commutative Algebra within the scope of Algebra 2 Experience with algebraic geometry is very helpful, but not required

Literatur

T.A. Springer . Linear Algebraic Groups J.E. Humphreys. Linear Algebraic Groups R. Carter, G. Segal, I. Macdonald. Lectures on Lie Groups and Lie Algebras

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 10
Studierende anderer Fakultäten: None

Inhalt

Measure concentration deals with the general fact that reasonable functions on large probability spaces typically take on values close to the average. This seminar provides an introduction to some of the existing techniques for establishing such results. Connections and applications to various geometric inequalities and some applications will also be discussed.

Voraussetzungen

Probability theory, measure- and integration theory

Literatur

Primarily: M. Ledoux, The Concentration of Measure Phenomenon, AMS, 2001. Additional literature: TBA.

Informationen

see http://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 4
Studierende anderer Fakultäten: 2

Inhalt

The idea of Mathematical Epidemiology is to understand the spread of diseases, to make forcast about the progression of diseases and to understand possible effects of interventions. In this seminar, we will consider typical model approaches and their analysis in this area. Starting with basic epidemic model, we will include more and more structure behind, also concerning demography. Another important problem are so-called vector-borne diseases (like Malaria) and their treatments. One aspect of the seminar will be also the consideration of data, how to extract important information and how to make reliable predictions. Different mathematical tools may be appropriate and used as modelling approaches, e.g. Ordinary differential equations, Delay differential equations and Partial differential equations, but also some statistical techniques.

Voraussetzungen

Mathematical models in Biology, Knowledge in Ordinary differential equations

Literatur

This seminar will be based on parts of the book “An Introduction to Mathematical Epidemiology” by Maia Martcheva and further original papers in this context dependent on the interests and previous knowledge of the participants.

Informationen

Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. If there are special interests, please contact me as soon as possible. Questions are always welcome, also in advance!

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Bachelor: 10
Studierende anderer Fakultäten: None

Inhalt

Die Fortschritte in 3d Rendering und as Aufkommen von 3D Druckverfahren eröffnet der mathematischen Visualisierung neue Möglichkeiten. Veranschaulichungen mathematischen Sachverhalte und Objekte können relativ einfach visualisiert und physisch realisiert werden. In diesem Seminar sollen die Studenten in kleinen Gruppen ein oder mehrere mathematische Modelle erstellen. Bei dem Modell kann es sich um eine Fläche, wie die Kuen'sche Fläche, einen Körper - wie das Oloid oder aber einen Sachverhalt - wie die Spur eines Brennpunktes einer Ellipse unter Abrollen oder die Vercknickbarkeit spezieller Vierecksnetze - handeln. Die Studenten sollen die Objekte verstehen, die nötigen Daten generieren und soweit aufbereiten, dass am Ende eine Visualisierung erstellt und/oder ein 3D Modell gedruckt werden kann. Dieses Modell soll dann im Vortrag vorgestellt und erklärt werden. Einige Beispiele können hier gesehen werden: https://www- m10.ma.tum.de/bin/view/Lehre/WS1415/ModelleSeminar Die zur Erstellung und Aufbereitung der Modelle nötigen Softwaresysteme werden im Seminar besprochen.

Voraussetzungen

Analysis und Lineare Algebra. Differentialgeometrie: Grundlagen und/oder Geometriekalküle bz. Geometrie, ein wenig Programmiererfahrung (wie z.B. python, java, Julia, c, etc...).

Literatur

Je nach zu bearbeitendem Modell passende Fachartikel.​

Informationen

Die Abhaltung (in Person, online, eine Mischung...) wird sich den Gegebenheiten im kommenden Wintersemester anpassen (müssen).

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Bachelor: 11
Studierende anderer Fakultäten: None

Inhalt

Das Seminar soll sich mit der mathematischen Modellierung biologischer Vorgänge im menschlischen Körper befassen. Behandelt werden dabei sowohl zelluläre Prozesse, wie auch die Funktion ganzer Organe. Typischerweise führt dies auf (nichtlineare) Differentialgleichungen, die anschließend durch geeignete Näherungsmethoden oder numerisch gelöst werden können.

Voraussetzungen

Interesse an Biologie, Chemie, mathematischer Modellierung und Differentialgleichungen.

Literatur

James Keener, James Sneyd: Mathematical Physiology, I: Cellular Physiology, Springer Verlag, New York, 2008. James Keener, James Sneyd: Mathematical Physiology, II: Systems Physiology, Springer Verlag, New York, 2008.

Informationen

Voraussichtlicher Termin: Do 14-16 Uhr

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Bachelor: 8
Studierende anderer Fakultäten: None

Inhalt

This seminar introduces the students to the analysis of actuarial mortality data to fit mathematical models used in the valuation of insurance and pension portfolios. It covers the mathematical analysis of regression models, defines the concept of force of mortality (hazard rate) and introduce some parametric models widely used by practitioners. The lecturers will show the application of these models to the analysis of actuarial datasets and of Human Mortality Data, and their use in pricing basic life insurance contract (e.g. annuities).

Voraussetzungen

MA0009

Literatur

A. S. Macdonald, S. J. Richards, and I, D. Currie (2018). Modelling Mortality with Actuarial Applications

Informationen

The preliminary online-meeting to the Seminar (Online-Seminarvorbesprechung) will take place on July 8th, 2021 at 17:00 in ZOOM. Please write an e-mail to min@tum.de to get an access to this ZOOM-meeting.

Sprache

deutsch

Anzahl an Plätzen

Bachelor: 8
Studierende anderer Fakultäten: None

Inhalt

Topologische Räume Stetigkeit Zusammenhang Kompaktheit Dimension Metrisierbarkeitssätze Polnische Räume Themen der deskriptiven Mengenlehre (Borel-Mengen, projektive Mengen, Determiniertheit) Topological Spaces Continuity Connected Spaces Compact Spaces Dimension Metrization Theorems Polish Spaces Selected Topics in Descriptive Set Theory (Borel sets, projective sets, Determinacy)

Voraussetzungen

Mathematische Grundvorlesungen

Literatur

Sieradski: Topology and Homotopy Dugundji: Topology Kechris: Classical Descriptive Set Theory

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Bachelor: 8
Studierende anderer Fakultäten: None

Inhalt

Random graphs are used as probabilistic models for complex networks. In the seminar we want to study several well know random graph models including the Erdös-Renyi random graph and the preferential attachment model. In particular, we will study the phase transition for the Erdös-Renyi random graph. During the seminar, we will learn important tools in the study of stochastic processes including couplings, stochastic order, probabilistic bounds and branching processes.

Voraussetzungen

Einführung in die Wahrscheinlichkeitstheorie und Statistik (MA0009) oder Einführung in die Wahrscheinlichkeitstheorie MA1401

Literatur

R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017)

Informationen

https://www-m5.ma.tum.de/Allgemeines/MA6011_2021W Es wird eine Vorbesprechung über Zoom stattfinden, bei der die Vortragsthemen verteilt werden.

Hauptseminare für Master-Studierende

Die Platzvergabe in den Master-Hauptseminaren erfolgt vor allem an Master-Studierende, die in diesen Studiengängen bereits jetzt eingeschrieben sind.

Nach der Auswahlrunde können sich aktuelle Bachelor-Studierende und externe Masterbewerber auf freie Plätze in Master-Hauptseminaren anmelden. Bitte klären Sie direkt mit der jeweiligen Seminarleitung, ob Sie noch teilnehmen können. Bei einer Zustimmung mailen Sie bitte an master (at) ma.tum.de, um zum Master-Seminar angemeldet zu werden. Setzen Sie in Ihrer Mail die Seminarleitung bitte cc.

Wichtige Information für Studierende von "Mathematics in Data Science"

Das Hauptseminar "Mathematics of Data Science" ist speziell für Ihren Studiengang konzipiert und hat 5 ECTS. Sollten Sie lieber ein anderes Hauptseminar besuchen, das üblicherweise nur 3 ECTS hat, müssen Sie eine zusätzliche Ausarbeitung abgeben, um auf 5 ECTS zu kommen. Des Weiteren müssen Sie bitte vorab mit Ihrem Fachstudienberater PD Dr. Peter Massopust klären, ob das Hauptseminar fachlich geeignet ist. Nach dem Seminar geben Sie bitte das Anrechnungsformular mit den Unterschriften der Seminarleiter*in und von Herrn Massopust im Infopoint Mathematik ab.

Angebotene Master-Seminare im Wintersemester 2021/22

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 10
Studierende anderer Fakultäten: None

Inhalt

We study probabilistic models for the evolutions of opinions under some exchange dynamics. Agents hold opinions (for instance an opinion can be an element of [0,1]) and will adjust to each other, following certain rules. How does the system evolve over time? Such models are widespread in economics and there are many challenges and open problems for probability theory.

Voraussetzungen

Probability Theory (compulsory) Markov processes (recommended)

Literatur

Opinion Exchange Dynamics Elchanan Mossel und Omer Tamuz Interacting particle systems for opinion dynamics: the Deffuant model and some generalizations Timo Hirscher

Informationen

We hope to have the seminar in presence, probably in blocked form towards the end of the term. The precise dates will be fixed together with the participants.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 12
Studierende anderer Fakultäten: 2

Inhalt

Fair division problems ask the fundamental question of how to allocate resources to agents fairly. The mathematical problems studied depend on the concrete context (e.g., divisible or indivisible resources) and various fairness criteria (e.g., envy-freeness, proportionality, maximin share). Here is a simple example: Imagine a cake that two people want to share fairly. Each has their own, private valuation function on the points of the cake. Is there a protocol they can use to divide the cake so that no person envies the piece of the other, but also no one has to reveal their valuation function? There is, and it is quite easy: (any) one person cuts two pieces, and the other person picks their favorite. Therefore, it is in the best interest of the cutter to cut two pieces of equal value for themselves and be happy with whatever piece the other person chooses. Quite impressively, this protocol is described in ancient scripts (Theogony and Bible), which were written at least 2700 years ago! Even though simple to state, abstractions of these problems can capture the essence of important real-life applications from political science and microeconomics to computer science and operations research. A great line of works has studied the conditions under which a desired fair solution always exists (or does not) and the algorithmic complexity required to achieve (near) optimum solutions. In this seminar, we will glance at some of the most-studied fair division problems of the last decades, meet colorful ideas to attack them, and understand their algorithmic and optimization aspects. The original papers we will study involve techniques from algebraic topology, optimization, or approximation algorithms.

Voraussetzungen

Mathematical maturity and curiosity.

Literatur

Original articles

Informationen

TBD

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 8
Studierende anderer Fakultäten: None

Inhalt

We will have a closer look at Gaussian processes and related methods in light of their applications for machine learning.

Voraussetzungen

Basic knowledge of probability theory and statistics is required. Knowledge of machine learning basics would be useful.

Literatur

Main literature: Carl Edward Rasmussen, Christopher K.I. Williams „Gaussian Processes for Machine Learning“ (MIT Press 2006); available at http://www.gaussianprocess.org/ Further literature will be provided in due time.

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 4
Studierende anderer Fakultäten: None

Inhalt

Massive testing is an important ingredient to control infectious diseases such as the current COVID-19 pandemic. Group testing methodologies, where multiple different specimens are tested as a pool using a single test, can help increase the efficiency by reducing the number of required tests. In this seminar, we will study the extensive mathematical literature regarding the problem of determining appropriate designs of the group testing protocol. In particular, we aim to cover under which assumptions group testing makes sense at all, and if yes, which group size is optimal.

Voraussetzungen

MA5441 Fundamentals of Statistics

Literatur

Ding-Zhu Du, Frank Kwang Hwang. Combinatorial Group Testing and Its Applications, World Scientific, 1993 Ding-Zhu Du, Frank Kwang Hwang. Pooling Designs And Nonadaptive Group Testing: Important Tools For Dna Sequencing, World Scientific, 2006 Matthew Aldridge, Oliver Johnson, Jonathan Scarlett. Group testing: an information theory perspective Now Publishers, 2019 Further literature for each seminar topic will be provided to the participants in the form of research articles.

Informationen

The seminar will take place in blocks on 3-5 afternoons throughout the semester.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 2
Studierende anderer Fakultäten: None

Inhalt

In recent years, there has been an increasing interest in topics at the intersection of economics and computer science, as witnessed by the continued rapid rise of research areas such as algorithmic game theory and computational social choice. This development is due to the emergence of computational networks such as the Internet as well as the need to get a grip on algorithmic questions in economics. In this seminar, we will deal with both the theoretical foundations as well as their computational properties and possible applications.

Voraussetzungen

Experience in formally proving mathematical statements (standard proof techniques) Basic knowledge of complexity theory is useful (e.g., module IN0011)

Literatur

David C. Parkes and Sven Seuken: "Economics and Computation" (guest key published during overview meeting) Brandt et al.: "Handbook of Computational Social Choice" (freely available as PDF)

Informationen

All students have to apply for the seminar. Further information (including the application procedure) can be found on the course homepage: https://dss.in.tum.de/teaching/ws-21-22/49-teaching/semester/winter-semester-2021-22/256-seminar-on-markets-algorithms-incentives-and-networks-ws21-22.html Please attend the overview meeting if you are interested in participating.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 12
Studierende anderer Fakultäten: None

Inhalt

This seminar is particularly tailored to the students of the Master of "Mathematics in Data Science" in order to offer them 5 ECTS. The seminar explores relevant contributions of mathematics in data science. We consider both theoretical (T) and practical/algorithmic (P) aspects. The topics include “Deep learning” (T+P) “Identification of neural networks 1” “Identification of neural networks 2” “Approximation theory” of neural networks (T) ”Reinforcement Learning” (T+P) “Stochastic gradient descent” (T+P) “Optimization for deep learning” (T+P) “Consensus based optimization” (T+P) “Johnson-Lindenstrauss Lemma + Clustering (k-means etc.)” (T+P) “Compressed sensing” (T+P) “Johnson-Lindenstrauss Lemma and Restricted Isometry property” (T) “Learning with kernels and Support Vector Machines” (T+P)

Voraussetzungen

The prerequisite of the seminar are the basics of Linear Algebra, Analysis, Optimization, Probability and the seminar is particularly tailored to student who already attended the course Foundations of Data Analysis

Literatur

The seminar will be based on book chapters and research papers, which are available online: http://www.deeplearningbook.org/ http://www.ems-ph.org/journals/show_pdf.php?issn=0213-2230&vol=10&iss=3&rank=2 https://www.mins.ee.ethz.ch/pubs/files/nn-id-2019.pdf https://arxiv.org/pdf/1804.01592 & https://arxiv.org/pdf/1907.00485 https://arxiv.org/pdf/1901.02220 http://rail.eecs.berkeley.edu/deeprlcourse-fa17/index.html http://papers.nips.cc/paper/5355-stochastic-gradient-descent-weighted-sampling-and-the-randomized-kaczmarz-algorithm.pdf https://arxiv.org/pdf/1912.08957.pdf https://arxiv.org/pdf/1909.09249 https://arxiv.org/pdf/2003.05086 https://arxiv.org/pdf/2001.11988 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.4812&rep=rep1&type=pdf https://arxiv.org/pdf/1408.4045.pdf https://link.springer.com/content/pdf/10.1007/s00365-007-9003-x.pdf https://arxiv.org/pdf/1009.0744.pdf https://stuff.mit.edu/afs/athena/course/9/9.s915/OldFiles/www/classes/dealing_with_data.pdf https://www.cs.utah.edu/~piyush/teaching/learning-with-kernels.pdf

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 7
Studierende anderer Fakultäten: None

Inhalt

Can we estimate the time when humanity did leave Africa? Can we obtain, from genetic data only, size and history of a population? Population genetics allows to answer such questions, purely in looking into the signature of mutations. In this seminar, we will start with a review of the basis of population genetics (Kingman coalescent, measures for genetic diversity, site-frequency spectrum) to proceed thereafter to more advanced mathematical models that allow to analyze the evolution of so far neglected biological systems with generation overlap (bacteria, viruses, seeds of plants but also trees or long lived mammals). In the seminar course we aim to discuss the existing literature in this area with the objective of developing better suited mathematical models.

Voraussetzungen

Basic stochastics.

Literatur

Durrett, R. (2008). Probability Models for DNA Sequence Evolution (Springer). Original papers for the more specialized talks.

Informationen

Falls ein Termin Freitags 14:00 möglich wäre, so würden wir das begrüßen.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 8
Studierende anderer Fakultäten: 2

Inhalt

The idea of Mathematical Epidemiology is to understand the spread of diseases, to make forcast about the progression of diseases and to understand possible effects of interventions. In this seminar, we will consider typical model approaches and their analysis in this area. Starting with basic epidemic model, we will include more and more structure behind, also concerning demography. Another important problem are so-called vector-borne diseases (like Malaria) and their treatments. One aspect of the seminar will be also the consideration of data, how to extract important information and how to make reliable predictions. Different mathematical tools may be appropriate and used as modelling approaches, e.g. Ordinary differential equations, Delay differential equations and Partial differential equations, but also some statistical techniques.

Voraussetzungen

Mathematical models in Biology, Knowledge in Ordinary differential equations

Literatur

This seminar will be based on parts of the book “An Introduction to Mathematical Epidemiology” by Maia Martcheva and further original papers in this context dependent on the interests and previous knowledge of the participants.

Informationen

Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. If there are special interests, please contact me as soon as possible. Questions are always welcome, also in advance!

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Master: 2
Studierende anderer Fakultäten: None

Inhalt

Das Seminar soll sich mit der mathematischen Modellierung biologischer Vorgänge im menschlischen Körper befassen. Behandelt werden dabei sowohl zelluläre Prozesse, wie auch die Funktion ganzer Organe. Typischerweise führt dies auf (nichtlineare) Differentialgleichungen, die anschließend durch geeignete Näherungsmethoden oder numerisch gelöst werden können.

Voraussetzungen

Interesse an Biologie, Chemie, mathematischer Modellierung und Differentialgleichungen.

Literatur

James Keener, James Sneyd: Mathematical Physiology, I: Cellular Physiology, Springer Verlag, New York, 2008. James Keener, James Sneyd: Mathematical Physiology, II: Systems Physiology, Springer Verlag, New York, 2008.

Informationen

Voraussichtlicher Termin: Do 14-16 Uhr

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 8
Studierende anderer Fakultäten: None

Inhalt

The seminar will give an introduction to nonlinear methods for statistical inference of cause-effect relationships in multivariate data. The considered methodology builds on structural causal models that not only model stochastic dependencies among the observed variables but also make predictions about the effects of external interventions. In this context, non-linear relationships among the variables may help to reveal detailed causal relations. When applying for participation, please send a TUM grade transcript to david.strieder@tum.de.

Voraussetzungen

Basic statistics and probability + a Master level statistics course.

Literatur

We will consider selected papers from the literature such as: Peters, Jonas; Mooij, Joris M.; Janzing, Dominik; Schölkopf, Bernhard: Causal discovery with continuous additive noise models. J. Mach. Learn. Res. 15 (2014), 2009–2053. Zhang, Kun; Hyvarinen, Aapo: On the Identifiability of the Post-Nonlinear Causal Model. https://arxiv.org/abs/1205.2599 Zhang, Kun; Hyvärinen, Aapo: Nonlinear functional causal models for distinguishing cause from effect. Statistics and causality, 185–201, Wiley Ser. Probab. Stat., Wiley, Hoboken, NJ, 2016. 62J02 (62A01 62B10) Bühlmann, Peter; Peters, Jonas; Ernest, Jan: CAM: causal additive models, high-dimensional order search and penalized regression. Ann. Statist. 42 (2014), no. 6, 2526–2556. Rothenhäusler, Dominik; Ernest, Jan; Bühlmann, Peter Causal: inference in partially linear structural equation models. Ann. Statist. 46 (2018), no. 6A, 2904–2938. 62G99 (62H99 68T99) Agrawal, Raj; Squires, Chandler; Prasad, Neha; Uhler, Caroline: The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables. https://arxiv.org/abs/2102.07921

Informationen

Preliminary meeting in September 2021.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 8
Studierende anderer Fakultäten: None

Inhalt

In this seminar we discuss both theoretical issues and numerical analysis for carefully chosen optimal control problems with PDEs. The topics are based on current research literature and can build a basis for master theses.

Voraussetzungen

Numerical Methods for PDEs

Literatur

to be announced

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 5
Studierende anderer Fakultäten: None

Inhalt

tba

Voraussetzungen

tba

Literatur

http://www.hairer.org/notes/RoughPaths.pdf https://arxiv.org/pdf/1603.03788.pdf https://arxiv.org/abs/1810.10971 https://arxiv.org/abs/2005.08897 https://arxiv.org/pdf/1905.08494.pdf more literature will be added at a later time

Informationen

Sprache

deutsch

Anzahl an Plätzen

Master: 4
Studierende anderer Fakultäten: None

Inhalt

Topologische Räume Stetigkeit Zusammenhang Kompaktheit Dimension Metrisierbarkeitssätze Polnische Räume Themen der deskriptiven Mengenlehre (Borel-Mengen, projektive Mengen, Determiniertheit) Topological Spaces Continuity Connected Spaces Compact Spaces Dimension Metrization Theorems Polish Spaces Selected Topics in Descriptive Set Theory (Borel sets, projective sets, Determinacy)

Voraussetzungen

Mathematische Grundvorlesungen

Literatur

Sieradski: Topology and Homotopy Dugundji: Topology Kechris: Classical Descriptive Set Theory

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Master: 4
Studierende anderer Fakultäten: None

Inhalt

Random graphs are used as probabilistic models for complex networks. In the seminar we want to study several well know random graph models including the Erdös-Renyi random graph and the preferential attachment model. In particular, we will study the phase transition for the Erdös-Renyi random graph. During the seminar, we will learn important tools in the study of stochastic processes including couplings, stochastic order, probabilistic bounds and branching processes.

Voraussetzungen

Einführung in die Wahrscheinlichkeitstheorie und Statistik (MA0009) oder Einführung in die Wahrscheinlichkeitstheorie MA1401

Literatur

R. van der Hofstad. Random Graphs and Complex Networks. Volume 1. Cambridge Series in Statistical and Probabilistic Mathematics (2017)

Informationen

https://www-m5.ma.tum.de/Allgemeines/MA6011_2021W Es wird eine Vorbesprechung über Zoom stattfinden, bei der die Vortragsthemen verteilt werden.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

deutsch

Anzahl an Plätzen

Master: 6
Studierende anderer Fakultäten: None

Inhalt

Das Seminar ist ein gemeinsamer Lektüre- und Diskussionskurs des Buches "Algorithms from the Book" von Kenneth Lange (SIAM, 2020). Es beschäftigt sich mit berühmten und erfolgreichen Algorithmen und ihren mathematischen Grundlagen. Kenneth Lange arbeitet derzeit an einer Neuauflage des Buches. Wir werden neue Kapitel zur preview benutzen dürfen.

Voraussetzungen

Solide Kenntnisse in Analysis, linearer Algebra und Numerik.

Literatur

Algorithms from the Book von Kenneth Lange, SIAM, 2020. Über die Bibliothek können Sie auf eine digitale Version des Buchs im Volltext zugreifen

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 20
Studierende anderer Fakultäten: None

Inhalt

The seminar will cover advanced topics in deep learning from interpretable deep learning, over uncertainty quantification, to disentangled generative or physics informed models. You should be familiar with feed-forward, convolutional, and recurrent neural networks, as well as know how to train them. You can read up on these topics at https://www.deeplearningbook.org/. • Chapter 6: Deep Feedforward Networks • Chapter 8: Optimization for Training Deep Models • Chapter 9: Convolutional Networks • Chapter 10: Sequence Modeling: Recurrent and Recursive Nets

Voraussetzungen

Basic maths, basic deep learning

Literatur

The material discussed in the seminar is based on research papers assigned to each student and a following literature review.

Informationen

The seminar will be held as a block over the course of two days (date TBA) at the Institute of Computational Biology, Helmholtz Zentrum München.

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 5
Studierende anderer Fakultäten: 2

Inhalt

Functional inequalities provide a method to compare functions to each other in view of certain features. How symmetric is a function under certain operations? How wiggly is it? How close is it to a given set functions? Such questions play an important role in mathematical physics, differential geometry, PDE analysis and many more fields, and functional inequalities give an answer in terms of robust integral expression. In this seminar, we shall encounter several well-known functional inequalities, like rearrangement, Hardy-Littlewood-Sobolev, logarithmic Sobolev and Hausdorff-Young inequalities. The proofs will provide information on the optimal constants and the optimizers, which achieve equality. In each case, the method of proof rests on some deep insight and has an inherent beauty. Applications, for instance to the estimate on the rates of equilibration in particle systems or to bound the Ricci curvature of manifolds, will be discussed depending on the interest of the participants.

Voraussetzungen

Analysis, LADS and Maßtheorie are a must. Basic knowledge in functional analysis and/or PDEs is helpful for some topics, but is not at all necessary to enjoy the seminar.

Literatur

For the specific functional inequalities mentioned above, we follow E.Lieb und M.Loss: "Analysis" (GSM 14, AMS). For further inequalities and the mentioned applications, additional material will be provided.

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 5
Studierende anderer Fakultäten: None

Inhalt

Chains of infinite order, first introduced by Doblin and Fortet in 1937, are the generalization of k-step Markov chains when the parameter k approaches infinity. The study of those chains is of significance in a variety of fields, such as Probability Theory, Statistical Mechanics and Ergodic Theory. For further information, please visit the seminar's website https://www-m5.ma.tum.de/Allgemeines/CIO_2021W

Voraussetzungen

Introduction to Probability and Statistics, Markov Chains, Measure Theory

Literatur

We will read several old and new papers together. Please visit the website of the seminar https://www-m5.ma.tum.de/Allgemeines/CIO_2021W for a list of those papers.

Informationen

Sprache

englisch

Anzahl an Plätzen

Master: 7
Studierende anderer Fakultäten: None

Inhalt

Linear algebraic groups are an important class of groups that come with the structure of an algebraic variety. Examples include the general linear group, the special linear group or the orthogonal group over a field. In this seminar, we will develop the foundations of the theory of linear algebraic groups. We will discuss the basic definitions, important subgroups such as tori and Borel subgroups, the relationship between a linear algebraic group and its Lie algebra, as well as the root datum of a linear algebraic group. The endpoint of the seminar will be a discussion of the classification of reductive groups. The most important tools for our course come from linear algebra and algebraic geometry. The necessary prerequisites from algebraic geometry will be explained in the seminar, with the level of detail depending on the participants' backgrounds. The theory of linear algebraic groups has a number of applications in algebraic geometry, finite group theory and many other subjects. Moreover, while the foundations are well-understood and accessible, open questions related to linear algebraic groups are ubiquitous in modern mathematical research.

Voraussetzungen

Commutative Algebra within the scope of Algebra 2 Experience with algebraic geometry is very helpful, but not required

Literatur

T.A. Springer . Linear Algebraic Groups J.E. Humphreys. Linear Algebraic Groups R. Carter, G. Segal, I. Macdonald. Lectures on Lie Groups and Lie Algebras

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 5
Studierende anderer Fakultäten: 5

Inhalt

Machine learning and uncertainty quantification (UQ) are ubiquitous in modern science and engineering applications. In the last two decades, UQ for complex physical processes has been developed rapidly with focus on grid-based process models such as finite element models which are well established in engineering applications. On the other hand, machine learning techniques have not traditionally been applied to physics-based models. The recent surge in data-driven models based on machine learning techniques such as deep learning is changing the computational science and engineering landscape. Novel hybrid models based on neural networks are emerging and are already enhancing traditional methods. In this seminar we discuss theoretical and computational aspects that arise from combining PDE-based models and neural networks, in particular, physics-informed neural networks (PINNs), neural networks for PDE approximation, and applications in UQ and turbulence models.

Voraussetzungen

Advanced topics in Machine Learning, Statistics, and Numerics of PDEs are covered thus we require a basic knowledge in these areas, e.g. the courses MA1401, MA3303, IN2346. Ideally, participants have prior knowledge covered in the following courses: Numerical methods for Uncertainty Quantification (MA5348) Physics-based Machine Learning (MW2450)

Literatur

The material discussed in the seminar is based on recent research papers. Examples are: Physics-informed Deep Learning for Scientific Computing https://arxiv.org/abs/2103.09655 Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review https://arxiv.org/abs/2102.11802 The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems https://link.springer.com/article/10.1007/s40304-018-0127-z Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control https://arxiv.org/abs/2105.14094 Efficient training of physics‐informed neural networks via importance sampling https://onlinelibrary.wiley.com/doi/abs/10.1111/mice.12685 A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models. https://arxiv.org/abs/1910.01547 Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo https://arxiv.org/abs/2008.01604 Data-driven discovery of coordinates and governing equations https://arxiv.org/abs/1904.02107 Towards physics-informed deep learning for turbulent flow prediction https://arxiv.org/abs/1911.08655 VAMPnets for deep learning of molecular kinetics https://arxiv.org/abs/1710.06012 SchNet: A continuous-filter convolutional neural network for modeling quantum interactions https://arxiv.org/abs/1706.08566 Clebsch–Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network https://arxiv.org/abs/1806.09231

Informationen

Die 5 Export-Plätze sind für Studierende der Fakultät Maschinenwesen/Mechanical Engineering

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 15
Studierende anderer Fakultäten: None

Inhalt

Computational pathology encompasses algorithms and methods that address​ scientific and clinical questions in pathology. In the few last years,​ traditional analyses are challenged with deep learning methods that​ allow for more standardised, robust and powerful applications. In this​ seminar, we will study recent research papers that develop or apply​ deep learning methods in a pathology context. Whenever possible, we​ will re-implement the applied methods, analyse the used technologies​ and discuss the biomedical and clinical implications. After successful completion of the module, the students will be able​ to read and evaluate scientific literature on computational pathology,​ and they have learned how to extract computational content and​ re-implement parts of the analysis. Finally, the course will​ strengthen the presentation and discussion skills of the participants.

Voraussetzungen

Fundamentals in linear algebra and statistics, basic software knowledge in a higher-level programming language (such as Matlab, R, Python, etc), interest in biological issues.

Literatur

• van der Laak, J., Litjens, G., and Ciompi, F. (2021). Deep learning in histopathology: the path to the clinic. Nat. Med. 27, 775–784. • Fuchs, T.J., and Buhmann, J.M. (2011). Computational pathology: challenges and promises for tissue analysis. Comput. Med. Imaging Graph. 35, 515–530.

Informationen

Dieses Seminar ist für Studierende der TUM School of Education geeignet.

Sprache

englisch

Anzahl an Plätzen

Master: 14
Studierende anderer Fakultäten: None

Inhalt

This seminar is based on the book “An introduction to infinite-dimensional analysis” by Guiseppe da Prato (Springer, 2006). We will discuss stochastic concepts such as Gaussian measures in Hilbert spaces, Brownian motion and gradient systems. The topic brings together concepts from analysis, probability and statistical mechanics, such as Markov semigroups, stochastic dynamical systems and invariant measures. The book is pedagogical, but a background in functional analysis, measure theory and probability is advantageous. Concepts such as integration in Banach spaces will be introduced as required.

Voraussetzungen

The book is pedagogical, but a background in functional analysis, measure theory and probability is advantageous.

Literatur

Guiseppe da Prato, An introduction to infinite-dimensional analysis, Springer 2006

Informationen