Seminars and workshops

Dates for seminars and workshops in the summer semester 2021

Kalender blau: Grafik: Kathrin Ruf

Registration for seminars and workshops for the summer semester 2021 will take place via the matching system again. 

Seminars that are suitable for students of the TUM School of Education contain a corresponding note in the seminar description.

20 January 2021: Program announced for summer semester 2021

25 January (10:00) - 31 January 2021: Students register using the matching system

2 February - 7 February 2021: Lecturer's selection round

23 February 2021: results are available in the matching system

 

How are seminar places allocated?

The allocation of places in the workshops and seminars takes place in two stages:
 

You register using the matching system during the current semester for one of the seminars or one of the workshops offered in the following semester. The supervising tutors make a selection from the list of applicants. In the matching system you can see in which seminar you have been allocated a place. Shortly before the start of the semester you will be registered for the exam and can then see the registration in TUMonline under your "registered examinations".

If you were not allocated a place in the matching or if you would like to take part in a second seminar, please ask the respective lecturers of a seminar with remaining places, if you may take part. If they agree please email bachelor (at) ma.tum.de or master (at) ma.tum.de and cc the seminar’s lecturer to be registered for the Bachelor's or Master's seminar.

Presenting Math: Workshops for Bachelor students

Workshops are offered on selected mathematical topics. Each participant presents her or his topic to the others in a short lecture, followed by group discussion. Regular participation in the workshop is therefore required.

Due to organizational reasons, there is only a restricted number of places available for registration. Please choose other topics, if necessary. 

Students of other departments may only register for available places after the second selection round. In order to do so, please submit an informal application to bachelor (at) ma.tum.de.

Dates

The workshops, including the lectures, take place in the first week of classes during the summer semester.

Recommended requirements:

Analysis 1 and Linear Algebra 1

Workshops offered in the summer semester 2021

Language

deutsch

Number of places

Bachelor: 13
Persons from other faculties: None

Content

Wann und wie konvergiert das Newton-Verfahren? Dieser Frage werden wir in diesem Workshop auf den Grund gehen - und dabei so manch andere spannende Entdeckung machen: Wie bringt man Ordnung ins Chaos? Was hat es mit dem Apfelmännchen auf sich? Anhand der Buches von Robert Devaney begeben wir uns auf einen Streifzug durch die Theorie und Praxis der dynamischen Systeme.

Requirements

Spaß an Computerexperimenten

Literature

Devaney, R.L. (2020). A First Course in Chaotic Dynamical Systems: Theory and Experiment (2nd ed.). CRC Press. https://doi.org/10.1201/9780429280665, https://ebookcentral.proquest.com/lib/munchentech/detail.action?docID=6182018

Informations

Sie erarbeiten in Einzelarbeit und Gesprächen mit mir bis Anfang April einen ca. 30 minütigen Vortrag über ein Kapitel (5-17) des Buches, den Sie in der ersten Vorlesungswoche des Sommersemesters vortragen. Eine Vorbesprechung findet in der letzten Vorlesungswoche Mitte Februar statt.

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

In diesem Workshop beschäftigen wir uns mit Diskreten Dynamischen Systemen. Wir lernen einige grundlegende Begriffe und Eigenschaften kennen. Besonders spannend ist z.B. das mögliche chaotische Verhalten. Darüber hinaus sollen diese theoretischen Erkenntnisse auf Probleme aus den Lebenswissenschaften angewandt werden. Bei einigen Themen können auch eigene Simulationen erstellt werden.

Requirements

(Kenntnisse des erstes Semesters des Mathe-Studiums)

Literature

R.L. Devaney: A First Course in Chaotic Dynamical Systems R.A. Holmgren: A First Course in Discrete Dynamical Systems F. Adler: Modeling the Dynamics of Life

Informations

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Es sollen interessante Ergebnisse aus der diskreten Mathematik besprochen werden. Zu den Themen gehören Färbungen, Kombinatorik, Graphentheorie, Netzwerke und Fehlererkennung.

Requirements

Analysis 1 (MA0001) und Lineare Algebra 1 (MA0004)

Literature

A. Beutelspacher und M.-A. Zschiegner. Diskrete Mathematik für Einsteiger. Springer, 5. Auflage, 2014.

Informations

Siehe https://www-m5.ma.tum.de/Allgemeines/MA0006_2021S Es wird eine Vorbesprechung mit Themenvergabe über Zoom stattfinden.

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Die Topologie untersucht Mengen mit einer (anschaulichen oder abstrakten) geometrischen Struktur und stetige Abbildungen zwischen diesen sogennanten topologischen Räumen. Zu ihren Grundbegriffen zählen neben der Stetigkeit: Offene und abgeschlossene Mengen, Umgebungen, Zusammenhang, Kompaktheit, Konvergenz, Metrisierbarkeit. Ziel des Workshops ist eine Einführung in dieses moderne und grundlegende Teilgebiet der Mathematik. Die Teilnehmerinnen und Teilnehmer stellen anhand von ausführlicher Lehrbuchliteraur ausgewählte Themen in kurzen Vorträgen vor und beteiligen sich an der sich ergebenden Diskussion. Die Vorträge werden auf Deutsch (alternativ Englisch) gehalten, wobei ein Kontakt mit der englischsprachigen Literatur angestrebt wird. Die Inhalte des Workshops unterstützen die Grundvorlesungen zur Analysis und Linearen Algebra. Vor allem in Form von metrischen Räumen spielen topologische Begriffe und Denkweisen dort an vielen Stellen eine wichtige Rolle.

Requirements

Mathematische Grundvorlesungen zur Analysis und Linearen Algebra

Literature

A. Sieradski: An Introduction to Topology and Homotopy O. Deiser: Analysis 2 Die Literatur wird den Teilnehmern digital zur Verfügung gestellt.

Informations

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Wir werden uns mit einigen Schmankerl der Geometrie befassen. Einige mögliche Themen sind: Knoteninvarianten, Zöpfe und die Zopfgruppe, Eulersche Polyederformel, regelmäßige und Penrose Parkettierungen, Bandornamente (oder Friese), Triangulierungen von Flächen Knoten und Kettenbrüche

Requirements

Sie müssen wissen, was eine Gruppe ist und etwas geometrisches Anschauungsvermögen mitbringen.

Literature

C. Adams, The knot book Coxeter-Rigby, Frieze patterns, triangulated polygons, and dichromatic symmetry Weitere Literatur finden Sie auf der Webseite https://www.groups.ma.tum.de/algebra/scheimbauer/

Informations

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Wer gerne Rätsel löst, ist dabei wohl auch schon einmal über Löwen, Springer oder Zwerge gestolpert. Schließlich bedienen sich viele Knobeleien gerne derartiger Protagonisten, um die Aufgabe anschaulich und allgemein verständlich darzustellen. Aber was macht ein interessantes Rätsel aus? Besonders fesselnd sind diejenigen, die trotz ihrer Kürze den Denker dazu zwingen, einen neuen Blickwinkel einzunehmen. Lässt er sich darauf ein, wartet oft eine überraschend elegante Lösung als Belohnung. In diesem Workshop kommt der Knobelspaß nicht zu kurz! Wir werden eine Auswahl schöner Rätsel mit eleganten Lösungen und die zugrunde liegenden mathematischen Methoden diskutieren.

Requirements

* Analysis 1 * Lineare Algebra und Diskrete Strukturen 1

Literature

* Mathematical Puzzles: A Connoisseur's Collection, Peter Winkler * The Art of Mathematics -- Coffee Time in Memphis, Béla Bollobás * Das Buch der Beweise, Martin Aigner und Günter M. Ziegler

Informations

Die Vorträge sind an zwei Tagen in der ersten Vorlesungswoche (12. bis 16. April).

Language

deutsch

Number of places

Bachelor: 15
Persons from other faculties: None

Content

Wir werden uns mit verschiedenen Fragen rund um das Thema Zahlen beschäftigen, und dabei viele interessante Beispiele von Mengen von Zahlen kennenlernen. Dabei wird gezeigt, wie sich die verschiedenen Rechenbereiche mathematisch konstruieren lassen. Ein weiteres Ziel ist, Erfahrung im Vorbereiten und Halten eines Seminarvortrags zu sammeln.

Requirements

Lineare Algebra 1, Analysis 1

Literature

H.-D. Ebbinghaus et. al., Zahlen, 2. Auflage, Springer, 1988. A. Schmidt, Einführung in die algebraische Zahlentheorie, Springer, 2007

Informations

Abhaltung nach aller Voraussicht über Zoom. Bei Bedarf kann der Workshop gedoppelt werden.

Language

deutsch

Number of places

Bachelor: 8
Persons from other faculties: None

Content

In diesem Workshop behandeln wir kleine und große, antike und neue, reine und angewandte "offene" Probleme der Mathematik - aus Analysis, Algebra, Topologie, Zahlentheorie, der theoretischen Informatik u.a. Feldern. Alle diskutierten Probleme haben gemeinsam, dass man sie recht schnell verstehen kann - aber scheinbar nicht so einfach lösen ...

Requirements

Analysis 1&2, Lineare Algebra 1&2

Literature

Wird in Form von Onlinematerial (themenspezifische Artikel) nach Anmeldung bekannt gegeben.

Informations

Der Workshop wird als Blockveranstaltung zu Beginn des Semesters abgehalten.

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Das Buch der Beweise von Aigner und Ziegler ist ein mathematischer Klassiker. Es enthält einige der schönsten und elegantesten Beweise aus gewählter Sätze der elementaren Algebra, Analysis und Zahlentheorie. Im Seminar sollen einige der Beweise aus dem Buch vorgestellt werden. Ziel ist es, anhand dieser Beweise und Aussagen zu lernen, wie man Mathematik auch in kurzen Vorträgen vorstellen kann.

Requirements

Analysis 1 & Lineare Algebra 1

Literature

M.Aigner und G.M.Ziegler: Das Buch der Beweise, Springer 2010 ( 3.Auflage )

Informations

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Wir werden in unserem Workshop Quaternionen behandeln. Als Grundlage sollen (hauptsächlich) die entsprechenden Kapitel (7. und Teile von 8 und 9) aus dem Buch ​ "Zahlen" von Ebbinghaus et al, Springer 1992. dienen.​ ​ Die Quaternionen sind eine von Hamilton eingeführte "Erweiterung" komplexen Zahlen; modern gesprochen eine 4-dim. reelle Divisionsalgebra.​ Sie haben sich als ausgesprochen nützlich zur Beschreibung von 3-dim Geometrie herausgestellt, was vor allem daran liegt, dass sich das normale Skalarprodukt, das Kreuzprodukt und Drehungen im R^3 alle elegant mit quaternionischer Multiplikation darstellen lassen.​ ​ Mögliche Vortragsthemen wären z.B.​ * Quaternionen als Verallgemeinerung der komplexen Zahlen​ * Oktonen als Verallgemeinerung der Quaternionen​ * Quaternionen und Rotationen in R^3 und R^4​ * Eulerwinkel, SLERP und Interpolation von Drehungen​ * ...

Requirements

LADS1, Analysis1

Literature

Ebbinghaus et al.​ "Zahlen"​ Springer 1992

Informations

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Im Workshop "Die Mathematik hinter Spielen und Puzzles" lernen und erforschen Sie die mathematische und rechnerische Modellierung von Spielen und Puzzles. Einige Puzzles, die wir studieren werden, sind Schiebepuzzles, farbige Würfel und Puzzles zum Zerlegen und Zusammensetzen. Die Mathematik hinter den Spielen und Puzzles umfaßt Themen aus der Kombinatorik, diskrete Konfigurationsräume, diskrete Geometrie, algorithmisches Denken, diskrete Wahrscheinlichkeitstheorie, kombinatorische Spieltheorie und mehr.

Requirements

Analysis 1, Lineare Algebra 1

Literature

Verschiedene Bücher und Artikel über Unterhaltungsmathematik und verwandte Themen.

Informations

This seminar is suitable for students of the TUM School of Education.

Language

deutsch

Number of places

Bachelor: 8
Persons from other faculties: None

Content

Während die meisten mathematischen Zaubertricks relativ leicht zu durchschauen sind, diskutieren wir in diesem Workshop über die mathematischen Hintergründe von Tricks, deren Resultat trotz Kenntnis des Vorgehens erstaunlich oder zumindest nur schwer nachvollziehbar ist. Hierbei erhält man Einblick in eine Vielzahl mathematisch anspruchsvoller Themengebiete wie Kombinatorik, Stochastik, Graphen-, Gruppen- und Kodierungstheorie.

Requirements

Vorlesungen des 1. Semesters

Literature

Ehrhard Behrends: Mathematik und Zaubern: Ein Einstieg für Mathematiker, Springer 2017 (https://link-springer-com.eaccess.ub.tum.de/book/10.1007/978-3-658-17505-4)

Informations

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Wir betrachten kleine mathematische Ergebnisse mit überraschenden, elementaren Beweisen. Die Aufgaben können mit Hilfe der Linearen Algebra formuliert und mit grundlegenden Beweistechniken gelöst werden. Dabei erhalten wir einen ersten Einblick in die Themenbereiche Geometrie, Graphentheorie und Kombinatorik.

Requirements

* Analysis 1 * Lineare Algebra und Diskrete Strukturen 1

Literature

* Thirty-three Miniatures (Matousek, 2010) * Diskrete Mathematik: Eine Entdeckungsreise (Matousek & Nesetril, 2007)

Informations

Die Vorträge finden an zwei Tagen in der ersten Vorlesungswoche (12. bis 16. April) statt.

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Ziel des Workshops ist eine Einführung zu "erzeugenden Funktionen". Die Idee ist dabei, interessierende Zahlenfolgen als Koeffizienten einer Potenzreihe (also einer Reihe, deren Summanden wie bei Exponential- und Sinusreihe die Form a_k x^k haben, engl. "power series") aufzufassen und sich mit dieser Potenzreihe zu beschäftigen. So können analytische und vor allem auch algebraische Methoden eingesetzt werden, um Aussagen über Eigenschaften der Folgenglieder (z.B. Rekursionsformel oder explizite Darstellung, asymptotisches Verhalten, Identitäten mit anderen Folgen) zu beweisen. --- Zu Anwendungsfeldern der Methode zählen so unterschiedliche Gebiete wie Kombinatorik, Differenzengleichungen und Wahrscheinlichkeitsrechnung; die Vortragsthemen stellen eine Auswahl typischer Beispiele vor.

Requirements

Lineare Algebra 1 und Analysis 1

Literature

H.S. Wilf: generatingfunctionology; mit Ergänzungen aus anderen Quellen

Informations

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Das Buch der Beweise ist ein Buch der Mathematiker Martin Aigner und Günter M. Ziegler und stellt eine Sammlung besonders eleganter mathematischer Beweise zu klassischen mathematischen Problemen dar. Die Idee zu so einem Buch stammt von Paul Erdös (1913-1996), einem charismatischen ungarischen Mathematiker. Im Workshop werden exemplarisch Beweise aus diesem Buch behandelt. Ziel ist es, verschiedene Beweisprinzipien kennenzulernen.

Requirements

Analysis und algebraische Grundkenntnisse. Im Vorwort des Buches ist zu lesen: "... dass wir für die Lektüre nicht mehr Mathematik voraussetzen wollten, als man im Grundstudium lernt. Ein bisschen Lineare Algebra, ein bisschen Analysis und Zahlentheorie, und ein gerüttelt Maß elementarer Konzepte und Ideen aus der Diskreten Mathematik sollten ausreichen, um alles in diesem Buch zu verstehen und zu genießen."

Literature

Martin Aigner und Günter M. Ziegler, Das BUCH der Beweise, Springer, 2010.

Informations

Termine und Art der Veranstaltung (Präsenz- oder Online-Veranstaltung) müsstesen erst noch festgelegt werden.

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Dieser Workshop wird besonders elegante Beweise aus verschiedenen Teilgebieten der Mathematik diskutieren. Als Grundlage dient das "Das BUCH der Beweise'' von M. Aigner und G.M. Ziegler.

Requirements

Grundkenntnisse Analysis, Lineare Algebra, Diskrete Strukturen

Literature

M. Aigner und G. M. Ziegler, "Das Buch der Beweise", Springer, 3. Auflage, 2010.

Informations

siehe https://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

Seminars for Bachelor's students

For each seminar offered to Bachelor's and Master’s students, there is a separate registration process in the matching system. Please only register for seminars labeled "Bachelor". Places in the seminars labeled "Master" are reserved for Master’s students who are already enrolled in these degree programs.

After the selection round, you can register for available places in the Master’s advanced seminars. Please contact the respective seminar lecturer to apply for one of the remaining places. If he/she agrees, please send an email to master (at) ma.tum.de and cc the seminar's lecturer to be registered for the Master's seminar.

Bachelor's seminars offered in the summer semester 2021

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 1
Persons from other faculties: None

Content

In recent years, there has been an increasing interest in topics at the intersection of economics and computer science, as witnessed by the 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. The emphasis in this seminar lies on the independent study of classic economics papers as well as more recent papers from computer science. Among the topics to be covered are matching theory, mechanism design, and voting theory.

Requirements

It is expected that participants are experienced in formally proving mathematical statements and are familiar with standard proof techniques. Ideally, the participants completed at least one of the courses "Computational Social Choice" or "Algorithmic Game Theory." Additionally, basic knowledge of complexity theory is useful (e.g., module IN0011).

Literature

See course homepage (http://dss.in.tum.de/teaching) and get the password in the seminar overview meeting.

Informations

Registration is only possible through the lecturers and by application only. The seminar overview / presentation ("Vorbesprechung") is mandatory; see the homepage (http://dss.in.tum.de/teaching) for more information.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 6
Persons from other faculties: None

Content

Graph theory is full of beautiful results that have strong interactions with combinatorics and important applications in optimization and computer science. We will cover some fundamental results that build upon the basics you have learned about graphs in your introductory courses (such as "Diskrete Strukturen", "Algorithmische Diskrete Mathematik"). For example, we will learn which graphs can be drawn in the plane without any crossings, how to find such a drawing using linear algebra, and what this has to do with coloring a map of countries with few colors. For a better overview, consider keywords like perfect graphs, Kuratowski's theorem, Tutte embedding, Hadwiger's conjecture, Turan's theorem, Ramsey's theorem, or the Tutte-Berge formula.

Requirements

You should be familiar with basic notions about graphs (undirected graphs, directed graphs, paths, cycles, spanning trees, matchings).

Literature

Reinhard Diestel - Graph Theory + some extra material

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 5
Persons from other faculties: 2

Content

Quantum mechanics describes the laws of nature in the microcosm. This seminar will give an introduction for mathematicians into the basic concepts and notions of quantum mechanics such as states, observables and channels as well as entanglement or correlation inequalities. We will explore the mathematical results and theorems at the foundations of the field.

Requirements

Basic coarses in analysis and linear algebra as well as elementary Hilbert space techniques are assumed. A first coarse in functional analysis is helpful but not necessary for all of the talks.

Literature

T. Heinosaari, M. Ziman, “Guide to Mathematical Concepts of Quantum Theory,” Acta Physica Solvaca, vol. 58, pp. 487–674, 2008 + mathematical textbooks and original literatur to selected chapters

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 2
Persons from other faculties: 2

Content

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. 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.

Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

Literature

Maia Martcheva: An Introduction to Mathematical Epidemiology, Springer 2015 (available as ebook in the TUM library)

Informations

Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. Questions are always welcome!

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 5
Persons from other faculties: None

Content

This seminar will treat Boolean functions and their analytical properties. Boolean functions are among the most basic objects in theoretical computer science. We will discuss foundational results as well as several applications ranging from problems in social choice, cryptography, learning theory, property testing, to hardness of approximation results.

Requirements

Participants should have completed the introductory lectures Analysis 1+2, Lineare Algebra und Diskrete Strukturen 1+2. They should have a solid understanding of basic probability theory and a keen interest in applications of mathematical concepts to computer science.

Literature

Primarily R. O'Donnell, Analysis of Boolean Functions, Cambridge University Press, 2014. Further references will be provided.

Informations

This will be offered as a block seminar at the beginning of the term.

This seminar is suitable for students of the TUM School of Education.

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Die Diskrete Differentialgeometrie befasst sich mit der Entwicklung diskreter Analoga von Begriffen und Methoden der klassischen Differentialgeometrie. Sie findet Anwendungen in Computergraphik, Architektur, theoretischer Physik und Numerik. In dem Seminar soll dieses Spektrum anhand ausgewählter klassischer und moderner Artikel ausgeleuchtet werden.

Requirements

Kenntnisse in Geometrie und Differentialgeometrie. ​

Literature

einige Artikel, die die Breite der mögliche Themen zeigen sind beispielsweise:​ - "The discrete quantum pendulum", A. Bobenko, N. Kutz, U. Pinkall ​ - "Discrete Elastic Rods", Miklos Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, Eitan Grinspun​ - "Discrete Surfaces with Constant Negative Gaussian Curvature and the Hirota Equation", A.I. Bobenko, U. Pinkall​ - "Oriented mixed area and discrete minimal surfaces", C. Müller, J. Wallner​ - Kapitel aus dem Buch "Discrete Differential Geometry: Integrable Structure", Bobenko und Suris, Graduate Studies in Mathematics, Vol. 98, AMS, 2008

Informations

This seminar is suitable for students of the TUM School of Education.

Language

deutsch

Number of places

Bachelor: 5
Persons from other faculties: None

Content

Im Mittelpunkt des Seminars soll die qualitative und geometrische Theorie nichtlinearer gewöhnlicher Differentialgleichungen stehen. Hierzu werden wir uns zunächst mit der Analysis auf Mannigfaltigkeiten beschäftigen. Im Anschluß sollen dann mit Hilfe dieser Methoden verschiedene grundlegende Resultate aus der Theorie dynamischer Systeme bewiesen werden. Einige Höhepunkte werden dabei das Theorem von Hartman-Grobman (nebst Satz über die stabile Mannigfaltigkeit), das Kupka-Smale Theorem, sowie Peixoto's Theorem sein. Bei Interesse können gerne auch weiterführende Themen vergeben werden.

Requirements

Grundvorlesungen Analysis und Lineare Algebra, Gewöhnliche Differentialgleichungen, möglichst auch Nichtlineare Dynamik: Grundlagen

Literature

Jacob Palis und Welington de Melo: Geometric Theory of Dynamical Systems. An Introduction, Springer Verlag Berlin 1982.

Informations

Termin: Donnerstag 14:15-15:45 Die (verpflichtende) Vorbesprechung findet voraussichtlich am Freitag, den 26.2.2021 um 16:15 Uhr online statt.

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: None

Content

In this seminar we study number fields, which are finite extensions of the rational numbers Q. These are of particular interest in arithmetic, since questions on integral solutions of equations can often be solved through an investigation of suitable number fields. A typical example is to ask for a classification of all primes p that are a sum of two perfect squares. Using the ring of Gaussian integers Z[i] in the number field Q(i), the answer can be found without much technical calculations: Either p is 2 or congruent to 1 modulo 4. In the seminar we will introduce invariants of number fields such as the discriminant and the class number, and deduce a formula for the class number of imaginary quadratic number fields.

Requirements

Algebra 1

Literature

Neukirch, Algebraic Number Theory/Algebraische Zahlentheorie, Chapter 1 Yichao Tian, Lecture notes on Algebraic Number Theory

Informations

The seminar will be held by Prof. Eva Viehmann or Dr. Johannes Anschütz (guest professor for the summer term 2021)

This seminar is suitable for students of the TUM School of Education.

Language

deutsch

Number of places

Bachelor: 6
Persons from other faculties: None

Content

We will discuss Markov chains and mixing times. One question of interest is how long it takes until a Markov chain approaches its stationary distribution up to a given error. An application concerns mixing a deck of cards: How long does one need to shuffle a deck of cards?

Requirements

Einführung in die Wahrscheinlichkeitstheorie (MA1401); Markovketten (MA2404) and probability theory (MA2409) are useful.

Literature

David Levin, Yuval Peres and Elizabeth Wilmer: Markov chains and mixing times. Second edition. Link to a pdf version of the book: https://pages.uoregon.edu/dlevin/MARKOV/mcmt2e.pdf

Informations

https://www-m5.ma.tum.de/Allgemeines/MA6011_2021S There will be a first meeting via zoom where every participant can choose a topic for his/her talk. Depending on the participants, the seminar will be in German or English.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 8
Persons from other faculties: None

Content

We will have a closer look at the mathematical foundations of neural networks. Beginning with a general overview of the framework of machine learning, we will compare artificial with biological neural networks, look into their mathematical representations and basic results in approximation theory, learn about their training from the viewpoint of optimization theory and discuss some of their applications.

Requirements

Analysis 1&2, Lineare Algebra 1&2, basic knowledge in statistics/probability theory.

Literature

Will be provided.

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 5
Persons from other faculties: None

Content

Non-pharmaceutical control measures for emerging infectious diseases are central, as at the beginning of an emerging epidemic, no vaccination is available. Non-pharmaceutical control measures are, for example, social distancing, screening, and contact tracing. Contact tracing is particularly challenging to model and to analyze, as that control measure is based on the behavior of single individuals. This observation indicates that simple compartmental models, as often used in mathematical epidemiology, are difficult to formulate. In this seminar, we will review several approaches for the formulation and the analysis of contact tracing.

Requirements

Interest in mathematical biology (MA3601 would be perfect, but is not necessary).

Literature

We will read published papers. An overview over the literature, approaches etc. can be found in the review article here: https://www.sciencedirect.com/science/article/pii/S2468042720301093

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: 4

Content

The use of mathematical modeling and numerical simulation is a rapidly growing field. Numerical simulations can be used to predict groundwater pollution, to understand bacteria growth, to describe earthquake phenomena and to replace destructive experiments in optimal material design or to improve patient specific treatment. Many of these applications are modeled by partial differential equations (PDEs) that can be elliptic, parabolic or hyperbolic, of any order (even fractional), linear or non-linear, stationary or evolutionary in time. For this reason, specific numerical techniques are required to solve these problems. Some of them are, for example, isogeometric analysis, discontinuous Galerkin discretizations, fractional kernel compression or model order reduction schemes. Moreover, highly parallel algorithms are required which exploit the potential of modern supercomputers . The aim of this seminar is to familiarize with advanced modelling concepts and numerical techniques to deal with complex applications. Different topics will be tailored to the individual interests and allow a focus on PDE analysis, applications but also on high performance computing aspects. For more details please see the website: https://www-m2.ma.tum.de/bin/view/Allgemeines/PDESEM21

Requirements

Grundvorlesungen in Numerik insbesondere zu partiellen DGL. Hilfreich für die Theorie Themen sind Kenntnisse in Funktionalanalysis, partiellen DGL und Modellierung.

Literature

Specialized references will be handed out within the first meeting. This is then tailored to the specific topic.

Informations

I first virtual meeting will be held in March where we present different topics in more detail. Students can also specify their personal interest beforehand.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 1
Persons from other faculties: None

Content

As a general principle, in developing mathematical models of real-world time-varying phenomena one distinguishes the set of physical or internal feedback laws (that yield an evolutionary equation) from the environment in which the system lies. The state of the latter is then represented through parameters and is assumed to be unaffected by the system "dynamics". Such parameters in real-world situations and particularly in the life sciences are rarely constant over time. This has various reasons, like absence of lab conditions, adaption processes, seasonal effects on different time scales, or an intrinsic "background noise". Or simply some systems can be decomposed into components so that, provided the influence of some of them is understood, without the requirement to precisely know their explicit form, they can be seen as a non-constant time-varying input for the others. Besides, sometimes it is desirable to include regulation or control strategies into a model (e.g., harvesting and fishing, dosing of drugs or radiation, stimulating chemicals or catalytic submissions), as well as extrinsic noise, and to study their effects. The theory of non-autonomous dynamical systems deals with these questions and with the analysis of the dynamical behaviour of such systems. In this seminar we shall study the fundamental theoretical tools such as the fomalisms of "skew-product flows" and "processes", the specificity of pullback attraction as opposed to forward attraction (which are indistinguishable in autonomous systems), and the notions of exponential dichotomy and dichotomy spectrum. Moreover, we shall unveil the incredible amount of complexity that the presence of time produces by surveying the theory of non-autonomous bifurcations (which can still be considered in its infancy) and the creation of chaotic behaviour. Attention will always be posed in the analysis of concrete models coming from physics or biosciences. In summary, we shall start to discover the universe through the dependence on time and the mathematical universe of time-dependent systems.

Requirements

Analysis 1,2 as well as the lectures on measure and integration as well as a first course in ordinary differential equations.

Literature

Kloeden, Peter E., and Martin Rasmussen. Nonautonomous dynamical systems. No. 176. American Mathematical Soc., 2011. Sell, George R. "Topological dynamics and differential equations." Von Nostrand Reinhold, Princeton, NJ (1971).

Informations

Language

deutsch

Number of places

Bachelor: 8
Persons from other faculties: None

Content

Teilbarkeit, Primzahlen, Kongruenzen, zahlentheoretische Funktionen, Verteilung der Primzahlen, insbesondere Primzahlen in arithmetischen Progressionen und Primzahlsatz, Algorithmen der Zahlentheorie. Im Verlauf des Seminars werden auch zahlreiche offene Probleme über Primzahlen angesprochen werden. Die Zahlentheorie bietet zudem viele Möglichkeiten, eigene Experimente mit dem Computer durchzuführen.

Requirements

Mathematische Grundvorlesungen.

Literature

Forster: Algorithmische Zahlentheorie Hardy/Wright: An Introduction to the Theory of Numbers Nathanson: Elementary Methods in Number Theory Niven/Zuckerman/Montgomery: An Introduction to the Theory of Numbers Deiser: Die Unendlichkeit der Primzahlen

Informations

Die Vorträge können auf Deutsch oder Englisch abgehalten werden. Die Literatur steht überwiegend digital zur Verfügung.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: None

Content

We study various models of random spanning trees and forests of graphs and lattices, in particular the uniform spanning tree and the minimal spanning tree. We will learn the connection of those trees to probabilistic objects such as random walks and percolation. Time permitting we will explore the connection to critical phenomena in statistical physics.

Requirements

Measuren theory, Probability theory.

Literature

Main source: Lyons, Russell, and Yuval Peres. Probability on trees and networks. Vol. 42. Cambridge University Press, 2017.‏ (also available online) We will possibly also read a few relevant papers.

Informations

The seminar will take place in the English language. Based on the corona situation, the seminar might have to take place online.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: 2

Content

This course will cover Alon and Spencer's influential textbook "The Probabilistic Method" on probabilistic methods in combinatorics. Specific topics will include linearity of expectation, the second moment method, correlation inequalities, random graphs, and phase transitions. These methods are useful for studying research problems in stochastic topology.

Requirements

Probability theory (MA2409)

Literature

1) The probabilistic method by Alon and Spencer (4th Ed) 2) A probability path by Sidney I. Resnick

Informations

Advanced seminars for Master's students

Places in the advanced seminars labeled "Master" are generally allocated to Master’s students who are already enrolled in these degree programs!

After the selection round, current Bachelor's students and external Master’s applicants can apply for any remaining places in the Master’s advanced seminars. Please contact the respective seminar lecturer to apply for one of the remaining places. If he/she agrees, please send an email to master (at) ma.tum.de and cc the seminar's lecturer to be registered for the Master's seminar.

 

Important information for students of "Mathematics in Data Science"

The advanced seminar "Mathematics of Data Science" was specially developed for this specific degree program and is worth 5 ECTS. Should you prefer to attend an alternative advanced seminar that is usually worth only 3 ECTS, you must complete an additional requirement to earn 5 ECTS. Further, you should consult your academic advisor, PD Dr. Peter Massopust in advance, to ensure that the seminar is suited to your academic goals. After the seminar, please have the credit recognition form signed by the seminar leader and Mr. Massopust and submit it to the Infopoint of the Department of Mathematics. Credit Recognition - seminar

Masters seminars offered during the summer semester 2021

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 6
Persons from other faculties: None

Content

Graph theory is full of beautiful results that have strong interactions with combinatorics and important applications in optimization and computer science. We will cover some fundamental results that build upon the basics you have learned about graphs in your introductory courses (such as "Diskrete Strukturen", "Algorithmische Diskrete Mathematik"). For example, we will learn which graphs can be drawn in the plane without any crossings, how to find such a drawing using linear algebra, and what this has to do with coloring a map of countries with few colors. For a better overview, consider keywords like perfect graphs, Kuratowski's theorem, Tutte embedding, Hadwiger's conjecture, Turan's theorem, Ramsey's theorem, or the Tutte-Berge formula.

Requirements

You should be familiar with basic notions about graphs (undirected graphs, directed graphs, paths, cycles, spanning trees, matchings).

Literature

Reinhard Diestel - Graph Theory + some extra material

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 4
Persons from other faculties: 2

Content

Quantum mechanics describes the laws of nature in the microcosm. This seminar will give an introduction for mathematicians into the basic concepts and notions of quantum mechanics such as states, observables and channels as well as entanglement or correlation inequalities. We will explore the mathematical results and theorems at the foundations of the field.

Requirements

Basic coarses in analysis and linear algebra as well as elementary Hilbert space techniques are assumed. A first coarse in functional analysis is helpful but not necessary for all of the talks.

Literature

T. Heinosaari, M. Ziman, “Guide to Mathematical Concepts of Quantum Theory,” Acta Physica Solvaca, vol. 58, pp. 487–674, 2008 + mathematical textbooks and original literatur to selected chapters

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 10
Persons from other faculties: 2

Content

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. 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.

Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

Literature

Maia Martcheva: An Introduction to Mathematical Epidemiology, Springer 2015 (available as ebook in the TUM library)

Informations

Further organisation, e.g. choice of preferred topic for the talk etc. will be done after the group of participants is fixed. Questions are always welcome!

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 12
Persons from other faculties: None

Content

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)

Requirements

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

Literature

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

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 6
Persons from other faculties: None

Content

Non-pharmaceutical control measures for emerging infectious diseases are central, as at the beginning of an emerging epidemic, no vaccination is available. Non-pharmaceutical control measures are, for example, social distancing, screening, and contact tracing. Contact tracing is particularly challenging to model and to analyze, as that control measure is based on the behavior of single individuals. This observation indicates that simple compartmental models, as often used in mathematical epidemiology, are difficult to formulate. In this seminar, we will review several approaches for the formulation and the analysis of contact tracing.

Requirements

Interest in mathematical biology (MA3601 would be perfect, but is not necessary).

Literature

We will read published papers. An overview over the literature, approaches etc. can be found in the review article here: https://www.sciencedirect.com/science/article/pii/S2468042720301093

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 4
Persons from other faculties: None

Content

In mathematical finance, stochastic volatility can be modelled in different ways. The present seminar considers two different modelling frameworks based on neural networks and dynamic copulas. Remaining topics of the seminar deal with asymptotic properties of estimators and statistical tools for model validation.

Requirements

MA4405, MA3702

Literature

1) Büchel, P., Kratochwil, M., Nagl, M. and Rösch, D. (2020). Deep calibration of financial models: Turning theory into practice. Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3667070 2) Toulis, P. and Airoldi, E. M. (2017). Asymptotic and finite-sample properties of estimators based on stochastic gradients. Link: https://projecteuclid.org/download/pdfview_1/euclid.aos/1498636871 3) Nasri, B. R, and Remillard, B. N. (2019). Copula-based dynamic models for multivariate time series. Link: https://www.sciencedirect.com/science/article/pii/S0047259X18302008 4) Lee, D., Zhang, K., and Kosorok, M. R. (2021). The binary expansion randomized ensemble test. Link: https://arxiv.org/abs/1912.03662

Informations

The preliminary meeting to the Seminar (Seminarvorbesprechung) will be announced at https://www.groups.ma.tum.de/mathfinance/lehre/sommersemester-2021/

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 8
Persons from other faculties: 4

Content

The use of mathematical modeling and numerical simulation is a rapidly growing field. Numerical simulations can be used to predict groundwater pollution, to understand bacteria growth, to describe earthquake phenomena and to replace destructive experiments in optimal material design or to improve patient specific treatment. Many of these applications are modeled by partial differential equations (PDEs) that can be elliptic, parabolic or hyperbolic, of any order (even fractional), linear or non-linear, stationary or evolutionary in time. For this reason, specific numerical techniques are required to solve these problems. Some of them are, for example, isogeometric analysis, discontinuous Galerkin discretizations, fractional kernel compression or model order reduction schemes. Moreover, highly parallel algorithms are required which exploit the potential of modern supercomputers . The aim of this seminar is to familiarize with advanced modelling concepts and numerical techniques to deal with complex applications. Different topics will be tailored to the individual interests and allow a focus on PDE analysis, applications but also on high performance computing aspects. For more details please see the website: https://www-m2.ma.tum.de/bin/view/Allgemeines/PDESEM21

Requirements

Grundvorlesungen in Numerik insbesondere zu partiellen DGL. Hilfreich für die Theorie Themen sind Kenntnisse in Funktionalanalysis, partiellen DGL und Modellierung.

Literature

Specialized references will be handed out within the first meeting. This is then tailored to the specific topic.

Informations

I first virtual meeting will be held in March where we present different topics in more detail. Students can also specify their personal interest beforehand.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 9
Persons from other faculties: None

Content

This seminar will study and investigate some recent statistical models and methods, which are useful for data analysis. On the modeling side we will look at general regression models and mixture models used for clustering and classification. The methods involve classical and Bayesian approaches. To compare the performance for the different approaches, students have first to agree on an interesting data set from the kaggle or uci data bases. Some suggestions for data sets will be given in links below. The goal of the seminar is to understand the theory of the model and the method and to apply it to a larger data set using R. Since common data sets will be used, the students will learn about the pros and cons of several approaches. Regression approaches: Topic 1: Linear methods for regression: - Tasks: Develop a linear regression model for the chosen regression data set allowing for nonlinear and interaction effects. Perform variable selection and allow for shrinkage methods - General Reference: Chapter 3 of Hastie, Tibshirani, Friedman (2009) Topic 2: Basis Expansions and regularization - Tasks: Introduce splines, GAM models and develop a GAM model for the chosen regression data set - General Reference: Chapter 5 of Hastie, Tibshirani, Friedman (2009) Topic 3: Kernel smoothing methods in regression - Tasks: Introduce kernel density methods useful for regression and apply them for the chosen regression data - General Reference: Chapter 6 of Hastie, Tibshirani, Friedman (2009) Topic 4: Hamilitonian Monte Carlo (HMC) methods for regression models - Tasks: Introduce HMC methods and perform an HMC analysis for the chosen regression data set - General Reference: Stan's User Guide, Part 1, Section 1 and Thomas and Tu (2020) Topic 5: Regression trees and random forests - Tasks: Introduce regression trees and random forests. Develop a first a regression tree model for the chosen regression tree data set and then perform a random forest prediction for the chosen regression data. - General Reference: Section 9.2 and Chapter 15 of Hastie, Tibshirani, Friedman (2009) Topic 6: Boosting methods for regression - Tasks: Introduce boosting methods for regression data and perform a boosting analysis for the chosen regression data set - General Reference: Chapter 10 of Hastie, Tibshirani, Friedman (2009) Model based clustering: Topic 7: Model based clustering using multivariate Gaussian mixture models - Tasks: Introduce Gaussian mixture models and their estimation using the EM algorithm. Use the Gaussian mixture model to cluster the chosen data set - General References: Chapter 1, Section 2.8 and Chapter 3 of McLachlan and Peel (2000) and Fraley and Raftery (2002), McNicholas (2016) Topic 8: Determining the number of components in mixture models - Tasks: Introduce available methods and apply them to the chosen data set. - General Reference: Chapter 6 of McLachlan and Peel (2004) Topic 9: Variables selection methods for Gaussian mixture models - Tasks: Introduce the variable selection methods and apply them to the chosen data set. – General Reference: Fop and Murphy (2018)

Requirements

This seminar is open for Master students only. Prerequisites are GLM and/or Computational statistics. Knowledge in R is assumed.

Literature

Methods references: - Hastie, Tibshirani, Friedmann (2009) The Elements of Statistical Learning Data Mining, Inference, and Prediction (2nd edition) Springer Science+Business Media, LLC 2009, Corrected at 12th printing 2017 - McLachlan and Peel (2004) Finite mixture models. John Wiley & Sons - McNicholas, P. D. (2016). Model-based clustering. Journal of Classification, 33(3), 331-373. - Fraley and Raftery (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American statistical Association, 97(458), 611-631. - Fop and Murphy (2018). Variable selection methods for model-based clustering. Statistics Surveys, 12, 18-65. - Thomas and Tu, W. (2020). Learning Hamiltonian Monte Carlo in R. The American Statistician, 1-28. Software Links: HMC: STAN software and tutorials: stan tutorials: https://mc-stan.org/users/documentation/tutorials stan user guide: https://mc-stan.org/docs/2_25/stan-users-guide/index.html stan package rstanarm: https://cran.r-project.org/web/packages/rstanarm/index.html Regression: Possible regression data sets: - Students performance in exams: This data set consists of 1000 observations. The response would be a score they achieved (math score, reading score or writing score). Some covariates are gender, ethnicity, and parental level of education. To have a continuous covariate, one of the scores can be used as a covariate. (https://www.kaggle.com/spscientist/students-performance-in-exams) - Chocolate Bar Ratings: This data set has 1800 observations. The response would be the rating of the chocolate and some covariates are CompanyLocation, CocoaPercent and BeanLocation. (https://www.kaggle.com/rtatman/chocolate-bar-ratings) - Metro Interstate Traffic Volume: There are 48000 observations in this data set. The response would be traffic_volume and some covariates are temp, snow, and date. Here the effect of time has to be modelled as well. (https://archive.ics.uci.edu/ml/datasets/Metro+Interstate+Traffic+Volume) - Health Insurance costs: This data set has 1338 observations. The response is charges and covariates are age, bmi, sex, children, smoker and region. (https://www.kaggle.com/mariapushkareva/medical-insurance-cost-with-linear-regression) - Burn-out data: The main goal is to predict the burn-out rate of employees in different company type (Service / Product) with other co-variates (Gender, Work from home, ...etc). The training data set has 22750 observations, while the test data set has 12250 observations. (https://www.kaggle.com/blurredmachine/are-your-employees-burning-out?select=train.csv) Possible clustering data sets - Yeast data set: Its dimension is 1484 x 8. It contains 10 classes with diverse sample sizes, i.e., imbalanced data in terms of classes. Thus, the data set is not so easy to classify into 10 classes, and one may need to combine some classes. (https://archive.ics.uci.edu/ml/datasets/Yeast) - Wisconsin breast cancer data set with diagnosis (benign/malignant) and features of the tumors. (https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+(Diagnostic))

Informations

Applications should include a CV, courses passed and two topics the student is most interested. A first online meeting will be arranged in the first week of March. The seminar is online and attendance of all meetings are required for passing the seminar.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 5
Persons from other faculties: None

Content

This seminar will treat Boolean functions and their analytical properties. Boolean functions are among the most basic objects in theoretical computer science. We will discuss foundational results as well as several applications ranging from problems in social choice, cryptography, learning theory, property testing, to hardness of approximation results.

Requirements

Participants should have completed the introductory lectures Analysis 1+2, Lineare Algebra und Diskrete Strukturen 1+2. They should have a solid understanding of basic probability theory and a keen interest in applications of mathematical concepts to computer science.

Literature

Primarily R. O'Donnell, Analysis of Boolean Functions, Cambridge University Press, 2014. Further references will be provided.

Informations

This will be offered as a block seminar at the beginning of the term.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 10
Persons from other faculties: 2

Content

The seminar will be concerned with statistical model selection for graphical causal models. These models represent the joint distribution of a collection of observations in a convenient and accessible form by means of a graph. The models are causal in the sense that they also furnish a model for the joint distribution in settings in which the considered system is subject to external interventions, thus providing a means to predict the effects of such interventions. The seminar participants will present research papers that propose---under different assumptions---methods to learn the graphical structure underlying a graphical causal model. When applying for participation, students should email a TUM grade transcript to mathias.drton@tum.de.

Requirements

Basic Statistics + a Master level statistics course. Ideally, participation in the summer semester course "Graphical models in Statistics".

Literature

We will consider selected papers that were discussed in Drton M, Maathuis MH. 2017. Structure learning in graphical modeling. Annual Review of Statistics and Its Application 4:1, 365-393. Heinze-Deml C, Maathuis MH, and Meinshausen N. 2018. Causal structure learning. Annual Review of Statistics and Its Application 5:1, 371-391. Relevant more recent literature includes papers from machine learning conferences: NeurIPS: https://papers.nips.cc/papers/search?q=causal+learning https://papers.nips.cc/papers/search?q=learning+DAG ICML, AISTATS, UAI: http://proceedings.mlr.press/v119/ https://aistats.org/other.html https://www.auai.org [you may filter/search titles for "causal discovery" or "causal structure"].

Informations

Preliminary meeting in early March 2021 (video conference).

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 7
Persons from other faculties: None

Content

The class FNP (for Function NP) contains all search problems whose decision version is in NP. Such problems, in addition to a “yes/no” answer, ask for a witness in case the answer is “yes.” Evidently, there are search problems whose decision version is always “yes”: computing a mixed Nash equilibrium, computing a pure Nash equilibrium in special games, or computing a consensus-halving, are all problems that have at least one solution. Are these problems as hard as other problems in FNP for which the existence of a solution is not guaranteed? To answer this question, a subclass of FNP called TFNP (for Total Function NP) was defined in 1989. We will study the most well-known subclasses of TFNP, such as PPAD, PPA, PLS, and PPP, and explore many important problems that are complete for some of these classes. These problems come from algorithmic game theory, fairness, local optimization, or cryptography.

Requirements

Basic knowledge of computational complexity

Literature

Original research articles

Informations

Participants will be assigned research papers and are expected to deliver a presentation, demonstrating in-depth understanding of the discussed problem, key technical ideas and proofs, related bibliography, and open questions.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 6
Persons from other faculties: None

Content

Our globalised society currently faces several important challenges: The SARS-CoV-2 pandemic, climate change, social inequality -- to name just a few. Many of these are inherently of dynamical nature and so tools and ideas from the theory of Dynamical Systems are crucial for a thorough understanding. Within this seminar, we will survey classical and recent approaches to these challenges by looking at selected original works. This is a joint online seminar with the University of Paderborn. A preparatory meeting will take place on April 8, 2pm via Zoom. If you are interested in participating, please send an email to Oliver Junge (https://www-m3.ma.tum.de/Allgemeines/OliverJunge).

Requirements

Basic knowledge of dynamical systems is beneficial, but not mandatory.

Literature

Lai-Sang Young: Towards a Mathematical Model of the Brain. Journal of Statistical Physics 180, 612–629 (2020). Jean-Philippe Bouchaud, Marc Mézard: Wealth condensation in a simple model of economy, Physica A, 282, 536-545 (2000). Rainer Hegselmann, Ulrich Krause: Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of artificial societies and social simulation 5, 3 (2002). G. Giordano, F. Blanchini, R. Bruno et al. Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nat Med 26, 855–860 (2020). Johannes Köhler, Lukas Schwenkel, Anne Koch, Julian Berberich, Patricia Pauli, Frank Allgöwer. Robust and optimal predictive control of the COVID-19 outbreak. Annual Reviews in Control (2020). Daniel H. Rothman, Carbon-cycle catastrophes: a dynamical systems perspective, SIAM News 52 (2019).

Informations

This seminar is suitable for students of the TUM School of Education.

Language

deutsch

Number of places

Master: 8
Persons from other faculties: None

Content

Im Mittelpunkt des Seminars soll die qualitative und geometrische Theorie nichtlinearer gewöhnlicher Differentialgleichungen stehen. Hierzu werden wir uns zunächst mit der Analysis auf Mannigfaltigkeiten beschäftigen. Im Anschluß sollen dann mit Hilfe dieser Methoden verschiedene grundlegende Resultate aus der Theorie dynamischer Systeme bewiesen werden. Einige Höhepunkte werden dabei das Theorem von Hartman-Grobman (nebst Satz über die stabile Mannigfaltigkeit), das Kupka-Smale Theorem, sowie Peixoto's Theorem sein. Bei Interesse können gerne auch weiterführende Themen vergeben werden.

Requirements

Grundvorlesungen Analysis und Lineare Algebra, Gewöhnliche Differentialgleichungen, möglichst auch Nichtlineare Dynamik: Grundlagen

Literature

Jacob Palis und Welington de Melo: Geometric Theory of Dynamical Systems. An Introduction, Springer Verlag Berlin 1982.

Informations

Termin: Donnerstag 14:15-15:45 Die (verpflichtende) Vorbesprechung findet voraussichtlich am Freitag, den 26.2.2021 um 16:15 Uhr online statt.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 4
Persons from other faculties: None

Content

In recent years, there has been an increasing interest in topics at the intersection of economics and computer science, as witnessed by the 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. The emphasis in this seminar lies on the independent study of classic economics papers as well as more recent papers from computer science. Among the topics to be covered are matching theory, mechanism design, and voting theory.

Requirements

It is expected that participants are experienced in formally proving mathematical statements and are familiar with standard proof techniques. Ideally, the participants completed at least one of the courses "Computational Social Choice" or "Algorithmic Game Theory." Additionally, basic knowledge of complexity theory is useful (e.g., module IN0011).

Literature

See course homepage (http://dss.in.tum.de/teaching) and get the password in the seminar overview meeting.

Informations

Registration is only possible through the lecturers and by application only. The seminar overview / presentation ("Vorbesprechung") is mandatory; see the homepage (http://dss.in.tum.de/teaching) for more information.

Language

englisch

Number of places

Master: 10
Persons from other faculties: None

Content

In this seminar we study number fields, which are finite extensions of the rational numbers Q. These are of particular interest in arithmetic, since questions on integral solutions of equations can often be solved through an investigation of suitable number fields. A typical example is to ask for a classification of all primes p that are a sum of two perfect squares. Using the ring of Gaussian integers Z[i] in the number field Q(i), the answer can be found without much technical calculations: Either p is 2 or congruent to 1 modulo 4. In the seminar we will introduce invariants of number fields such as the discriminant and the class number, and deduce a formula for the class number of imaginary quadratic number fields.

Requirements

Algebra 1

Literature

Neukirch, Algebraic Number Theory/Algebraische Zahlentheorie, Chapter 1 Yichao Tian, Lecture notes on Algebraic Number Theory

Informations

The seminar will be held by Prof. Eva Viehmann or Dr. Johannes Anschütz (guest professor for the summer term 2021)

This seminar is suitable for students of the TUM School of Education.

Language

deutsch

Number of places

Master: 6
Persons from other faculties: None

Content

We will discuss Markov chains and mixing times. One question of interest is how long it takes until a Markov chain approaches its stationary distribution up to a given error. An application concerns mixing a deck of cards: How long does one need to shuffle a deck of cards?

Requirements

Einführung in die Wahrscheinlichkeitstheorie (MA1401); Markovketten (MA2404) and probability theory (MA2409) are useful.

Literature

David Levin, Yuval Peres and Elizabeth Wilmer: Markov chains and mixing times. Second edition. Link to a pdf version of the book: https://pages.uoregon.edu/dlevin/MARKOV/mcmt2e.pdf

Informations

https://www-m5.ma.tum.de/Allgemeines/MA6011_2021S There will be a first meeting via zoom where every participant can choose a topic for his/her talk. Depending on the participants, the seminar will be in German or English.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 7
Persons from other faculties: None

Content

As a general principle, in developing mathematical models of real-world time-varying phenomena one distinguishes the set of physical or internal feedback laws (that yield an evolutionary equation) from the environment in which the system lies. The state of the latter is then represented through parameters and is assumed to be unaffected by the system "dynamics". Such parameters in real-world situations and particularly in the life sciences are rarely constant over time. This has various reasons, like absence of lab conditions, adaption processes, seasonal effects on different time scales, or an intrinsic "background noise". Or simply some systems can be decomposed into components so that, provided the influence of some of them is understood, without the requirement to precisely know their explicit form, they can be seen as a non-constant time-varying input for the others. Besides, sometimes it is desirable to include regulation or control strategies into a model (e.g., harvesting and fishing, dosing of drugs or radiation, stimulating chemicals or catalytic submissions), as well as extrinsic noise, and to study their effects. The theory of non-autonomous dynamical systems deals with these questions and with the analysis of the dynamical behaviour of such systems. In this seminar we shall study the fundamental theoretical tools such as the fomalisms of "skew-product flows" and "processes", the specificity of pullback attraction as opposed to forward attraction (which are indistinguishable in autonomous systems), and the notions of exponential dichotomy and dichotomy spectrum. Moreover, we shall unveil the incredible amount of complexity that the presence of time produces by surveying the theory of non-autonomous bifurcations (which can still be considered in its infancy) and the creation of chaotic behaviour. Attention will always be posed in the analysis of concrete models coming from physics or biosciences. In summary, we shall start to discover the universe through the dependence on time and the mathematical universe of time-dependent systems.

Requirements

Analysis 1,2 as well as the lectures on measure and integration as well as a first course in ordinary differential equations.

Literature

Kloeden, Peter E., and Martin Rasmussen. Nonautonomous dynamical systems. No. 176. American Mathematical Soc., 2011. Sell, George R. "Topological dynamics and differential equations." Von Nostrand Reinhold, Princeton, NJ (1971).

Informations

Language

deutsch

Number of places

Master: 4
Persons from other faculties: None

Content

Teilbarkeit, Primzahlen, Kongruenzen, zahlentheoretische Funktionen, Verteilung der Primzahlen, insbesondere Primzahlen in arithmetischen Progressionen und Primzahlsatz, Algorithmen der Zahlentheorie. Im Verlauf des Seminars werden auch zahlreiche offene Probleme über Primzahlen angesprochen werden. Die Zahlentheorie bietet zudem viele Möglichkeiten, eigene Experimente mit dem Computer durchzuführen.

Requirements

Mathematische Grundvorlesungen.

Literature

Forster: Algorithmische Zahlentheorie Hardy/Wright: An Introduction to the Theory of Numbers Nathanson: Elementary Methods in Number Theory Niven/Zuckerman/Montgomery: An Introduction to the Theory of Numbers Deiser: Die Unendlichkeit der Primzahlen

Informations

Die Vorträge können auf Deutsch oder Englisch abgehalten werden. Die Literatur steht überwiegend digital zur Verfügung.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 8
Persons from other faculties: None

Content

We study various models of random spanning trees and forests of graphs and lattices, in particular the uniform spanning tree and the minimal spanning tree. We will learn the connection of those trees to probabilistic objects such as random walks and percolation. Time permitting we will explore the connection to critical phenomena in statistical physics.

Requirements

Measuren theory, Probability theory.

Literature

Main source: Lyons, Russell, and Yuval Peres. Probability on trees and networks. Vol. 42. Cambridge University Press, 2017.‏ (also available online) We will possibly also read a few relevant papers.

Informations

The seminar will take place in the English language. Based on the corona situation, the seminar might have to take place online.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 12
Persons from other faculties: None

Content

Applicants for the seminar should email the following 3 components to ankerst@tum.de at the time of the seminar request in order to be eligible for consideration. Incomplete applications will not be accepted and topics will be assigned by strength of application. 1) Statement of agreement to mandatory attendance at all sessions (Thursdays 2-3:30pm) to pass seminar; tardiness or early departure counts as a missed seminar. 2) TUM Master’s grade transcript. 3) Top 5 papers to present by priority 1 (top) to 5 (least) chosen from the literature list. Short paragraph of motivation for the top paper, and others as desired. Candidates will be selected on strength of research and motivation for these descriptions. In this seminar students will learn recent statistical methodology advances to meet the emerging needs for the control of infectious diseases. Applications will include population-wide pandemic surveillance, epidemiology, and vaccine clinical trial design, requiring advanced statistical topics in Bayesian Markov Chain Monte Carlo estimation, spatio-temporal modeling, and analysis of censored survival data. Students will research the statistical methodology forming the foundation of a recent paper in order to effectively teach important concepts to a class of peers in the field. By the end of the seminar, students will have learned state-of-the-art statistical techniques in infectious disease research.

Requirements

Successful completion of Applied Regression, Computational Statistics, Generalized Linear Models

Literature

1) Ainslie KEC, et al. Maximum likelihood estimation of influenza vaccine effectiveness against transmission from the household and from the community. Stat Med. 2018;37(6):970-982. 2) Bastos LS, et al. A modelling approach for correcting reporting delays in disease surveillance data. Stat Med. 2019;38(22):4363-4377. 3) Brown AC, et al. Evaluating the ALERT algorithm for local outbreak onset detection in seasonal infectious disease surveillance data. Stat Med. 2020;39(8):1145-1155. 4) Cassidy R, et al. Modelling, Bayesian inference, and model assessment for nosocomial pathogens using whole-genome-sequence data. Stat Med. 2020;39(12):1746-1765. 5) Cengiz Ü, et al. A new statistical early outbreak detection method for biosurveillance and performance comparisons. Stat Med. 2019;38(27):5236-5258. 6) Chen P, et al. Early dengue outbreak detection modeling based on dengue incidences in Singapore during 2012 to 2017. Stat Med. 2020;39(15):2101-2114. 7) Dehbi HM, et al. Early phase dose-finding trials in virology. Stat Med. 2021;40(2):240-253. 8) Fisher LH, et al. Ecological inference for infectious disease data, with application to vaccination strategies. Stat Med. 2020;39(3):220-238. 9) Gabriel EE, et al. Optimizing and evaluating biomarker combinations as trial-level general surrogates. Stat Med. 2019;38(7):1135-1146. 10) Lee S, et al. Online estimation of the case fatality rate using a run-off triangle data approach: An application to the Korean MERS outbreak in 2015. Stat Med. 2019;38(14):2664-2679. 11) Pak D, et al. Analyzing left-truncated and right-censored infectious disease cohort data with interval-censored infection onset. Stat Med. 2021;40(2):287-298. 12) Oh EJ, Shepherd BE, Lumley T, Shaw PA. Raking and regression calibration: Methods to address bias from correlated covariate and time-to-event error. Stat Med. 2020. Epub ahead of print. 13) Pugh S, Heaton MJ, Hartman B, Berrett C, Sloan C, Evans AM, Gebretsadik T, Wu P, Hartert TV, Lee RL. Estimating seasonal onsets and peaks of bronchiolitis with spatially and temporally uncertain data. Stat Med. 2019;38(11):1991-2001. 14) Veres-Ferrer EJ, Pavía JM. Elasticity as a measure for online determination of remission points in ongoing epidemics. Stat Med. 2020 Nov. Epub ahead of print. 15) Yan QL, Tang SY, Xiao YN. Impact of individual behaviour change on the spread of emerging infectious diseases. Stat Med. 2018;37(6):948-969. 16) Zou J, Zhang Z, Yan H. A hybrid hierarchical Bayesian model for spatiotemporal surveillance data. Stat Med. 2018 Dec 10;37(28):4216-4233.

Informations

Before enrolling, please bear in mind that mandatory attendance for all sessions occurring on Thursdays 2-3:30 pm throughout the semester is required in order to pass the seminar. Unfortunately exceptions cannot be made for work, other seminars or courses.

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 6
Persons from other faculties: 2

Content

This course will cover Alon and Spencer's influential textbook "The Probabilistic Method" on probabilistic methods in combinatorics. Specific topics will include linearity of expectation, the second moment method, correlation inequalities, random graphs, and phase transitions. These methods are useful for studying research problems in stochastic topology.

Requirements

Probability theory (MA2409)

Literature

1) The probabilistic method by Alon and Spencer (4th Ed) 2) A probability path by Sidney I. Resnick

Informations

This seminar is suitable for students of the TUM School of Education.

Language

englisch

Number of places

Master: 7
Persons from other faculties: None

Content

Transfer operators describe the evolution of stochastic processes on a large (macroscopic) scale. They have numerous applications, and a key aim of this seminar is to learn about various application areas. Different types of transfer operators exist, notably Markov semigroups, Frobenius-Perron operators and Koopman operators. A summary of the relevant theory will be given at the start of the seminar. This seminar is does not require prerequisites beyond calculus, numerics and stochastics from the Bachelor level. Interested participants are welcome to study the underlying theory further (e.g., as described in the book by Lakota and Mackey), but this is not required. The seminar will run as online seminar jointly between TUM and Imperial College London.

Requirements

Calculus, numerics and stochastics on a Bachelor level.

Literature

Research papers and reviews on the topic. Background material for further reading: Andrzej Lasota und Michael C. Mackey: Chaos, fractals, and noise, Springer 1994.

Informations