Seminars and workshops

Dates for seminars and workshops in the summer semester 2020

Kalender blau: Grafik: Kathrin Ruf

15 January 2020: Program announced for summer semester 2020

20 January (12 o'clock) - 26 January 2020: Students register using TUMonline

27 January - 31 January 2020: First round

3 February (12 o'clock) - 9 February 2020: Students register (second choice) using TUMonline

10 February - 14 February 2020: Second round

How are seminar places allocated?

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

You register using TUMonline 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. Should you not get a place, then you will be informed via e-mail.

Should you not receive a place in the seminar or workshop you indicated in stage 1, you can apply again using TUMonline for one of the available places in another seminar. The supervising tutors make a selection from the list of applicants.

The Examination Board allocates free places to students who were not allocated a place in stages 1 or 2. If you have not yet been allocated a place, please submit an informal application indicating your preferences (non-binding) from those seminar or workshop places remaining to:

Presenting Math (Workshops) for Bachelor students

Workshops are offered on selected mathematical topics. Each participant presents his or her 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

MA6002 Workshop – FPSO version 2014

For the old version (FPSO 2014) of our Bachelor's program Mathematics we can only offer very view topics for the workshop. Please register only for the specific workshops for your program version. These workshops take place in the first week of classes during the summer semester, too. Recommended requirements are Analysis 1 and Linear Algebra and Discrete Structures 1.

Workshops offered in the summer semester 2020

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Komplexe Zahlen, Polarkoordinaten, Einheitswurzeln, Fundamentalsatz der Algebra (mit anschaulichen Beweisen), komplexe Funktionen und ihre Visualisierung, komplexe Exponentialfunktion und ihre Abbildungseigenschaften

Requirements

Analysis 1 und Lineare Algebra 1

Literature

Oliver Deiser: Einführung in die Mathematik 1 & 2

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 und Lineare Algebra 1

Literature

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

Informations

siehe http://www-m5.ma.tum.de/Allgemeines/MA6002_2020S

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Der Workshop vertieft Ihre Grundlagen aus der linearen Algebra zur mathematischen Beschreibung von Ebene und Raum, indem Sie im Rahmen des Moduls MA 0006 "Mathematisches Studieren" eine eigene mathematische Präsentation erarbeiten.

Requirements

Analysis 1 und lineare Algebra 1

Literature

Kapitel~4 aus der "Einf\"uhrung in die Mathematik 1.2" von Oliver Deiser, http://www.aleph1.info/?call=Puc&permalink=ema12_4

Informations

https://www-m8.ma.tum.de/foswiki/pub/M8/Allgemeines/CarolineLasser/Workshop_Matrix_SS20.pdf

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Wir beschäftigen uns mit der Situation, dass eine Gruppe von Personen gemeinsam versucht, eine demokratische Entscheidung für eine von mehreren Alternativen zu finden - ein Problem aus dem interdisziplinären Gebiet "Social choice theory". Im Fall der Entscheidung zwischen lediglich zwei Alternativen ist relativ klar, was "Mehrheit entscheidet" bedeuten soll - aber bei drei oder mehr Alternativen wird typischerweise keine Option eine unbestreitbare (absolute) Mehrheit erreichen. Wir werden mehrere Eigenschaften definieren, die wir wahrscheinlich gerne als Anforderungen für ein gerechtes, demokratisches Abstimmungsverfahren festsetzen möchten, und untersuchen, welche davon bei bestimmten bekannten Abstimmungsverfahren erfüllt sind. Es stellt sich heraus, dass schon drei - für sich genommen eigentlich sehr natürlich wirkende - Forderungen miteinander beweisbar inkompatibel sind; das ist eine Konsequenz des Unmöglichkeitssatzes von Arrow. Der Workshop findet auf deutsch statt; die zugrundeliegende Literatur ist aber - wie nahezu alle mathematische Fachliteratur - in (einfachem) Englisch geschrieben.

Requirements

Mathematische Fachsprache des 1. Semesters

Literature

Alan D. Taylor: Mathematics and politics

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

Lineare Algebra

Literature

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

Informations

https://www.or.tum.de/en/teaching/summer2020/schmankerl/

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Welche modernen Werkzeuge sollte jeder Mathematiker kennen? In diesem Workshop lernen wir die populärsten Software-Tools kennen, die heutzutage von Mathematikern weltweit eingesetzt werden. Erfahrungen mit Programmen wie Matlab und R oder Versionsverwaltungen wie Git erleichtern nicht nur den Alltag in Studium und Forschung, sondern sind auch hochgefragte Fähigkeiten in der Industrie. In diesem Workshop sollen Studierende die Funktionsweisen und Anwendungsgebiete von ausgewählten Software-Lösungen kennenlernen und in Kurzvorträgen (30 Minuten) vorstellen. Dabei soll auch auf praktische Fragestellungen wie "Wie installiere ich XY? Wie gelange ich an eine Lizenz? Wofür kann ich XY in meinem Studium verwenden? Wie sieht ein einfaches Code-Beispiel aus?" eingegangen werden. In der Liste der besprochenen Werkzeuge werden sich Programme wie Matlab, Mathematica, Maple, Sage, R, WolframAlpha, LaTeX, LaTeX Beamer, LaTeX TikZ oder Git finden.

Requirements

Literature

Informations

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Mathematik der Evolution Populationsgenetik ist neben Epidemiologie und Ökologie der Teil der Biologie, der die tiefsten mathematischen Methoden nutzt. Genetische Daten (Informationen über Mutationen) können genutzt werden, um die Größe einer Population abzuschätzen, das Alter einer Varietät (wie die weiße Hautfarbe), oder die Zeit seit dem Aufbruch der Menschheit aus Afrika zu schätzen. In dem Workshop möchten wir uns mit der mathematischen Basis der Populationsgenetik beschäftigen, d.h. insbesondere mit dem Moran-Modell und dem Kingman Koaleszent.

Requirements

Der Workshop basiert auf den Vorlesungen des ersten Semesters.

Literature

J. Müller, Introduction into Basic Concepts in Population Genetics. Skript, TUM, 2020.

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

Der Workshop besteht aus zwei Teilen. Ein erstes Treffen wird in der Woche vor Vorlesungsbeginn (13. bis 17. April) stattfinden. Die Vorträge sind an zwei Tagen in der ersten Vorlesungswoche (20. bis 24. April).

Language

deutsch

Number of places

Bachelor: 8
Persons from other faculties: None

Content

Wir werden uns kleine und große offene Probleme aus verschiedenen Bereichen der Mathematik ansehen. Darunter: * Das P vs. NP Problem: Ist das Finden von Beweisen schwerer als das Nachvollziehen? * In welchen Dimensionen existieren Hadamard-Matrizen? * Wohnt in jeder ebenen Kurve ein Quadrat? * Wie lassen sich Matrizen am effizientesten multiplizieren? * Gibt es ungerade vollkommene Zahlen? * Gibt es einen "nowhere-zero point" für jede lineare Abbildung? * Wie groß kann der Überhang eines Bauklotz-Turmes sein? * Das Jacobi Problem: Was hat die Jacobi-Determinante mit Umkehrbarkeit zu tun?

Requirements

Analysis 1, LADS 1

Literature

Literatur wird individuell bekannt gegeben.

Informations

Language

deutsch

Number of places

Bachelor: 11
Persons from other faculties: None

Content

Das Buch der Beweise von Aigner und Ziegler ist mittlerweile zu einem Klassiker — zumindest unter Mathematikern — geworden. Es enth¨alt einige der sch¨onsten und elegantesten Beweise f¨ur ausgw¨ahlte S¨atze der elementaren Algebra, Analysis und Zahlentheorie. Dabei bedeutet ¨elementarnicht unbedingt, dass die Aussagen und ihre Beweise einfach sind, sondern vielmehr, dass man sie nach ein bis zwei Semestern Mathematikstudium problemlos verstehen (und in diesem Falle sogar: geniessen) kann. Im Seminar sollen einige der Beweise aus dem Buch vorgestellt werden, wobei der Schwerpunkt auf den S¨atzen aus der Analysis liegt.

Requirements

Mathematikstudium 1.Semester

Literature

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

Informations

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Dieser Workshop wird elegante Beweise aus verschiedensten Teilgebieten der Mathematik diskutieren. Als Grundlage dient das Buch "Proofs from THE BOOK" / "Das BUCH der Beweise" von M. Aigner und G. M. Ziegler.

Requirements

Analysis 1 Lineare Algebra 1 Diskrete Strukturen

Literature

"Proofs from THE BOOK" / "Das BUCH der Beweise" von M. Aigner und G. M. Ziegler.

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​ * Sätze von Caley und Hamilton * etc...

Requirements

LADS1, Analysis1

Literature

Ebbinghaus et al.​ "Zahlen"​ Springer 1992

Informations

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 Codierungstheorie.

Requirements

Mathematikveranstaltungen des ersten Semesters

Literature

Ehrhard Behrends: Mathematik und Zaubern: Ein Einstieg für Mathematiker, Springer 2017

Informations

Findet in der ersten Semesterwoche statt.

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Unter einem diskreten dynamischen System versteht man im einfachsten Fall eine rekursiv definierte Folge x(n+1) = f(n, x(n)). Im Zentrum des Workshops sollen sowohl grundlegende Resultate stehen (etwa Differenzenkalkül, elementare Lösungsmethoden) als auch qualitative Theorie (Fixpunkte, periodische Punkte, Stabilität, Bifurkationen, Chaos) und ausgewählte Anwendungen (z.B. aus der Analysis, Numerik, Physik, Biologie). Bei Interesse können auch tieferliegende Themen vergeben werden.

Requirements

Analysis 1 Lineare Algebra 1

Literature

Krause/Nesemann: Differenzengleichungen und diskrete dynamische Systeme, Teubner 1999 Devaney: A first course in chaotic dynamical systems: theory and experiment, Addison-Wesley, 1992

Informations

Die (verpflichtende) Vorbesprechung findet am Dienstag, den 18. Februar 2020 um 13:00 Uhr in Raum 03.06.011 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 Methoden (z.B. Differentialrechnung) 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 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

Der Workshop findet auf deutsch statt, ein Teil der Quellen ist - wie nahezu alle mathematische Fachliteratur - in (einfachem) Englisch geschrieben.

Language

deutsch

Number of places

Bachelor: 12
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 Räume müssen erst festgelegt werden.

Seminars for Bachelor students

Please note:

For each seminar offered to Bachelor's and Master’s students, there is a separate registration process in TUMonline. 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 second selection round, current Bachelor's students and external Master’s applicants can register for available places in the Master’s advanced seminars. In order to do so, please submit an informal application to master (at) ma.tum.de.

Bachelor seminars offered in the summer semester 2020

Language

englisch

Number of places

Bachelor: 6
Persons from other faculties: None

Content

In earlier times, infectious diseases were big threats to human population. Antibiotics helped to control some of these diseases, but not all; additionally more and more resistancies against classical antibiotics develop. Thus, a better, quantitative understanding of infection and the spread of epidemics, helps to decide for or against certain treatment strategies, also how to optimise treatments. Often, the dynamic behaviour for whole populations is described by differential equation models. PDEs allow e.g. for considering spatial models. For small populations, stochastic models may be more appropriate. We will discuss typical modelling approaches including their analysis as well as concrete examples for diseases and how to set up appropriate models.

Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

Literature

This seminar will be based on original papers as well as on parts of the books “Modeling to Inform Infectious Disease Control” by Niels G. Becker and “Mathematical Epidemiology” edited by Fred Brauer, Pauline van den Driessche and Jianhong Wu, dependent on the interests and previous knowledge of the participants.

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!

Language

englisch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Solving problems algorithmically is an important part of mathematics, in particular, of discrete mathematics. Designing an algorithm means breaking down an abstract task into a sequence of simple steps. A vast toolbox of techniques has been developed including divide-and-conquer, dynamic programming, and greedy algorithms. Their implementation often relies on suitable data structures. Choosing the right way to manage intermediate results and data may have a major influence on the efficiency in theory as well as in practice. One of the most prominent examples is Dijkstra's algorithm to compute a shortest path in a graph. Using a Fibonacci heap for its implementation allows to apply it to large-scale networks. Along that lines, we focus on algorithmic approaches to combinatorial problems in this seminar. We will look into the interplay of algorithm design and finding and using appropriate data structures.

Requirements

necessary: Algorithmische Diskrete Mathematik (MA2501)

Literature

"Algorithm Design", Jon Kleinberg, Éva Tardos and "Introduction to Algorithms", Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein

Informations

More information will be available at https://www.or.tum.de/teaching/summer2020/seminaralgorithms

Language

deutsch

Number of places

Bachelor: 6
Persons from other faculties: None

Content

Numerische Methoden zur Berechnung hoch-oszillatorischer Integrale

Requirements

Solide Kenntnisse in Analysis und linearer Algebra, Grundkenntnisse in Numerik.

Literature

Computing Highly Oscillatory Integrals; Alfredo Deano, Daan Huybrechs und Arieh Iserles (SIAM, 2018)

Informations

https://www-m8.ma.tum.de/foswiki/pub/M8/Allgemeines/CarolineLasser/Seminar_OscQuad_SS20.pdf

Language

englisch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

Wir werden ausgewählte Kapitel des Buches "Discrete Differential Geometry: Integrable Structure" von Bobenko und Suris durcharbeiten.

Requirements

LADS/Analysis Differentialgeometrie: Grundlagen

Literature

Alexander I. Bobenko, Yuri B. Suris, Discrete Differential Geometry: Integrable Structure, Graduate Studies in Mathematics, Vol. 98, AMS, 2008, xxiv + 404 p; hardcover ISBN-10: 0-8218-4700-7 ISBN-13: 978-0-8218-4700-8

Informations

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: None

Content

This seminar will cover random objects in high-dimensional space, in particular, random vectors, random matrices, and random projections. We will discuss a selection of theoretical skills for the analysis of these objects, such as concentration inequalities, covering and packing arguments, decoupling and symmetrization tricks, chaining, and comparison techniques for stochastic processes.

Requirements

Probability Theory and/or Probabilistic Methods and Algorithms for Data Analysis

Literature

R. Vershynin, High-Dimensional Probability - An Introduction with Applications in Data Science, Cambridge University Press

Informations

Students in the Master's program Mathematics in Data Science are also eligible; they will be required to give an extended presentation. The seminar will be held in blocks of multiple talks on Friday afternoons.

Language

englisch

Number of places

Bachelor: 5
Persons from other faculties: None

Content

This seminar will serve as an introduction to basic concepts of information theory. Topics to be discussed include information-theoretic quantities (entropies) and corresponding inequalities, differential entropies and continuous variables, as well as operational problems such as Shannon's noisy channel coding, data compression and rate distortion theory.

Requirements

Analysis 1 & 2, Lineare Algebra 1 & 2, Einführung in die diskrete Mathematik

Literature

Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, Wiley-Interscience; 2nd edition (2006). David MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press; First edition (2003). Additional literature TBA.

Informations

This seminar will be held in block-form at the beginning of term. Additional information: see here http://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: None

Content

We will discuss a selection of classical and more recent results of matrix analysis. Relevant topics include matrix norms, functional calculus, matrix monotone functions and convexity, matrix inequalities, majorization, matrix polynomials and polynomial identities, complete positivity, eigenvalues and Horn's conjecture.

Requirements

Linear Algebra 2 (MA1102)

Literature

R. Bhatia "Matrix Analysis" (Springer) and "Positive Definite Matrices" (Princeton). A. Horn and C. Johnson "Matrix Analysis" (Cambridge University Press) Additional literature: TBA.

Informations

The seminar will be held in block-form at the beginning of term. For additional information: see https://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

Language

deutsch

Number of places

Bachelor: 12
Persons from other faculties: None

Content

Die Vortragenden stellen verschiedene Paradoxien (aus Bereichen wie Wahlverfahren, Verkehrsplanung, Statistik) vor und analysieren diese. Das Seminar verfolgt ein innovatives Konzept; Literaturauswahl, Fixierungs- und Vorbereitungsworkshop eingeschlossen.

Requirements

Literature

Informations

Vorbesprechung: 24.02.2020, 16 Uhr, Glaskasten M9 (Adobe-Raum). Teilnahme unbedingt erforderlich, da das Konzept ausführlich besprochen werden soll.

Language

englisch

Number of places

Bachelor: 6
Persons from other faculties: None

Content

Stochastic processes with reinforcement are a very active area of research. The literature on the subject has been growing tremendously during the past 20 years. In the seminar, we will have a look at various important models. These include urn models, edge-reinforced random walks, vertex-reinforced random walk, processes in discrete and in continuous time. The common feature are random transition probabilities. They can change over time or they can be sampled before the motion starts. This exciting subject gives many opportunities to write a bachelor's or master's thesis.

Requirements

Probability theory (MA2409) and interest in the subject.

Literature

see http://www-m5.ma.tum.de/Allgemeines/MA6015_2020S

Informations

see http://www-m5.ma.tum.de/Allgemeines/MA6015_2020S Depending on the wishes of the participants the talks will be in English or German.

Language

deutsch

Number of places

Bachelor: 10
Persons from other faculties: None

Content

In der Presse werden Quantencomputer entweder als omnipotent beschrieben, als entscheidende Hilfsmittel, die Medizin, Gesellschaft, und Technik in ungeahnter Weise voranbringen könnten, oder aber als Hype und völliger Unsinn, als ein Spielzeug der Physiker ohne praktischen Nutzen[2]. Spätestens die Presseerklärung von GOOGLE, dass die "Quantenüberlegenheit" erreicht sei - also ein Problem gelöst wurde, das mit herkömmlichen Computern nicht in überschaubaren Zeiträumen gelöst werden könnte (was einige Tage darauf von IBM bezweifelt wurde), deutet an, dass sich Quantencomputer für relevante Anwendungen nutzen lassen [1]. In diesem Seminar werden wir weder die physikalische Basis von Quantencomputern diskutieren, noch die Kontroverse von GOOGLE und IBM aufgreifen, ob die Quantenüberlegenheit tatsächlich erreicht wurde. In diesem Seminar wollen wir uns auf der Basis des Buches "Hofmeister, Quantum Computing verstehen" [3] die mathematische Grundlage der Quantencomputer ansehen, und lernen wie Quantenalgorithmen aussehen. Im Rahmen des Seminars wollen wir verstehen, was wir tatsächlich von Quantencomputern zu erwarten haben, wo ihre Stärke liegt, und welche Probleme für Quantum Computing völlig ungeeignet sind. Bitte nehmen Sie an der Vorbesprechung Ende des Semesters teil. Das Seminar wendet sich primär an Bachelorstudent*innen. Interessierte Masterstudent*innen wenden sich bitte direkt an die Veranstalter: hoesel@t-online.de oder johannes.mueller@mytum.de Quantum Computing In this seminar, we aim to understand the mathematics of quantum computing and investigate the principles of quantum algorithms. The seminar is based on [3]. We do not intend to step into the discussion between GOOGLE and IBM if quantum supremacy is reached nor will we aim to understand the physical basis of quantum computers. Please take part in the informal briefing for the seminar at the end of the present semester. The seminar is primarily meant for bachelor students. Interested master students are asked to contact the supervisors of the seminar directly: hoesel@t-online.de johannes.mueller@mytum.de

Requirements

Grundlagenvorlesungen.

Literature

[1] F. Ature et al. Quantum supremacy using a programmable superconducting processor, Nature 574(2019), 505-510. [2] http://backreaction.blogspot.com/2019/06/quantum-supremacy-what-is-it-and-what.html [3] Mathias Homeister Quantum Computing verstehen Springer Vieweg, 2005

Informations

Lieber Hans-Peter, es wäre schön, wenn das Seminar wieder am Mo oder Fr stattfinden könnte; Herr Hösel muss eventuell wieder pendeln. Falls sich da etwas vershiebt, so melden wir uns sobald als möglich. Viele Grüße Johannes

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: None

Content

Self-interacting random walks are non-markovian models of random walks. They were designed in order to find models that better describe real-world phenomena than the simple random walk does. The analysis of those models required the development of a beautiful and sophisticated methodology, part of which we will discuss in the seminar. The models that we discuss in the seminar include the self-avoiding random walk, the reinforced random walk, the exited random walk, and a few other models.

Requirements

Probability Theory or equivalent (necessary)

Literature

We will work through several papers from the last two decades.

Informations

The seminar will take place in english.

Language

deutsch

Number of places

Bachelor: 6
Persons from other faculties: None

Content

Mengenbegriff, Mächtigkeiten und Kardinalzahlen, Wohlordnungen und Ordinalzahlen, Axiome der Mengenlehre und mengentheoretische Axiomatik, Auswahlaxiom und äquivalente Prinzipien, Kontinuumsproblem, Grundlagen der deskriptiven Mengenlehre

Requirements

Grundvorleungen in Mathematik (Analysis und Lineare Algebra)

Literature

Oliver Deiser: Einführung in die Mengenlehre Thomas Jech: Set Theory

Informations

Language

deutsch

Number of places

Bachelor: 6
Persons from other faculties: None

Content

Im Zentrum dieses Seminars soll der Satz über Implizite Funktionen stehen. Neben dem klassischen Satz und Verallgemeinerungen (z.B. unter Verzicht auf Differenzierbarkeit) wollen wir uns auch mit Anwendungen dieser Theoreme beschäftigen. Für besonders Interessierte können gerne auch weiterführende Themen vergeben werden - etwa über das Moser-Nash Theorem.

Requirements

Grundvorlesungen Analysis möglichst auch: Funktionalanalysis

Literature

Stephen G. Krantz und Harold R. Parks: The Implicit Function Theorem. History, Theory, and Applications, Birkhäuser 2002

Informations

Seminartermin: Do 14:15-15:45 Uhr

Language

englisch

Number of places

Bachelor: 4
Persons from other faculties: None

Content

We study one of the most famous problem in discrete optimization: the traveling salesperson problem (TSP). The seminar is based on classical and recent research articles. Topics of the seminar are exact and approximate algorithms for the TSP, structural properties, and (industry) applications of the TSP.

Requirements

Discrete Optimization or Combinatorial Optimization

Literature

The research articles will be presented in the first meeting.

Informations

Advanced seminars for Masters students

Places in the advanced seminars labeled “Master” are generally allocated to Master’s students who are already enrolled in these degree programs! They may register for one advanced seminar only.
After the second selection round, current Bachelor's students and external Master’s applicants can apply for any remaining places in the Master’s advanced seminars. To do so, please submit an informal application to master (at) ma.tum.de.

Important information for students of "Mathematics in Data Science"

The advanced seminar Mathematics in 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 2020

Language

englisch

Number of places

Master: 5
Persons from other faculties: None

Content

In earlier times, infectious diseases were big threats to human population. Antibiotics helped to control some of these diseases, but not all; additionally more and more resistancies against classical antibiotics develop. Thus, a better, quantitative understanding of infection and the spread of epidemics, helps to decide for or against certain treatment strategies, also how to optimise treatments. Often, the dynamic behaviour for whole populations is described by differential equation models. PDEs allow e.g. for considering spatial models. For small populations, stochastic models may be more appropriate. We will discuss typical modelling approaches including their analysis as well as concrete examples for diseases and how to set up appropriate models.

Requirements

Mathematical models in Biology, Knowledge in Ordinary differential equations

Literature

This seminar will be based on original papers as well as on parts of the books “Modeling to Inform Infectious Disease Control” by Niels G. Becker and “Mathematical Epidemiology” edited by Fred Brauer, Pauline van den Driessche and Jianhong Wu, dependent on the interests and previous knowledge of the participants.

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!

Language

englisch

Number of places

Master: 6
Persons from other faculties: None

Content

Stochastic processes with reinforcement are a very active area of research. The literature on the subject has been growing tremendously during the past 20 years. In the seminar, we will have a look at various important models. These include urn models, edge-reinforced random walks, vertex-reinforced random walk, processes in discrete and in continuous time. The common feature are random transition probabilities. They can change over time or they can be sampled before the motion starts. This exciting subject gives many opportunities to write a bachelor's or master's thesis.

Requirements

Probability theory (MA2409) and interest in the subject.

Literature

see http://www-m5.ma.tum.de/Allgemeines/MA6015_2020S

Informations

see http://www-m5.ma.tum.de/Allgemeines/MA6015_2020S Depending on the wishes of the participants the talks will be in English or German.

Language

englisch

Number of places

Master: 12
Persons from other faculties: None

Content

In this seminar students will be introduced to contemporary biostatistics topics gaining traction to meet the challenges stemming from emerging data sources in clinical medicine and public health. Upon assignment of a topic, students will summarize the literature, and identify a leading biostatistics methods and medical applications paper to present in detail. They will present these to the class as a lecture for 1 hour, followed by an open 30 minute discussion and question period, where all students will be required to actively participate. Before registering for the seminar please note the following restrictions as registration confirms acceptance of these requirements for passing the course. • Attendance to all seminar sessions is required to pass the seminar. • Students must check emails and meet deadlines set by emails. • Upon successful completion of the seminar, including attendance, the student may be eligible to write a Master’s thesis with Prof. Ankerst. If so, then the thesis must be on the topic of the seminar and registered to start no later than Oct 1 2020. Interested students who accept the requirements should provide a transcript of grades along with a statement of motivation for the seminar (email text up to two paragraphs) to ankerst@tum.de for consideration of selection. Topics: 1) Multiple imputation methods for handling missing data 2) Propensity score methods for performing treatment comparisons in observational data 3) Developing prediction models and treatment comparisons in electronic health records 4) Big data methods integrating multi-omics platforms 5) Survival analyses incorporating competing risks 6) Methods for analyzing microbiome data 7) Spatio-temporal models for mapping disease rates and disease clusters 8) Causal inference methods 9) Meta-analysis and network meta-regression 10) Advanced longitudinal data models 11) Graphical models in medicine 12) Hierarchical model applications in public health

Requirements

Applied regression Generalized linear models Multivariate statistics

Literature

Biostatistical journals including Biostatistics, Biometrics, and Statistics in Medicine Medical papers from PubMed

Informations

The seminar takes place Thursdays 2:15-15:45.

Language

englisch

Number of places

Master: 10
Persons from other faculties: None

Content

Classical Statistics warns that correlation does not imply causation, yet inferring cause-effect relationships is the fundamental goal of many scientific studies. This seminar gives an introduction to formal statistical modelling of cause-effect relationships and methods for their inference from data. To this end the participants will present chapters from a forthcoming textbook.

Requirements

Probability Theory, Basic Statistics. Please provide a CV and a list of courses in statistics and probability you passed.

Literature

Hernan MA, Robins JM (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC. Available at https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/ Focus will be on Parts I and II.

Informations

Preliminary meeting in early February 2020.

Language

englisch

Number of places

Master: 10
Persons from other faculties: None

Content

This advanced seminar provides an introduction to Clifford algebras and Clifford analysis. Both are extension of the classical theory of complex algebra and of complex functions to higher dimensions. In recent years, concepts from Clifford algebra and analysis have been applied to areas such as signal analysis and theoretical physics. In this seminar, the construction of Clifford algebras is presented as is the extension of holomorphic functions to monogenic functions via the Dirac operator. The generalization of the Cauchy Integral Theorem to monogenic functions is derived. Applications to polynomial B-splines are also presented.

Requirements

Analysis, linear algebra, basic algebra, complex function theory, functional analysis (recommended but not absolutely necessary)

Literature

Gürlebeck, Habetha & Sprößig: Funktionentheorie in der Ebene und im Raum. Birkhäuser Verlag, 2006 Gürlebeck & Sprößig: Quaternionic and Clifford Calculus for Physicists and Engineers. John Wiley & Sons, 1997. Ablamowicz & Sobczyk: Lectures on Clifford (Geometric) Algebras and Applications. Birkhäuser Verlag, 2004. Kantor & Solodovnikov: Hypercomplex Numbers: An Elementary Introduction to Algebras. Springer Verlag, 1989. Original research papers.

Informations

Language

deutsch

Number of places

Master: 6
Persons from other faculties: None

Content

Numerische Methoden zur Berechnung hoch-oszillatorischer Integrale

Requirements

Solide Kenntnisse in Analysis und linearer Algebra, Grundkenntnisse in Numerik.

Literature

Computing Highly Oscillatory Integrals; Alfredo Deano, Daan Huybrechs und Arieh Iserles (SIAM, 2018)

Informations

https://www-m8.ma.tum.de/foswiki/pub/M8/Allgemeines/CarolineLasser/Seminar_OscQuad_SS20.pdf

Language

englisch

Number of places

Master: 5
Persons from other faculties: 5

Content

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. The emphasis in this seminar lies on the independent study of classic economics papers, but also, and in particular, more recent papers from computer science. Among the topics to be covered are matching theory, mechanism design, and voting theory.

Requirements

Basics of algorithms and complexity theory (P vs NP). Ideally, completed at least one of the courses "Computational Social Choice" or "Algorithmic Game Theory".

Literature

Please see the course homepage (https://dss.in.tum.de/teaching.html) or the list of papers of last year (http://go.tum.de/493086).

Informations

Registration is solely possible through the lecturers and by application only. Further information including the date of the seminar overview ("Vorbesprechung") and the application procedure will be available on the course homepage soon (https://dss.in.tum.de/teaching.html).

Language

englisch

Number of places

Master: 8
Persons from other faculties: None

Content

The goal of this seminar is to approach the notion of a higher category, motivated by its origins in algebraic topology and homological algebra. Homotopical algebra and higher categories appear naturally when studying an object up to a natural notion of equivalence and hence are ubiquituous in different areas of mathematics. We will start with the origin in homotopy theory by looking at topological spaces, simplicial sets, and chain complexes; classically studied via model categories following Quillen. Then we will turn to the basic theory of higher categories and discuss overviews of applications in various areas of mathematics, depending on the interest of the participants. Possible such outlook topics are the use and appearance in applied algebraic topology, derived deformation theory, derived algebraic geometry, and the Dold-Kan correspondence.

Requirements

Most of the motivation and examples will be drawn from Algebraic Topology, Category Theory, and Algebraic Geometry. We will assume some familiarity with basic notions (topological space, category, functor, chain complex), which will be used to illustrate the concepts. Feel free to contact me if you have questions about the prerequisites.

Literature

M. Hovey: Model Categories, AMS, 1999. M. P.G. Goerss, J.F. Jardine: Simplicial Homotopy Theory, Birkhäuser, 1999. D.G. Quillen: Homotopical Algebra, Springer, 1967. D.-C. Cisinski, Higher Categories and Homotopical Algebra, Cambridge University Press, 2019. J. Lurie, Higher Topos Theory, Princeton University Press, 2009

Informations

More detailed information about the content and more precise references will be made available on my website.

Language

englisch

Number of places

Master: 8
Persons from other faculties: None

Content

This seminar will cover random objects in high-dimensional space, in particular, random vectors, random matrices, and random projections. We will discuss a selection of theoretical skills for the analysis of these objects, such as concentration inequalities, covering and packing arguments, decoupling and symmetrization tricks, chaining, and comparison techniques for stochastic processes.

Requirements

Probability Theory and/or Probabilistic Methods and Algorithms for Data Analysis

Literature

R. Vershynin, High-Dimensional Probability - An Introduction with Applications in Data Science, Cambridge University Press

Informations

Students in the Master's program Mathematics in Data Science are also eligible; they will be required to give an extended presentation. The seminar will be held in blocks of multiple talks on Friday afternoons.

Language

englisch

Number of places

Master: 6
Persons from other faculties: None

Content

This seminar is based upon a list of papers on different areas of risk, perfomance, and investment management. Each participant presents one of the selected papers and discusses subsequent developments in the respective field. This provides a broad overview to all participants on the different fields, recent aspects, and historical development of the topics.

Requirements

Continuous Time Finance MA3702, Fixed Income Markets MA3703 (recommended), Investment Strategies MA5709 (recomended)

Literature

Papers will be presented at the preliminary meeting to the seminar (Seminarvorbesprechung). The date of the preliminary meeting will be announced at https://www.groups.ma.tum.de/en/mathfinance/lehre/summer-term-2020/

Informations

Language

englisch

Number of places

Master: 5
Persons from other faculties: None

Content

This seminar will serve as an introduction to basic concepts of information theory. Topics to be discussed include information-theoretic quantities (entropies) and corresponding inequalities, differential entropies and continuous variables, as well as operational problems such as Shannon's noisy channel coding, data compression and rate distortion theory.

Requirements

Analysis 1 & 2, Lineare Algebra 1 & 2, Einführung in die diskrete Mathematik

Literature

Thomas M. Cover and Joy A. Thomas, Elements of Information Theory, Wiley-Interscience; 2nd edition (2006). David MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press; First edition (2003). Additional literature TBA.

Informations

This seminar will be held in block-form at the beginning of term. Additional information: see here http://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

Language

englisch

Number of places

Master: 10
Persons from other faculties: 3

Content

Machine learning is about parametric nonlinear algorithms, whose parameters are optimized towards several tasks such as feature selection, dimensionality reduction, clustering, classification, regression, generation. We review the most important methods for these tasks by reading established and most recent scientific literature on the topics.

Requirements

Foundations of Data Analysis Probabilistic Methods and Algorithms of Data Analysis

Literature

Samples of literature Dimensionality reduction: Fornasier M., Rauhut H. (2011) Compressive Sensing. In: Scherzer O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY https://people.ricam.oeaw.ac.at/m.fornasier/CSFornasierRauhut.pdf Clustering (k-means etc.): Awasthi, Pranjal & Bandeira, Afonso & Charikar, Moses & Krishnaswamy, Ravishankar & Villar, Soledad & Ward, Rachel. (2014). Relax, No Need to Round: Integrality of Clustering Formulations. 10.1145/2688073.2688116. https://arxiv.org/pdf/1408.4045.pdf Noncoonvex optimisation: Jos e A Carrillo, Young-Pil Choi, Claudia Totzeck, and Oliver Tse. An analytical framework for consensus-based global optimization method. Mathematical Models and Methods in Applied Sciences, 28(06):1037-1066, 2018. https://arxiv.org/pdf/1602.00220.pdf Jason D. Lee, Ioannis Panageas, Georgios Piliouras, Max Simchowitz, Michael I. Jordan, and Benjamin Recht. First-order methods almost always avoid strict saddle points. Mathematical Programming, 176(1):311{337, 2019. https://arxiv.org/pdf/1710.07406.pdf Neural Networks: Bubacarr Bah, Holger Rauhut, Ulrich Terstiege, and Michael Westdickenberg. Learning deep linear neural networks: Riemannian gradient flows and convergence to global minimizers. arXiv:1910.05505, 2019. Banburski, Andrzej & Liao, Qianli & Miranda, Brando & Rosasco, Lorenzo & Liang, Bob & Hidary, Jack & Poggio, Tomaso. (2019). Theory III: Dynamics and Generalization in Deep Networks. https://arxiv.org/pdf/1903.04991.pdf Robust and Resource Efficient Identification of Shallow Neural Networks by Fewest Samples. Massimo Fornasier, Jan Vybíral, Ingrid Daubechies. http://de.arxiv.org/pdf/1804.01592.pdf Robust and Resource Efficient Identification of Two Hidden Layer Neural Networks. Massimo Fornasier, Timo Klock, Michael Rauchensteiner. http://de.arxiv.org/pdf/1907.00485.pdf

Informations

Language

englisch

Number of places

Master: 4
Persons from other faculties: None

Content

We will discuss a selection of classical and more recent results of matrix analysis. Relevant topics include matrix norms, functional calculus, matrix monotone functions and convexity, matrix inequalities, majorization, matrix polynomials and polynomial identities, complete positivity, eigenvalues and Horn's conjecture.

Requirements

Linear Algebra 2 (MA1102)

Literature

R. Bhatia "Matrix Analysis" (Springer) and "Positive Definite Matrices" (Princeton). A. Horn and C. Johnson "Matrix Analysis" (Cambridge University Press) Additional literature: TBA.

Informations

The seminar will be held in block-form at the beginning of term. For additional information: see https://www-m5.ma.tum.de/Allgemeines/Lehrveranstaltungen

Language

englisch

Number of places

Master: 5
Persons from other faculties: None

Content

Self-interacting random walks are non-markovian models of random walks. They were designed in order to find models that better describe real-world phenomena than the simple random walk does. The analysis of those models required the development of a beautiful and sophisticated methodology, part of which we will discuss in the seminar. The models that we discuss in the seminar include the self-avoiding random walk, the reinforced random walk, the exited random walk, and a few other models.

Requirements

Probability Theory or equivalent (necessary)

Literature

We will work through several papers from the last two decades.

Informations

The seminar will take place in english.

Language

englisch

Number of places

Master: 13
Persons from other faculties: None

Content

The seminar continues the lecture on Set Oriented Numerics from the winter semester 19/20. The goal of the seminar will be to develop a Julia implementation of the GAIO software package. To this end, group discussions will be combined with a collaborative software development on gitlab. Each participant will be responsible for one particular aspect of the package, but everybody will be able to contribute to all parts. The seminar will be concluded by a little workshop where everbody gives a brief talk about his contributions.

Requirements

MA 3333 Numerics of Dynamical Systems

Literature

- Dellnitz, M.; Froyland, G.; Junge, O.: The algorithms behind GAIO - Set oriented numerical methods for dynamical systems, in: B. Fiedler (ed.): Ergodic theory, analysis, and efficient simulation of dynamical systems, Springer, 2001. - Dellnitz, M.; Junge, O.: On the approximation of complicated dynamical behavior, SIAM Journal on Numerical Analysis, 36 (2), 1999. - Dellnitz, M.; Hohmann, A.: A subdivision algorithm for the computation of unstable manifolds and global attractors. Numerische Mathematik 75, pp. 293-317, 1997.

Informations

preliminary discussion: 7.2.20, 10:00, room t.b.a.

Language

deutsch

Number of places

Master: 6
Persons from other faculties: None

Content

Mengenbegriff, Mächtigkeiten und Kardinalzahlen, Wohlordnungen und Ordinalzahlen, Axiome der Mengenlehre und mengentheoretische Axiomatik, Auswahlaxiom und äquivalente Prinzipien, Kontinuumsproblem, Grundlagen der deskriptiven Mengenlehre

Requirements

Grundvorleungen in Mathematik (Analysis und Lineare Algebra)

Literature

Oliver Deiser: Einführung in die Mengenlehre Thomas Jech: Set Theory

Informations

Language

deutsch

Number of places

Master: 6
Persons from other faculties: None

Content

Im Zentrum dieses Seminars soll der Satz über Implizite Funktionen stehen. Neben dem klassischen Satz und Verallgemeinerungen (z.B. unter Verzicht auf Differenzierbarkeit) wollen wir uns auch mit Anwendungen dieser Theoreme beschäftigen. Für besonders Interessierte können gerne auch weiterführende Themen vergeben werden - etwa über das Moser-Nash Theorem.

Requirements

Grundvorlesungen Analysis möglichst auch: Funktionalanalysis

Literature

Stephen G. Krantz und Harold R. Parks: The Implicit Function Theorem. History, Theory, and Applications, Birkhäuser 2002

Informations

Seminartermin: Do 14:15-15:45 Uhr

Language

englisch

Number of places

Master: 6
Persons from other faculties: None

Content

We study one of the most famous problem in discrete optimization: the traveling salesperson problem (TSP). The seminar is based on classical and recent research articles. Topics of the seminar are exact and approximate algorithms for the TSP, structural properties, and (industry) applications of the TSP.

Requirements

Discrete Optimization or Combinatorial Optimization

Literature

The research articles will be presented in the first meeting.

Informations