Evento

Bachelor's programme in Mathematics

Bachelor's programme in Mathematics (2010 study regulations) (0084c_k120)

Module: Mathematics Seminar (0084cB1.1)

Seminar zur Visualisierung

LV: 19212411

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2 SWS

Konrad Polthier

Seminar

Submod: 0084cB1.1.1

Akt: 04.09.2023 12:00

Tue, 14:00 - 16:00 (A3/SR 115)

Description

Based on selected research literature, the students work out a relevant topic in visualization and computer graphics.

Usually, research articles are distributed which will be read, understood, presented, and illustrated with examples independently.

Therefore, own illustrations or implementations of the central algorithms can be used.

Every participant prepares a talk of maximally 90 minutes length containing discussion and questions.

Further, every participant writes a preparation to explain the content of the talk in detail and to summarize the topic in a structured way.

Topics are chosen from the following areas:

- general techniques in visualization

- visualization of vector fields

- rendering

- image processing

- smoothing of geometries

- discrete methods on 3D models

- animation

Additional appointments

Appointment series

A3/SR 115

Konrad Polthier

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Module: Data Structures and Data Abstraction (0086bA1.3)

Algorithms, Data Structures, and Data Abstraction

LV: 19300201

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4 SWS

Günther Rothe

Mahmoud Elashmawi

Lecture

Submod: 0086bA1.3.1

Akt: 20.09.2023 20:00

Tue, 14:00 - 16:00 (T9/Gr. Hörsaal)

Thu, 14:00 - 16:00 (T9/Gr. Hörsaal)

Description

Analysis of sorting algorithms: Mergesort, Quicksort, etc.
ADTs priority queue and dictionary and corresponding data structures: heaps, hashing, binary search trees, B-trees, etc.
Graph algorithms: breadth first search and depth first search, topolocigal sorting, minimum spanning trees, shortest paths.
Analysis on Strings.
Memory-management.
Algorithm design: divide-and-conquer, greedy algorithms, dynamic programming.
Mathematical analysis of algorithms: running time, space.

References

P. Morin: Open Data Structures, an open content textboox.
T. H. Cormen, C. Leiserson, R. Rivest, C. Stein: Introduction to Algorithms, MIT Press, 2009.
R. Sedgewick: Algorithms in Java (Part 1–5), Addison-Wesley, 2003.
G. Saake, S. Sattler: Algorithmen und Datenstrukturen, dpunkt.verlag, 2013.
M. Dietzfelbinger, K. Mehlhorn, P. Sanders. Algorithmen und Datenstrukturen: Die Grundwerkzeuge, Springer, 2014.
M.T. Goodrich, R. Tamassia: Data Structures and Algorithms in Java, Wiley, 2014.

Additional appointments

Appointment series

T9/Gr. Hörsaal

Günther Rothe

Mahmoud Elashmawi

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

T9/Gr. Hörsaal

Günther Rothe

Mahmoud Elashmawi

einmal, ab 19.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Algorithms, Data Structures, and Data Abstraction

LV: 19300202

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2 SWS

Günther Rothe

Mahmoud Elashmawi

Practice seminar

Submod: 0086bA1.3.2

Akt: 20.09.2023 20:00

Wed, 14:00 - 16:00 (T9/053 Seminarraum)

Mon, 08:00 - 10:00 (T9/051 Seminarraum)

Wed, 12:00 - 14:00 (T9/051 Seminarraum)

Fri, 16:00 - 18:00 (T9/051 Seminarraum)

Fri, 14:00 - 16:00 (T9/053 Seminarraum)

Fri, 16:00 - 18:00 (T9/053 Seminarraum)

Mon, 10:00 - 12:00 (T9/051 Seminarraum)

Wed, 16:00 - 18:00 (T9/049 Seminarraum)

Mon, 12:00 - 14:00 (T9/051 Seminarraum)

Wed, 08:00 - 10:00 (T9/051 Seminarraum)

Tue, 08:00 - 10:00 (T9/051 Seminarraum)

Additional appointments

Appointment series

T9/053 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

T9/051 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 16.10.2023, 08:00 - 10:00 (16 Termine)

T9/051 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

T9/051 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 20.10.2023, 16:00 - 18:00 (16 Termine)

T9/053 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

T9/053 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 20.10.2023, 16:00 - 18:00 (16 Termine)

T9/051 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 16.10.2023, 10:00 - 12:00 (16 Termine)

T9/049 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 18.10.2023, 16:00 - 18:00 (16 Termine)

T9/051 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 16.10.2023, 12:00 - 14:00 (16 Termine)

T9/051 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

T9/051 Seminarraum

Günther Rothe

Mahmoud Elashmawi

einmal, ab 17.10.2023, 08:00 - 10:00 (16 Termine)

Module: Algebra and Number Theory (0084cB2.5)

Algebra and Theory of Numbers

LV: 19200701

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB2.5.1

Akt: 04.09.2023 12:00

Wed, 08:00 - 10:00 (Hs A (Raum B.006, 200 Pl.))

Mon, 08:00 - 10:00 (T9/Gr. Hörsaal)

Description

Subject matter:
Selected topics from:

    Divisibility into rings (especially Z- and polynomial rings); residual classes and congruencies; modules and ideals
    Euclidean, principal ideal and factorial rings
    The quadratic law of reciprocity
    Primality tests and cryptography
    The structure of abel groups (or modules about main ideal rings)
    Symmetric function set
    Body extensions, Galois correspondence; constructions with compasses and rulers
    Non-Label groups (set of Lagrange, normal dividers, dissolvability, sylow groups)

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

Hs A (Raum B.006, 200 Pl.)

Alexander Schmitt

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

T9/Gr. Hörsaal

Alexander Schmitt

einmal, ab 16.10.2023, 08:00 - 10:00 (16 Termine)

Practice seminar for Algebra and Theory of Numbers

LV: 19200702

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2 SWS

Alexander Schmitt

Practice seminar

Submod: 0084cB2.5.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (A3/SR 119)

Thu, 12:00 - 14:00 (T9/049 Seminarraum)

Wed, 14:00 - 16:00 (A3/SR 119)

Additional appointments

Appointment series

A3/SR 119

Alexander Schmitt

einmal, ab 18.10.2023, 16:00 - 18:00 (16 Termine)

T9/049 Seminarraum

Alexander Schmitt

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Alexander Schmitt

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Module: Functional Analysis (0084cB2.2)

Functional Analysis

LV: 19201901

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4 SWS

Dirk Werner

Lecture

Submod: 0084cB2.2.1

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (A6/SR 025/026 Seminarraum)

Thu, 10:00 - 12:00 (A6/SR 025/026 Seminarraum)

Description

Content:
Functional analysis is the branch of mathematics dealing with the study of normed (or more generally, topological) vector spaces and continuous mappings between them. Analysis and Linear Algebra are thus linked.
The lecture deals with Banach and Hilbert spaces, linear operators and functionals as well as spectral theory of compact operators.

Target group: Students from the 3rd/4th semester on.
Requirements: Good command of the material of the lectures Analysis I/II and Linear Algebra I/II.

References

Literatur:

Dirk Werner: Funktionalanalysis, 8. Auflage, Springer-Verlag 2018

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Dirk Werner

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

A6/SR 025/026 Seminarraum

Dirk Werner

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

Tutorial: Functional Analysis

LV: 19201902

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2 SWS

Dirk Werner

Immanuel Zachhuber

Practice seminar

Submod: 0084cB2.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A3/SR 115)

Description

Inhalt:
Die Funktionalanalysis ist der Zweig der Mathematik, der sich mit der Untersuchung von normierten (oder allgemeiner topologischen) Vektorräumen und stetigen Abbildungen zwischen ihnen befasst. Hierbei werden Analysis, Topologie und Algebra verknüpft.
Die Vorlesung behandelt Banach- und Hilberträume, lineare Operatoren und Funktionale sowie Spektraltheorie kompakter Operatoren.

Zielgruppe: Studierende vom 4. Semester an.

Voraussetzungen: Sicheres Beherrschen des Stoffs der Vorlesungen Analysis I/II und Lineare Algebra I/II.

Literatur:

Dirk Werner: Funktionalanalysis, 6. Auflage, Springer-Verlag 2007, ISBN 978-3-540-72533-6
Hans Wilhelm Alt: Lineare Funktionalanalysis : eine anwendungsorientierte Einführung. 5. Auflage. Springer-Verlag, 2006, ISBN 3-540-34186-2
Harro Heuser: Funktionalanalysis: Theorie und Anwendung. 3. Auflage. Teubner-Verlag, 1992, ISBN 3-519-22206-X

Additional appointments

Appointment series

A3/SR 115

Dirk Werner

Immanuel Zachhuber

einmal, ab 20.10.2023, 10:00 - 12:00 (16 Termine)

Module: Discrete Mathematics I (0084cB3.2)

Discrete Geometrie I

LV: 19202001

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4 SWS

No lecturers

Lecture

Submod: 0084cB3.2.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (KöLu24-26/SR 006 Neuro/Mathe)

Tue, 10:00 - 12:00 (T9/SR 006 Seminarraum)

Description

This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
Basic structures in discrete geometry

polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Polytope theory
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes, shellability
shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
graphs, diameters, Hirsch (ex-)conjecture
Geometry of linear programming
linear programs, simplex algorithm, LP-duality
Combinatorial geometry / Geometric combinatorics
Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
Arrangements, zonotopes, zonotopal tilings, oriented matroids
Examples, examples, examples
regular polytopes, centrally symmetric polytopes
extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
combinatorial optimization and 0/1-polytopes

For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

References

G.M. Ziegler "Lectures in Polytopes"
J. Matousek "Lectures on Discrete Geometry"
Further literature will be announced in class.

Additional information

Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

No lecturers

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

T9/SR 006 Seminarraum

No lecturers

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Discrete Geometrie I

LV: 19202002

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2 SWS

Sophie Rehberg

Practice seminar

Submod: 0084cB3.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 032 Seminarraum)

Module: Numerical Mathematics II (0084cB3.4)

Basic Module: Numeric II

LV: 19202101

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4 SWS

Ana Djurdjevac

Lecture

Submod: 0084cB3.4.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 032 Seminarraum)

Mon, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Description

Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ana Djurdjevac

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Ana Djurdjevac

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Basic Module: Numeric II

LV: 19202102

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2 SWS

No lecturers

Practice seminar

Submod: 0084cB3.4.2

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 025/026 Seminarraum)

Module: Algebra I (0084cB3.3)

Basic Module: Algebra I

LV: 19202501

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB3.3.1

Akt: 04.09.2023 12:00

Mon, 12:00 - 16:00 (A3/Hs 001 Hörsaal)

Description

Content

This is the first part of a three semester course on algebraic geometry. Commutative algebra is the theory of commutative rings and their modules. It formally includes affine algebraic and local analytic geometry. Topics include:

Affine algebraic varieties
Rings, ideals, and modules
Noetherian rings
Local rings and localization
Primary decompositione
Finite and integral extensions
Dimension theory
Regular rings

Target Group

Students with the prerequisites mentioned below.

Prerequisites

Linear Algebra I+II
Algebra and Number Theory

References

Literature

Atiyah, M.F.; Macdonald, I.G.: Einführung in die kommutative Algebra. Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. 1969 ix+128 Seiten (This book is the best introduction to the subject with brief and clear descriptions.)
Further literature will be announced in the course.

Additional information

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexander Schmitt

einmal, ab 23.10.2023, 12:00 - 16:00 (15 Termine)

Practice seminar for Basic Module: Algebra I

LV: 19202502

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2 SWS

Marwan Benyoussef

Practice seminar

Submod: 0084cB3.3.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (KöLu24-26/SR 006 Neuro/Mathe)

Module: Differential Geometry I (0084cB3.5)

Differential Geometry I

LV: 19202601

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4 SWS

Konrad Polthier

Lecture

Submod: 0084cB3.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A3/SR 119)

Thu, 12:00 - 14:00 (A3/SR 119)

Description

Topics of the lecture will be:

curves and surfaces in Euclidean space,
metrics and (Riemannian) manifolds,
surface tension, notions of curvature,
vector fields, tensors, covariant derivative
geodesic curves, exponential map,
Gauß-Bonnet theorem, topology,
connection to discrete differential geometry.

This course is a BMS course and will be held in English on request.

Prerequisits:

Analysis I, II, III and Linear Algebra I, II

References

Literature

W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

Additional information

For further information, see Lecture Homepage.

Additional appointments

Appointment series

A3/SR 119

Konrad Polthier

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Konrad Polthier

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Differential Geometry I

LV: 19202602

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2 SWS

Konrad Polthier

Eric Zimmermann

Practice seminar

Submod: 0084cB3.5.2

Akt: 22.09.2023 16:00

Fri, 08:00 - 10:00 (A3/SR 115)

Fri, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Module: Analysis I (0084cA1.1)

Analysis I

LV: 19202801

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4 SWS

Holger Reich

Lecture

Submod: 0084cA1.1.1

Akt: 04.09.2023 12:00

Thu, 10:00 - 12:00 (A3/Hs 001 Hörsaal)

Tue, 10:00 - 12:00 (A3/Hs 001 Hörsaal)

Description

Content:
This is the first part of a three semester introduction into the basic mathematical field of Analysis. Differential and integral calculus in a real variable will be covered. Topics:

fundamentals, elementary logic, ordered pairs, relations, functions, domain and range of a function, inverse functions (injectivity, surjectivity)
numbers, induction, calculations in R, C
arrangement of R, maximum and minimum, supremum and infimum of real sets, supremum / infimum completeness of R, absolute value of a real number, Q is dense in R
sequences and series, limits, cauchy sequences, convergence criteria, series and basic principles of convergence
topological aspects of R, open, closed, and compact real sets
sequences of functions, series of functions, power series
properties of functions, boundedness, monotony, convexity
continuity, limits and continuity of functions, uniform continuity, intermediate value theorems, continuity and compactness
differentiability, concept of the derivative, differentiation rules, mean value theorem, local and global extrema, curvature, monotony, convexity
elementary functions, rational functions, root functions, exponential functions, angular functions, hyperbolic functions, real logarithm, inverse trigonometric functions, curve sketching
beginnings of integral calculus

Detailed Information can be found on the Homepage of 19202801 Analysis I.

References

Literature:

Bröcker, Theodor: Analysis 1, Spektrum der Wissenschaft-Verlag.
Forster, Otto: Analysis 1, Vieweg-Verlag.
Spivak, Michael: Calculus, 4th Edition.

Viele Analysis Bücher sind auch über die Fachbibliothek der FU Berlin elektronisch verfügbar.

Bei Schwierigkeiten mit den Grundbegriffen Menge, Abbildung etc. ist die folgende Ausarbeitung empfehlenswert:

Scheerer, Hans: Brückenkurs, Skript FU Berlin 2006.

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Holger Reich

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

A3/Hs 001 Hörsaal

Holger Reich

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Tutorial: Analysis I

LV: 19202802

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2 SWS

Holger Reich

Practice seminar

Submod: 0084cA1.1.2

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A3/SR 115)

Wed, 12:00 - 14:00 (A7/SR 140 Seminarraum (Hinterhaus))

Wed, 12:00 - 14:00 (A3/SR 115)

Thu, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Additional appointments

Appointment series

A3/SR 115

Holger Reich

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A7/SR 140 Seminarraum (Hinterhaus)

Holger Reich

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 115

Holger Reich

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 009 Seminarraum

Holger Reich

einmal, ab 19.10.2023, 14:00 - 16:00 (16 Termine)

Module: Lineare Algebra I (0084cA1.4)

Linear Algebra I

LV: 19201401

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4 SWS

Alexandru Constantinescu

Lecture

Submod: 0084cA1.4.1

Akt: 04.09.2023 12:00

Mon, 08:00 - 10:00 (A3/Hs 001 Hörsaal)

Wed, 08:00 - 10:00 (A3/Hs 001 Hörsaal)

Description

Content:

Basic terms/concepts: sets, maps, equivalence relations, groups, rings,
fields
Linear equation systems: solvability criteria, Gauss algorithm
Vector spaces: linear independence, generating systems and bases, dimension,
subspaces, quotient spaces, cross products in R3
Linear maps: image and rank, relationship to matrices, behaviour under
change of basis
Dual vector spaces: multilinear forms, alternating and symmetric bilinear
forms, relationship to matices, change of basis
Determinants: Cramer's rule, Eigenvalues and Eigenvectors

Prerequisites:

Participation in the preparatory course (Brückenkurs) is highly recommended.

References

Siegfried Bosch, Lineare Algebra, 4. Auflage, Springer-Verlag, 2008;
Gerd Fischer, Lernbuch Lineare Algebra und Analytische Geometrie, Springer-Verlag, 2017;
Bartel Leendert van der Waerden, Algebra Volume I, 9th Edition, Springer 1993;

Zu den Grundlagen

Kevin Houston, Wie man mathematisch denkt: Eine Einführung in die mathematische Arbeitstechnik für Studienanfänger, Spektrum Akademischer Verlag, 2012

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexandru Constantinescu

einmal, ab 16.10.2023, 08:00 - 10:00 (16 Termine)

A3/Hs 001 Hörsaal

Alexandru Constantinescu

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Practice seminar for Linear Algebra I

LV: 19201402

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2 SWS

N.N.

Practice seminar

Submod: 0084cA1.4.2

Akt: 04.09.2023 12:00

Fri, 14:00 - 16:00 (A3/SR 120)

Thu, 08:00 - 10:00 (A3/ 024 Seminarraum )

Tue, 08:00 - 10:00 (A3/SR 119)

Wed, 14:00 - 16:00 (A3/ 024 Seminarraum )

Additional appointments

Appointment series

A3/SR 120

N.N.

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A3/ 024 Seminarraum

N.N.

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

A3/SR 119

N.N.

einmal, ab 17.10.2023, 08:00 - 10:00 (16 Termine)

A3/ 024 Seminarraum

N.N.

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Module: Computerorientierte Mathematik I (0084cA1.6)

Computerorientated Mathematics I (5 LP)

LV: 19200501

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2 SWS

Claudia Schillings

Lecture

Submod: 0084cA1.6.1

Akt: 04.09.2023 12:00

Fri, 12:00 - 14:00 (T9/Gr. Hörsaal)

Description

Contents:
Computers play an important role in (almost) all situations in life today. Computer-oriented mathematics provides basic knowledge in dealing with computers for solving mathematical problems and an introduction to algorithmic thinking. At the same time, typical mathematical software such as Matlab and Mathematica will be introduced. The motivation for the questions under consideration is provided by simple application examples from the aforementioned areas. The content of the first part includes fundamental terms of numerical calculation: number representation and rounding errors, condition, efficiency and stability.

Homepage: All current information on lectures and lectures

References

Literatur: R. Kornhuber, C. Schuette, A. Fest: Mit Zahlen Rechnen (Skript zur Vorlesung)

Additional appointments

Appointment series

T9/Gr. Hörsaal

Claudia Schillings

einmal, ab 20.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Computerorientated Mathematics I (5 LP)

LV: 19200502

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2 SWS

Vesa Kaarnioja

Claudia Schillings

Practice seminar

Submod: 0084cA1.6.2

Akt: 15.09.2023 14:00

Fri, 16:00 - 18:00 (A3/SR 120)

Mon, 10:00 - 12:00 (A3/SR 120)

Wed, 10:00 - 12:00 (A3/SR 120)

Fri, 14:00 - 16:00 (A3/019 Seminarraum)

Fri, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Thu, 08:00 - 10:00 (A3/SR 119)

Mon, 16:00 - 18:00 (A3/SR 120)

Mon, 12:00 - 14:00 (A3/SR 119)

Mon, 14:00 - 16:00 (A3/SR 119)

Additional appointments

Appointment series

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 20.10.2023, 16:00 - 18:00 (16 Termine)

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 10:00 - 12:00 (16 Termine)

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

A3/019 Seminarraum

Vesa Kaarnioja

Claudia Schillings

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 007/008 Seminarraum

Vesa Kaarnioja

Claudia Schillings

einmal, ab 20.10.2023, 14:00 - 16:00 (17 Termine)

A3/SR 119

Vesa Kaarnioja

Claudia Schillings

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 16:00 - 18:00 (16 Termine)

A3/SR 119

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Module: Stochastics I (0084cA1.8)

Stochastics I

LV: 19200601

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4 SWS

Nicolas Perkowski

Lecture

Submod: 0084cA1.8.1

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A6/SR 031 Seminarraum)

Wed, 08:00 - 10:00 (A6/SR 031 Seminarraum)

Description

Inhalt:

Prinzipien des Zählens; Elemente der Kombinatorik
Modelle vom Zufall abhängiger Vorgänge: Wahrscheinlichkeitsräume, Wahrscheinlichkeitsmaße
Bedingte Wahrscheinlichkeiten; Unabhängigkeit; Bayes'sche Regel
Zufallsvariablen und ihre Verteilungen; Kenngrössen der Verteilungen: Erwartungswert und Varianz
Diskrete Verteilungen: Laplace-Verteilung; Binomialverteilung; geometrische Verteilung
Approximation der Binomialverteilung durch die Normalverteilung;
Approximation der Binomialverteilung durch die Poissonverteilung
Verteilungen mit Dichten: Gleichverteilung; Normalverteilung; Exponentialverteilung
Gemeinsame Verteilungen von mehreren Zufallsvariablen: diskret und mit Dichten; Unabhängigkeit von Zufallsvariablen; bedingte Verteilungen; Summen unabhängiger Zufallsvariablen und ihre Verteilungen
Kenngrößen gemeinsamer Verteilungen: Erwartungswert, Kovarianz und Korrelation; bedingte Erwartung
Grenzwertsätze: schwaches Gesetz der großen Zahl und relative Häufigkeiten; der zentrale Grenzwertsatz
Datenanalyse und deskriptive Statistik: Histogramme; empirische Verteilung; Kenngrößen von Stichprobenverteilungen; Beispiele irreführender deskriptiver Statistiken; lineare Regression
Elementare Begriffe und Techniken des Testens und Schätzens: Maximum-Likelihood-Prinzip; Konfidenzintervalle; Hypothesentests; Fehler erster und zweiter Art

References

Literatur:

E. Behrends: Elementare Stochastik, Springer, 2013
H.-O. Georgii: Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik, De Gruyter, 2007
U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik, Vieweg, 2005
D. Meintrup, S. Schäffler, Stochastik: Theorie und Anwendungen, Springer, 2005.
Die meisten der oben aufgeführten Bücher gibt es online über die UB.

Additional information

Zielgruppe: Studierende ab dem 3. Semester
Voraussetzungen: Grundkenntnisse aus Analysis und Linearer Algebra

Additional appointments

Appointment series

A6/SR 031 Seminarraum

Nicolas Perkowski

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 031 Seminarraum

Nicolas Perkowski

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Tutorial: Stochastics I

LV: 19200602

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2 SWS

Nicolas Perkowski

Immanuel Zachhuber

Practice seminar

Submod: 0084cA1.8.2

Akt: 04.09.2023 12:00

Mon, 12:00 - 14:00 (A7/SR 140 Seminarraum (Hinterhaus))

Fri, 14:00 - 16:00 (A3/SR 115)

Tue, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Additional appointments

Appointment series

A7/SR 140 Seminarraum (Hinterhaus)

Nicolas Perkowski

Immanuel Zachhuber

einmal, ab 16.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 115

Nicolas Perkowski

Immanuel Zachhuber

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A7/SR 140 Seminarraum (Hinterhaus)

Nicolas Perkowski

Immanuel Zachhuber

einmal, ab 17.10.2023, 08:00 - 10:00 (16 Termine)

Module: Analysis II (0084cA1.2)

Analysis II

LV: 19211601

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4 SWS

Claudia Schillings

Lecture

Submod: 0084cA1.2.1

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (T9/Gr. Hörsaal)

Thu, 10:00 - 12:00 (T9/Gr. Hörsaal)

Description

Content

Additions to Analysis I. Non-authentic integrals
Uniform convergence of function sequences. Power series. Sentence of Taylor.
Elements of topology. Standardized and metric spaces. Open quantities. Convergence. Completed quantities. Consistency. Compactness
Differential calculus of several variables. Partial, total and continuous differentiability. Block via the inverse function. Block of implicit functions.
Iterated integrals.
Ordinary differential equations. Basic terms, elementary solvable differential equations, existential and unambiguous results for systems.

References

O. Forster: Analysis 1 und 2. Vieweg/Springer.
Königsberger, K: Analysis 1,2, Springer.
E. Behrends: Analysis Band 1 und 2, Vieweg/Springer.
H. Heuser: Lehrbuch der Analysis 1 und 2, Teubner/Springer.

Additional appointments

Appointment series

T9/Gr. Hörsaal

Claudia Schillings

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

T9/Gr. Hörsaal

Claudia Schillings

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Analysis II

LV: 19211602

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2 SWS

Claudia Schillings

Practice seminar

Submod: 0084cA1.2.2

Akt: 04.09.2023 12:00

Wed, 08:00 - 10:00 (A3/SR 115)

Fri, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Mon, 10:00 - 12:00 (A6/SR 009 Seminarraum)

Wed, 16:00 - 18:00 (A7/SR 140 Seminarraum (Hinterhaus))

Additional appointments

Appointment series

A3/SR 115

Claudia Schillings

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

A6/SR 009 Seminarraum

Claudia Schillings

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 009 Seminarraum

Claudia Schillings

einmal, ab 16.10.2023, 10:00 - 12:00 (16 Termine)

A7/SR 140 Seminarraum (Hinterhaus)

Claudia Schillings

einmal, ab 18.10.2023, 16:00 - 18:00 (16 Termine)

Module: Lineare Algebra II (0084cA1.5)

Linear Algebra II

LV: 19211701

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4 SWS

Niels Lindner

Lecture

Submod: 0084cA1.5.1

Akt: 04.09.2023 12:00

Fri, 08:00 - 10:00 (A3/Hs 001 Hörsaal)

Wed, 12:00 - 14:00 (A3/Hs 001 Hörsaal)

Description

Contents:

Determinants
Eigenvalues and eigenvectors: diagonalizability, trigonalizability, Cayley-Hamilton theorem, Jordan normal form
Bilinear forms
Vector spaces with scalar product: Euclidean and unitary vector spaces, orthogonal projection, isometries, self-adjoint linear maps, Gram-Schmidt orthonormalization, principal axis transformation

Prerequisites:
Linear Algebra I

Literature:
will be announced in the lecture

Additional information

Whiteboard: Signing up for the course with the FU Whiteboard system is mandatory for participating. Whiteboard will also serve as a course homepage.

Active participation: A problem set will be published every week. Each problem set has to be solved within one week. Submissions are allowed by groups of max. two students. For active participation, 50% of the total possible amount of points have to be reached. Moreover, we expect active participation in the tutorials.

Regular participation: Participating in the lectures is recommended. Participation in the tutorials is required.

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Niels Lindner

einmal, ab 20.10.2023, 08:00 - 10:00 (16 Termine)

A3/Hs 001 Hörsaal

Niels Lindner

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Linear Algebra II

LV: 19211702

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2 SWS

Niels Lindner

Practice seminar

Submod: 0084cA1.5.2

Akt: 04.09.2023 12:00

Tue, 14:00 - 16:00 (A3/SR 119)

Tue, 12:00 - 14:00 (A6/SR 025/026 Seminarraum)

Mon, 10:00 - 12:00 (A6/SR 025/026 Seminarraum)

Fri, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Additional appointments

Appointment series

A3/SR 119

Niels Lindner

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 025/026 Seminarraum

Niels Lindner

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Niels Lindner

einmal, ab 16.10.2023, 10:00 - 12:00 (16 Termine)

A6/SR 025/026 Seminarraum

Niels Lindner

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

Module: Analysis III (0084cA1.3)

Analysis III

LV: 19201301

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4 SWS

Marita Thomas

Lecture

Submod: 0084cA1.3.1

Akt: 04.09.2023 12:00

Thu, 10:00 - 12:00 (A6/SR 031 Seminarraum)

Tue, 10:00 - 12:00 (A6/SR 031 Seminarraum)

Description

The lecture Analysis III is the final lecture of the cycle Analysis I-III.

^{Differentiation and integration in Rn},
extremes with and without constraints,
integration on surfaces,
the integrals of Gauss and Stokes and much more are discussed.

These basics are indispensable for a successful study of mathematics.

References

Literatur

H. Amann, J. Escher: Analysis 2, Birkhäuser Verlag, 2008.
H. Amann, J. Escher: Analysis 3, Birkhäuser Verlag, 2008.
O. Forster: Analysis 2, Springer Verlag, 2012.
O. Forster: Analysis 3, Vieweg+Teubner, 2012.
H. Heuser: Lehrbuch der Analysis 2, Vieweg+Teubner, 2012.
S. Hildebrandt: Analysis 2, Springer Verlag, 2003.
J. Jost: Postmodern Analysis, Springer Verlag, 2008.
K. Königsberger: Analysis 2, Springer Verlag, 2004.
W. Rudin: Principles of Mathematical Analysis, International Series in Pure & Applied Mathematics, 1976.

und für geschichtlich Interessierte:

O. Becker: Grundlagen der Mathematik, Verlag Karl Alber, Freiburg, 1964.
E. Hairer, G. Wanner: Analysis by its History, Springer, 2000.
V.J. Katz: A History of Mathematics, Harper Collins, New York, 1993.

Additional appointments

Appointment series

A6/SR 031 Seminarraum

Marita Thomas

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

A6/SR 031 Seminarraum

Marita Thomas

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Analysis III

LV: 19201302

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2 SWS

Marita Thomas

Sven Tornquist

Practice seminar

Submod: 0084cA1.3.2

Akt: 04.09.2023 12:00

Thu, 08:00 - 10:00 (KöLu24-26/SR 006 Neuro/Mathe)

Wed, 12:00 - 14:00 (A3/SR 119)

Fri, 14:00 - 16:00 (A3/SR 119)

Wed, 10:00 - 12:00 (A3/SR 119)

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

Marita Thomas

Sven Tornquist

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

A3/SR 119

Marita Thomas

Sven Tornquist

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Marita Thomas

Sven Tornquist

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A3/SR 119

Marita Thomas

Sven Tornquist

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

Mathematics (0084d_k120)

Module: Scientific Work in Mathematics (0084dB1.1)

Seminar Discrete Mathematics I

LV: 19202211

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2 SWS

Niels Lindner

Seminar

Submod: 0084dB1.1.1

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (A7/SR 140 Seminarraum (Hinterhaus))

Description

The Seminar on Discrete Mathematics I deals with linear codes. Such codes come into action when information is transmitted via error-prone channels, e.g., when typing card numbers, or in wireless networks. Linear codes use methods of linear algebra and discrete mathematics to detect or even correct transmission errors.

Additional information

Whiteboard: The main communication channel is the Whiteboard system at FU. The list of topics will be announced on the Whiteboard homepage of the course at the beginning of the winter term.

Prerequisites: Solid knowledge of linear algebra and basic knowledge of discrete mathematics is recommended.

Writing a report in professional LaTeX quality (about 5-8 pages) summarizing the main contents of your talk is mandatory for successful participation. The reports should include a literature review. The report has to be submitted before the talk. At least one weak before the final presentations, you will receive feedback on your report.

The final presentations should take about 45 minutes plus time for questions. Participating actively and regularly at all events of the seminar and submitting the summary in time is necessary for passing the seminar.

The final grade is composed of the talk (2/3) and the written report (1/3).

Additional appointments

Appointment series

A7/SR 140 Seminarraum (Hinterhaus)

Niels Lindner

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Masterseminar Stochastics

LV: 19208111

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2 SWS

Nicolas Perkowski

Seminar

Submod: 0084dB1.1.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 007/008 Seminarraum)

Description

Content: The seminar covers advanced topics of stochastics.

Detailed Information can be found on the Homepage of the seminar.

References

Literatur wir in der Vorbesprechung bekanntgegeben.

Literature will be announced in the preliminary discussion

Additional information

Prerequisites: Stochastics I and II.
Target Group: BMS Students, Master students and advanced Bachelor students.

Additional appointments

Appointment series

A6/SR 007/008 Seminarraum

Nicolas Perkowski

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

Seminar zur Visualisierung

LV: 19212411

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2 SWS

Konrad Polthier

Seminar

Submod: 0084cB1.1.1

Akt: 04.09.2023 12:00

Tue, 14:00 - 16:00 (A3/SR 115)

Description

Based on selected research literature, the students work out a relevant topic in visualization and computer graphics.

Usually, research articles are distributed which will be read, understood, presented, and illustrated with examples independently.

Therefore, own illustrations or implementations of the central algorithms can be used.

Every participant prepares a talk of maximally 90 minutes length containing discussion and questions.

Further, every participant writes a preparation to explain the content of the talk in detail and to summarize the topic in a structured way.

Topics are chosen from the following areas:

- general techniques in visualization

- visualization of vector fields

- rendering

- image processing

- smoothing of geometries

- discrete methods on 3D models

- animation

Additional appointments

Appointment series

A3/SR 115

Konrad Polthier

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Seminar Multiscale Methods in Molecular Simulations

LV: 19226511

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2 SWS

Luigi Delle Site

Seminar

Submod: 0084dB1.1.1

Akt: 21.09.2023 14:00

Fri, 12:00 - 14:00 (A3/SR 115)

Description

Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

The discussion will concerns both, specific computational coding and conceptual developments.

References

Related Basic Literature:

(1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

(2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

(3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science

Additional information

Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

Additional appointments

Appointment series

A3/SR 115

Luigi Delle Site

einmal, ab 20.10.2023, 12:00 - 14:00 (16 Termine)

Proseminar/Seminar Mathematik & Nachhaltigkeit

LV: 19229917

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2 SWS

Georg Loho

Seminar / Undergraduate Course

Submod: 0084dB1.1.1

Akt: 22.09.2023 14:00

Wed, 12:00 - 14:00 (A3/ 024 Seminarraum )

Seminar: Advanced Topics in Dynamical Systems

LV: 19239911

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2 SWS

Bernold Fiedler

Isabelle Schneider

Seminar

Submod: 0084dB1.1.1

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A7/SR 140 Seminarraum (Hinterhaus))

Proseminar/Seminar Mathematik, KI & Lehre

LV: 19240317

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2 SWS

Georg Loho

Seminar / Undergraduate Course

Submod: 0084dB1.1.1

Akt: 22.09.2023 16:00

Tue, 10:00 - 12:00 (A3/ 024 Seminarraum )

Sobolev- and BV-spaces

LV: 19247111

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2 SWS

Marita Thomas

Seminar

Submod: 0084dB1.1.1

Akt: 04.09.2023 12:00

Tue, 16:00 - 18:00 (A3/ 024 Seminarraum )

Module: Functional Analysis (0084dB2.2)

Functional Analysis

LV: 19201901

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4 SWS

Dirk Werner

Lecture

Submod: 0084cB2.2.1

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (A6/SR 025/026 Seminarraum)

Thu, 10:00 - 12:00 (A6/SR 025/026 Seminarraum)

Description

Target group: Students from the 3rd/4th semester on.
Requirements: Good command of the material of the lectures Analysis I/II and Linear Algebra I/II.

References

Literatur:

Dirk Werner: Funktionalanalysis, 8. Auflage, Springer-Verlag 2018

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Dirk Werner

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

A6/SR 025/026 Seminarraum

Dirk Werner

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

Tutorial: Functional Analysis

LV: 19201902

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2 SWS

Dirk Werner

Immanuel Zachhuber

Practice seminar

Submod: 0084cB2.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A3/SR 115)

Description

Dirk Werner: Funktionalanalysis, 6. Auflage, Springer-Verlag 2007, ISBN 978-3-540-72533-6
Hans Wilhelm Alt: Lineare Funktionalanalysis : eine anwendungsorientierte Einführung. 5. Auflage. Springer-Verlag, 2006, ISBN 3-540-34186-2
Harro Heuser: Funktionalanalysis: Theorie und Anwendung. 3. Auflage. Teubner-Verlag, 1992, ISBN 3-519-22206-X

Additional appointments

Appointment series

A3/SR 115

Dirk Werner

Immanuel Zachhuber

einmal, ab 20.10.2023, 10:00 - 12:00 (16 Termine)

Module: Algebra and Number Theory (0084dB2.5)

Algebra and Theory of Numbers

LV: 19200701

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB2.5.1

Akt: 04.09.2023 12:00

Wed, 08:00 - 10:00 (Hs A (Raum B.006, 200 Pl.))

Mon, 08:00 - 10:00 (T9/Gr. Hörsaal)

Description

Subject matter:
Selected topics from:

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

Hs A (Raum B.006, 200 Pl.)

Alexander Schmitt

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

T9/Gr. Hörsaal

Alexander Schmitt

einmal, ab 16.10.2023, 08:00 - 10:00 (16 Termine)

Practice seminar for Algebra and Theory of Numbers

LV: 19200702

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2 SWS

Alexander Schmitt

Practice seminar

Submod: 0084cB2.5.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (A3/SR 119)

Thu, 12:00 - 14:00 (T9/049 Seminarraum)

Wed, 14:00 - 16:00 (A3/SR 119)

Additional appointments

Appointment series

A3/SR 119

Alexander Schmitt

einmal, ab 18.10.2023, 16:00 - 18:00 (16 Termine)

T9/049 Seminarraum

Alexander Schmitt

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Alexander Schmitt

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Module: Mathematical Project (0084dB2.9)

Mathematical modeling in discussions of societal challenges

LV: 19246021

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4 SWS

Anina Mischau

Sarah Wolf

Joshua Wiebe

Projekt

Submod: 0084dB2.9.1

Akt: 22.09.2023 14:00

Wed, 14:00 - 18:00 (A3/SR 115)

Description

Dieses Projektseminar steht in Verbindung mit „Schule@DecisionTheatreLab“, einem Experimentallabor für Wissenschaftskommunikation gefördert von der Berlin University Alliance und dem Excellenzcluster MATH+. Das Projekt entwickelt ein innovatives Kommunikationsformat basierend auf mathematischen Modellen und führt dieses mit Gruppen von Schüler*innen durch. Decision Theatres sind Diskussionsveranstaltungen, in denen Teilnehmende eine gesellschaftliche Herausforderung mit Wissenschaftler*innen diskutieren und dabei mit einem mathematischen Modell experimentieren können.

Das Projektseminar ist interdisziplinär ausgerichtet und verbindet mathematische Forschung mit didaktischen und sozialwissenschaftlichen Perspektiven. So werden z.B. einerseits Grundlagen des Kommunikationsformats vorgestellt (bspw. mathematische und agenten-basierte Modellierung oder die Arbeit mit empirischen Informationen), aber auch ein Bezug zum Mathematikunterricht an Schulen und damit zur Vermittlung von Mathematik erarbeitet. Andererseits arbeiten die Studierenden direkt an der Vorbereitung, Durchführung, Beobachtung und Auswertung von Decision Theatre Veranstaltungen mit.

In dem Projektseminar ist ein intensiver Austausch zwischen Studierenden aus dem Monostudiengang und aus dem Lehramtsstudiengang der Mathematik intendiert. Über das Kennenlernen von und die Mitwirkung in einem aktuellen mathematischen wie didaktischen Forschungsprojekt und dessen Abläufe wie Methoden erhalten die Studierende die Chance jeweils ihren Blick über den Tellerand ihres Studiengangs hinaus zu erweitern. Darüber hinaus ergeben sich jeweils folgende spezifische Schwerpunkte.

Fokus für Studierende im Studiengang Lehramt Mathematik:

Chancen der Einbettung des Kommunikationsformates im Mathematikunterricht
neue Perspektiven auf Modellieren im Unterricht
Unterrichtsbeobachtung
Interaktion mit Schüler*innengruppen

Fokus für Studierende im Studiengang Mathematik (Bachelor):

Agenten-basierte Modelle: Definition, Implementierung, Sensitivitätsanalyse und Kalibrierung
synthetische Populationen: Daten, Algorithmen, Software Tools
Weiterentwicklung von mathematischen Modellen im Dialog mit Nicht-Wissenschaftler*innen (z.B. Schüler*innen)

References

Wird in der ersten Sitzung bekannt gegeben.

Additional information

Die Veranstaltungen mit Schüler*innen können ggf außerhalb der üblichen Veranstaltungszeit stattfinden.

Voraussetzungen:

mindestens ein Interesse an Programmieren, grundlegende Programmierkenntnisse wären wünschenswert
Interesse an mathematischer Modellierung und gesellschaftlichen Diskursen
im Kurs wird die Modellierungsumgebung NetLogo verwendet, die Bereitschaft, sich hier einzuarbeiten, ist also erforderlich

Additional appointments

Appointment series

A3/SR 115

Anina Mischau

Sarah Wolf

Joshua Wiebe

einmal, ab 18.10.2023, 14:00 - 18:00 (16 Termine)

Module: Special topics in Mathematics (0084dB2.11)

Discrete Geometrie I

LV: 19202001

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4 SWS

No lecturers

Lecture

Submod: 0084cB3.2.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (KöLu24-26/SR 006 Neuro/Mathe)

Tue, 10:00 - 12:00 (T9/SR 006 Seminarraum)

Description

polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Polytope theory
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes, shellability
shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
graphs, diameters, Hirsch (ex-)conjecture
Geometry of linear programming
linear programs, simplex algorithm, LP-duality
Combinatorial geometry / Geometric combinatorics
Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
Arrangements, zonotopes, zonotopal tilings, oriented matroids
Examples, examples, examples
regular polytopes, centrally symmetric polytopes
extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
combinatorial optimization and 0/1-polytopes

References

G.M. Ziegler "Lectures in Polytopes"
J. Matousek "Lectures on Discrete Geometry"
Further literature will be announced in class.

Additional information

Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

No lecturers

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

T9/SR 006 Seminarraum

No lecturers

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Discrete Geometrie I

LV: 19202002

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2 SWS

Sophie Rehberg

Practice seminar

Submod: 0084cB3.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 032 Seminarraum)

Module: Special topics in Pure Mathematics (0084dB2.12)

Mathematisches Panorama

LV: 19236101

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2 SWS

Anina Mischau

Lecture

Submod: 0084dB2.12.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (A6/SR 025/026 Seminarraum)

Description

This is for a course in German - Short explanation in English:

Mathematical Panorama is a two-hour overview course for First-Semester students of Mathematics (in particular, but not only, for teacher students) that presents the wide field of modern Mathematics - its history, its topics, its problems, its methods, some basic concepts, applications, etc.

This could be augmented by another two-hour course Mathematical Panorama II (next summer); both courses together count as the four-hour course Panorama of Mathematics (which is listed in some curricula at FU Berlin). There will also be a seminar in the summer term, where some topics connected to the course are treated actively (by the participants).

References

Günter M. Ziegler und Andreas Loos: Panorama der Mathematik, Springer-Spektrum 2018, in Vorbereitung (wird in Auszügen zur Verfügung gestellt)
Hans Wußing, 6000 Jahre Mathematik: Eine kulturgeschichtliche Zeitreise, Springer 2009
- Band 1: Von den Anfängen bis Leibniz und Newton
- Band 2: Von Euler bis zur Gegenwart
Heinz-Wilhelm Alten et al., 4000 Jahre Algebra, Springer 2008
Christoph J. Scriba, 5000 Jahre Geometrie, Springer 2009
Heinz Niels Jahnke, Geschichte der Analysis: Texte zur Didaktik der Mathematik, Spektrum 1999
Richard Courant und Herbert Robbins, What is Mathematics?, Oxford UP 1941 (deutsch: Springer 2010)
Phillip J. Davis, Reuben Hersh, The Mathematical Experience, Mariner Books 1999

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Anina Mischau

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

Übung zu: Mathematisches Panorama

LV: 19236102

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2 SWS

Marcus Weber

Anina Mischau

Practice seminar

Submod: 0084dB2.12.2

Akt: 04.09.2023 12:00

Mon, 16:00 - 18:00 (A6/SR 025/026 Seminarraum)

Module: Algebra I (0084dB3.3)

Basic Module: Algebra I

LV: 19202501

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB3.3.1

Akt: 04.09.2023 12:00

Mon, 12:00 - 16:00 (A3/Hs 001 Hörsaal)

Description

Content

Affine algebraic varieties
Rings, ideals, and modules
Noetherian rings
Local rings and localization
Primary decompositione
Finite and integral extensions
Dimension theory
Regular rings

Target Group

Students with the prerequisites mentioned below.

Prerequisites

Linear Algebra I+II
Algebra and Number Theory

References

Literature

Atiyah, M.F.; Macdonald, I.G.: Einführung in die kommutative Algebra. Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. 1969 ix+128 Seiten (This book is the best introduction to the subject with brief and clear descriptions.)
Further literature will be announced in the course.

Additional information

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexander Schmitt

einmal, ab 23.10.2023, 12:00 - 16:00 (15 Termine)

Practice seminar for Basic Module: Algebra I

LV: 19202502

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2 SWS

Marwan Benyoussef

Practice seminar

Submod: 0084cB3.3.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (KöLu24-26/SR 006 Neuro/Mathe)

Module: Numerical Mathematics II (0084dB3.4)

Basic Module: Numeric II

LV: 19202101

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4 SWS

Ana Djurdjevac

Lecture

Submod: 0084cB3.4.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 032 Seminarraum)

Mon, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Description

Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ana Djurdjevac

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Ana Djurdjevac

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Basic Module: Numeric II

LV: 19202102

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2 SWS

No lecturers

Practice seminar

Submod: 0084cB3.4.2

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 025/026 Seminarraum)

Module: Differential Geometry I (0084dB3.5)

Differential Geometry I

LV: 19202601

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4 SWS

Konrad Polthier

Lecture

Submod: 0084cB3.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A3/SR 119)

Thu, 12:00 - 14:00 (A3/SR 119)

Description

Topics of the lecture will be:

curves and surfaces in Euclidean space,
metrics and (Riemannian) manifolds,
surface tension, notions of curvature,
vector fields, tensors, covariant derivative
geodesic curves, exponential map,
Gauß-Bonnet theorem, topology,
connection to discrete differential geometry.

This course is a BMS course and will be held in English on request.

Prerequisits:

Analysis I, II, III and Linear Algebra I, II

References

Literature

W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

Additional information

For further information, see Lecture Homepage.

Additional appointments

Appointment series

A3/SR 119

Konrad Polthier

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Konrad Polthier

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Differential Geometry I

LV: 19202602

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2 SWS

Konrad Polthier

Eric Zimmermann

Practice seminar

Submod: 0084cB3.5.2

Akt: 22.09.2023 16:00

Fri, 08:00 - 10:00 (A3/SR 115)

Fri, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Module: Higher Algorithmics with applications (0084dB3.7)

Advanced Algorithms

LV: 19303501

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4 SWS

László Kozma

Lecture

Submod: 0084dB3.7.1

Akt: 04.09.2023 12:00

Mon, 10:00 - 12:00 (T9/SR 005 Übungsraum)

Fri, 10:00 - 12:00 (T9/SR 005 Übungsraum)

Description

This course will focus on the design and analysis of algorithms, with topics including:

general principles of algorithm design,
randomized algorithms,
dynamic programming,
flow problems on graphs,
amortized analysis and advanced data structures,
theory of NP-completeness,
approximation methods for hard problems,
other topics.

Prerequisites are basic knowledge of algorithms and relevant mathematics. All Bachelor and Master students interested in advanced algorithmic techniques are welcome. Lectures are in English.

References

Cormen, Leiserson, Rivest, Stein: Introduction to Algorithms, 4th Ed. MIT Press 2022
Kleinberg, Tardos: Algorithm Design Addison-Wesley 2005.

Additional information

Target audience

All Master and Bachelor students who are interested in algorithms.

Prerequisites

Basic familiarity with the design and analysis of algorithms.

Additional appointments

Appointment series

T9/SR 005 Übungsraum

László Kozma

einmal, ab 23.10.2023, 10:00 - 12:00 (15 Termine)

T9/SR 005 Übungsraum

László Kozma

einmal, ab 20.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Advanced Algorithms

LV: 19303502

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2 SWS

László Kozma

Practice seminar

Submod: 0084dB3.7.2

Akt: 04.09.2023 12:00

Wed, 14:00 - 16:00 (T9/049 Seminarraum)

Wed, 08:00 - 10:00 (A7/SR 031)

Module: Analysis I (0084dA1.1)

Analysis I

LV: 19202801

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4 SWS

Holger Reich

Lecture

Submod: 0084cA1.1.1

Akt: 04.09.2023 12:00

Thu, 10:00 - 12:00 (A3/Hs 001 Hörsaal)

Tue, 10:00 - 12:00 (A3/Hs 001 Hörsaal)

Description

Content:
This is the first part of a three semester introduction into the basic mathematical field of Analysis. Differential and integral calculus in a real variable will be covered. Topics:

fundamentals, elementary logic, ordered pairs, relations, functions, domain and range of a function, inverse functions (injectivity, surjectivity)
numbers, induction, calculations in R, C
arrangement of R, maximum and minimum, supremum and infimum of real sets, supremum / infimum completeness of R, absolute value of a real number, Q is dense in R
sequences and series, limits, cauchy sequences, convergence criteria, series and basic principles of convergence
topological aspects of R, open, closed, and compact real sets
sequences of functions, series of functions, power series
properties of functions, boundedness, monotony, convexity
continuity, limits and continuity of functions, uniform continuity, intermediate value theorems, continuity and compactness
differentiability, concept of the derivative, differentiation rules, mean value theorem, local and global extrema, curvature, monotony, convexity
elementary functions, rational functions, root functions, exponential functions, angular functions, hyperbolic functions, real logarithm, inverse trigonometric functions, curve sketching
beginnings of integral calculus

Detailed Information can be found on the Homepage of 19202801 Analysis I.

References

Literature:

Bröcker, Theodor: Analysis 1, Spektrum der Wissenschaft-Verlag.
Forster, Otto: Analysis 1, Vieweg-Verlag.
Spivak, Michael: Calculus, 4th Edition.

Viele Analysis Bücher sind auch über die Fachbibliothek der FU Berlin elektronisch verfügbar.

Bei Schwierigkeiten mit den Grundbegriffen Menge, Abbildung etc. ist die folgende Ausarbeitung empfehlenswert:

Scheerer, Hans: Brückenkurs, Skript FU Berlin 2006.

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Holger Reich

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

A3/Hs 001 Hörsaal

Holger Reich

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Tutorial: Analysis I

LV: 19202802

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2 SWS

Holger Reich

Practice seminar

Submod: 0084cA1.1.2

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A3/SR 115)

Wed, 12:00 - 14:00 (A7/SR 140 Seminarraum (Hinterhaus))

Wed, 12:00 - 14:00 (A3/SR 115)

Thu, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Additional appointments

Appointment series

A3/SR 115

Holger Reich

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A7/SR 140 Seminarraum (Hinterhaus)

Holger Reich

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 115

Holger Reich

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 009 Seminarraum

Holger Reich

einmal, ab 19.10.2023, 14:00 - 16:00 (16 Termine)

Module: Analysis II (0084dA1.2)

Analysis II

LV: 19211601

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4 SWS

Claudia Schillings

Lecture

Submod: 0084cA1.2.1

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (T9/Gr. Hörsaal)

Thu, 10:00 - 12:00 (T9/Gr. Hörsaal)

Description

Content

Additions to Analysis I. Non-authentic integrals
Uniform convergence of function sequences. Power series. Sentence of Taylor.
Elements of topology. Standardized and metric spaces. Open quantities. Convergence. Completed quantities. Consistency. Compactness
Differential calculus of several variables. Partial, total and continuous differentiability. Block via the inverse function. Block of implicit functions.
Iterated integrals.
Ordinary differential equations. Basic terms, elementary solvable differential equations, existential and unambiguous results for systems.

References

O. Forster: Analysis 1 und 2. Vieweg/Springer.
Königsberger, K: Analysis 1,2, Springer.
E. Behrends: Analysis Band 1 und 2, Vieweg/Springer.
H. Heuser: Lehrbuch der Analysis 1 und 2, Teubner/Springer.

Additional appointments

Appointment series

T9/Gr. Hörsaal

Claudia Schillings

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

T9/Gr. Hörsaal

Claudia Schillings

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Analysis II

LV: 19211602

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2 SWS

Claudia Schillings

Practice seminar

Submod: 0084cA1.2.2

Akt: 04.09.2023 12:00

Wed, 08:00 - 10:00 (A3/SR 115)

Fri, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Mon, 10:00 - 12:00 (A6/SR 009 Seminarraum)

Wed, 16:00 - 18:00 (A7/SR 140 Seminarraum (Hinterhaus))

Additional appointments

Appointment series

A3/SR 115

Claudia Schillings

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

A6/SR 009 Seminarraum

Claudia Schillings

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 009 Seminarraum

Claudia Schillings

einmal, ab 16.10.2023, 10:00 - 12:00 (16 Termine)

A7/SR 140 Seminarraum (Hinterhaus)

Claudia Schillings

einmal, ab 18.10.2023, 16:00 - 18:00 (16 Termine)

Module: Analysis III (0084dA1.3)

Analysis III

LV: 19201301

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4 SWS

Marita Thomas

Lecture

Submod: 0084cA1.3.1

Akt: 04.09.2023 12:00

Thu, 10:00 - 12:00 (A6/SR 031 Seminarraum)

Tue, 10:00 - 12:00 (A6/SR 031 Seminarraum)

Description

The lecture Analysis III is the final lecture of the cycle Analysis I-III.

^{Differentiation and integration in Rn},
extremes with and without constraints,
integration on surfaces,
the integrals of Gauss and Stokes and much more are discussed.

These basics are indispensable for a successful study of mathematics.

References

Literatur

H. Amann, J. Escher: Analysis 2, Birkhäuser Verlag, 2008.
H. Amann, J. Escher: Analysis 3, Birkhäuser Verlag, 2008.
O. Forster: Analysis 2, Springer Verlag, 2012.
O. Forster: Analysis 3, Vieweg+Teubner, 2012.
H. Heuser: Lehrbuch der Analysis 2, Vieweg+Teubner, 2012.
S. Hildebrandt: Analysis 2, Springer Verlag, 2003.
J. Jost: Postmodern Analysis, Springer Verlag, 2008.
K. Königsberger: Analysis 2, Springer Verlag, 2004.
W. Rudin: Principles of Mathematical Analysis, International Series in Pure & Applied Mathematics, 1976.

und für geschichtlich Interessierte:

O. Becker: Grundlagen der Mathematik, Verlag Karl Alber, Freiburg, 1964.
E. Hairer, G. Wanner: Analysis by its History, Springer, 2000.
V.J. Katz: A History of Mathematics, Harper Collins, New York, 1993.

Additional appointments

Appointment series

A6/SR 031 Seminarraum

Marita Thomas

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

A6/SR 031 Seminarraum

Marita Thomas

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Analysis III

LV: 19201302

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2 SWS

Marita Thomas

Sven Tornquist

Practice seminar

Submod: 0084cA1.3.2

Akt: 04.09.2023 12:00

Thu, 08:00 - 10:00 (KöLu24-26/SR 006 Neuro/Mathe)

Wed, 12:00 - 14:00 (A3/SR 119)

Fri, 14:00 - 16:00 (A3/SR 119)

Wed, 10:00 - 12:00 (A3/SR 119)

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

Marita Thomas

Sven Tornquist

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

A3/SR 119

Marita Thomas

Sven Tornquist

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Marita Thomas

Sven Tornquist

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A3/SR 119

Marita Thomas

Sven Tornquist

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

Module: Linear Algebra I (0084dA1.4)

Linear Algebra I

LV: 19201401

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4 SWS

Alexandru Constantinescu

Lecture

Submod: 0084cA1.4.1

Akt: 04.09.2023 12:00

Mon, 08:00 - 10:00 (A3/Hs 001 Hörsaal)

Wed, 08:00 - 10:00 (A3/Hs 001 Hörsaal)

Description

Content:

Basic terms/concepts: sets, maps, equivalence relations, groups, rings,
fields
Linear equation systems: solvability criteria, Gauss algorithm
Vector spaces: linear independence, generating systems and bases, dimension,
subspaces, quotient spaces, cross products in R3
Linear maps: image and rank, relationship to matrices, behaviour under
change of basis
Dual vector spaces: multilinear forms, alternating and symmetric bilinear
forms, relationship to matices, change of basis
Determinants: Cramer's rule, Eigenvalues and Eigenvectors

Prerequisites:

Participation in the preparatory course (Brückenkurs) is highly recommended.

References

Siegfried Bosch, Lineare Algebra, 4. Auflage, Springer-Verlag, 2008;
Gerd Fischer, Lernbuch Lineare Algebra und Analytische Geometrie, Springer-Verlag, 2017;
Bartel Leendert van der Waerden, Algebra Volume I, 9th Edition, Springer 1993;

Zu den Grundlagen

Kevin Houston, Wie man mathematisch denkt: Eine Einführung in die mathematische Arbeitstechnik für Studienanfänger, Spektrum Akademischer Verlag, 2012

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexandru Constantinescu

einmal, ab 16.10.2023, 08:00 - 10:00 (16 Termine)

A3/Hs 001 Hörsaal

Alexandru Constantinescu

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Practice seminar for Linear Algebra I

LV: 19201402

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2 SWS

N.N.

Practice seminar

Submod: 0084cA1.4.2

Akt: 04.09.2023 12:00

Fri, 14:00 - 16:00 (A3/SR 120)

Thu, 08:00 - 10:00 (A3/ 024 Seminarraum )

Tue, 08:00 - 10:00 (A3/SR 119)

Wed, 14:00 - 16:00 (A3/ 024 Seminarraum )

Additional appointments

Appointment series

A3/SR 120

N.N.

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A3/ 024 Seminarraum

N.N.

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

A3/SR 119

N.N.

einmal, ab 17.10.2023, 08:00 - 10:00 (16 Termine)

A3/ 024 Seminarraum

N.N.

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Module: Linear Algebra II (0084dA1.5)

Linear Algebra II

LV: 19211701

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4 SWS

Niels Lindner

Lecture

Submod: 0084cA1.5.1

Akt: 04.09.2023 12:00

Fri, 08:00 - 10:00 (A3/Hs 001 Hörsaal)

Wed, 12:00 - 14:00 (A3/Hs 001 Hörsaal)

Description

Contents:

Determinants
Eigenvalues and eigenvectors: diagonalizability, trigonalizability, Cayley-Hamilton theorem, Jordan normal form
Bilinear forms
Vector spaces with scalar product: Euclidean and unitary vector spaces, orthogonal projection, isometries, self-adjoint linear maps, Gram-Schmidt orthonormalization, principal axis transformation

Prerequisites:
Linear Algebra I

Literature:
will be announced in the lecture

Additional information

Whiteboard: Signing up for the course with the FU Whiteboard system is mandatory for participating. Whiteboard will also serve as a course homepage.

Regular participation: Participating in the lectures is recommended. Participation in the tutorials is required.

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Niels Lindner

einmal, ab 20.10.2023, 08:00 - 10:00 (16 Termine)

A3/Hs 001 Hörsaal

Niels Lindner

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Linear Algebra II

LV: 19211702

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2 SWS

Niels Lindner

Practice seminar

Submod: 0084cA1.5.2

Akt: 04.09.2023 12:00

Tue, 14:00 - 16:00 (A3/SR 119)

Tue, 12:00 - 14:00 (A6/SR 025/026 Seminarraum)

Mon, 10:00 - 12:00 (A6/SR 025/026 Seminarraum)

Fri, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Additional appointments

Appointment series

A3/SR 119

Niels Lindner

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 025/026 Seminarraum

Niels Lindner

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Niels Lindner

einmal, ab 16.10.2023, 10:00 - 12:00 (16 Termine)

A6/SR 025/026 Seminarraum

Niels Lindner

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

Module: Computer-Oriented Mathematics I (0084dA1.6)

Computerorientated Mathematics I (5 LP)

LV: 19200501

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2 SWS

Claudia Schillings

Lecture

Submod: 0084cA1.6.1

Akt: 04.09.2023 12:00

Fri, 12:00 - 14:00 (T9/Gr. Hörsaal)

Description

Homepage: All current information on lectures and lectures

References

Literatur: R. Kornhuber, C. Schuette, A. Fest: Mit Zahlen Rechnen (Skript zur Vorlesung)

Additional appointments

Appointment series

T9/Gr. Hörsaal

Claudia Schillings

einmal, ab 20.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Computerorientated Mathematics I (5 LP)

LV: 19200502

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2 SWS

Vesa Kaarnioja

Claudia Schillings

Practice seminar

Submod: 0084cA1.6.2

Akt: 15.09.2023 14:00

Fri, 16:00 - 18:00 (A3/SR 120)

Mon, 10:00 - 12:00 (A3/SR 120)

Wed, 10:00 - 12:00 (A3/SR 120)

Fri, 14:00 - 16:00 (A3/019 Seminarraum)

Fri, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Thu, 08:00 - 10:00 (A3/SR 119)

Mon, 16:00 - 18:00 (A3/SR 120)

Mon, 12:00 - 14:00 (A3/SR 119)

Mon, 14:00 - 16:00 (A3/SR 119)

Additional appointments

Appointment series

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 20.10.2023, 16:00 - 18:00 (16 Termine)

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 10:00 - 12:00 (16 Termine)

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

A3/019 Seminarraum

Vesa Kaarnioja

Claudia Schillings

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 007/008 Seminarraum

Vesa Kaarnioja

Claudia Schillings

einmal, ab 20.10.2023, 14:00 - 16:00 (17 Termine)

A3/SR 119

Vesa Kaarnioja

Claudia Schillings

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

A3/SR 120

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 16:00 - 18:00 (16 Termine)

A3/SR 119

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Vesa Kaarnioja

Claudia Schillings

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Module: Stochastics I (0084dA1.8)

Stochastics I

LV: 19200601

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4 SWS

Nicolas Perkowski

Lecture

Submod: 0084cA1.8.1

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A6/SR 031 Seminarraum)

Wed, 08:00 - 10:00 (A6/SR 031 Seminarraum)

Description

Inhalt:

Prinzipien des Zählens; Elemente der Kombinatorik
Modelle vom Zufall abhängiger Vorgänge: Wahrscheinlichkeitsräume, Wahrscheinlichkeitsmaße
Bedingte Wahrscheinlichkeiten; Unabhängigkeit; Bayes'sche Regel
Zufallsvariablen und ihre Verteilungen; Kenngrössen der Verteilungen: Erwartungswert und Varianz
Diskrete Verteilungen: Laplace-Verteilung; Binomialverteilung; geometrische Verteilung
Approximation der Binomialverteilung durch die Normalverteilung;
Approximation der Binomialverteilung durch die Poissonverteilung
Verteilungen mit Dichten: Gleichverteilung; Normalverteilung; Exponentialverteilung
Gemeinsame Verteilungen von mehreren Zufallsvariablen: diskret und mit Dichten; Unabhängigkeit von Zufallsvariablen; bedingte Verteilungen; Summen unabhängiger Zufallsvariablen und ihre Verteilungen
Kenngrößen gemeinsamer Verteilungen: Erwartungswert, Kovarianz und Korrelation; bedingte Erwartung
Grenzwertsätze: schwaches Gesetz der großen Zahl und relative Häufigkeiten; der zentrale Grenzwertsatz
Datenanalyse und deskriptive Statistik: Histogramme; empirische Verteilung; Kenngrößen von Stichprobenverteilungen; Beispiele irreführender deskriptiver Statistiken; lineare Regression
Elementare Begriffe und Techniken des Testens und Schätzens: Maximum-Likelihood-Prinzip; Konfidenzintervalle; Hypothesentests; Fehler erster und zweiter Art

References

Literatur:

E. Behrends: Elementare Stochastik, Springer, 2013
H.-O. Georgii: Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik, De Gruyter, 2007
U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik, Vieweg, 2005
D. Meintrup, S. Schäffler, Stochastik: Theorie und Anwendungen, Springer, 2005.
Die meisten der oben aufgeführten Bücher gibt es online über die UB.

Additional information

Zielgruppe: Studierende ab dem 3. Semester
Voraussetzungen: Grundkenntnisse aus Analysis und Linearer Algebra

Additional appointments

Appointment series

A6/SR 031 Seminarraum

Nicolas Perkowski

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 031 Seminarraum

Nicolas Perkowski

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Tutorial: Stochastics I

LV: 19200602

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2 SWS

Nicolas Perkowski

Immanuel Zachhuber

Practice seminar

Submod: 0084cA1.8.2

Akt: 04.09.2023 12:00

Mon, 12:00 - 14:00 (A7/SR 140 Seminarraum (Hinterhaus))

Fri, 14:00 - 16:00 (A3/SR 115)

Tue, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Additional appointments

Appointment series

A7/SR 140 Seminarraum (Hinterhaus)

Nicolas Perkowski

Immanuel Zachhuber

einmal, ab 16.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 115

Nicolas Perkowski

Immanuel Zachhuber

einmal, ab 20.10.2023, 14:00 - 16:00 (16 Termine)

A7/SR 140 Seminarraum (Hinterhaus)

Nicolas Perkowski

Immanuel Zachhuber

einmal, ab 17.10.2023, 08:00 - 10:00 (16 Termine)

Master's programme in Mathematics

Master's programme in Mathematics (2011 study regulations) (0280b_MA120)

Module: Basismodul Differentialgeometrie I (0280bA1.1)

Differential Geometry I

LV: 19202601

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4 SWS

Konrad Polthier

Lecture

Submod: 0084cB3.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A3/SR 119)

Thu, 12:00 - 14:00 (A3/SR 119)

Description

Topics of the lecture will be:

curves and surfaces in Euclidean space,
metrics and (Riemannian) manifolds,
surface tension, notions of curvature,
vector fields, tensors, covariant derivative
geodesic curves, exponential map,
Gauß-Bonnet theorem, topology,
connection to discrete differential geometry.

This course is a BMS course and will be held in English on request.

Prerequisits:

Analysis I, II, III and Linear Algebra I, II

References

Literature

W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

Additional information

For further information, see Lecture Homepage.

Additional appointments

Appointment series

A3/SR 119

Konrad Polthier

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Konrad Polthier

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Differential Geometry I

LV: 19202602

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2 SWS

Konrad Polthier

Eric Zimmermann

Practice seminar

Submod: 0084cB3.5.2

Akt: 22.09.2023 16:00

Fri, 08:00 - 10:00 (A3/SR 115)

Fri, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Module: Introductory Module Algebra I (0280bA2.1)

Basic Module: Algebra I

LV: 19202501

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB3.3.1

Akt: 04.09.2023 12:00

Mon, 12:00 - 16:00 (A3/Hs 001 Hörsaal)

Description

Content

Affine algebraic varieties
Rings, ideals, and modules
Noetherian rings
Local rings and localization
Primary decompositione
Finite and integral extensions
Dimension theory
Regular rings

Target Group

Students with the prerequisites mentioned below.

Prerequisites

Linear Algebra I+II
Algebra and Number Theory

References

Literature

Atiyah, M.F.; Macdonald, I.G.: Einführung in die kommutative Algebra. Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. 1969 ix+128 Seiten (This book is the best introduction to the subject with brief and clear descriptions.)
Further literature will be announced in the course.

Additional information

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexander Schmitt

einmal, ab 23.10.2023, 12:00 - 16:00 (15 Termine)

Practice seminar for Basic Module: Algebra I

LV: 19202502

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2 SWS

Marwan Benyoussef

Practice seminar

Submod: 0084cB3.3.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (KöLu24-26/SR 006 Neuro/Mathe)

Module: Aufbaumodul Algebra III (0280bA2.3)

Advanced Module: Algebra III

LV: 19222301

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2 SWS

Klaus Altmann

Lecture

Submod: 0280bA2.3.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 009 Seminarraum)

Description

Course contents: a selection of the following topics

properties of morphisms (proper, projective, smooth)
divisors
(quasi-)coherent sheaves
cohomology
Hilbert functions

References

G.R. Kempf: Algebraic varieties. London Mathematical Society Lecture Note
Series. 172. Cambridge: Cambridge University Press. 1993. x, 163 p.

A. Schmitt: Homological algebra, lecture notes.

J.L. Taylor: Several complex variables with connections to algebraic
geometry and Lie groups. Graduate Studies in Mathematics. 46. Providence,
RI: American Mathematical Society. 2002. xvi, 507 p.

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Klaus Altmann

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Advanced Module: Algebra III

LV: 19222302

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2 SWS

Klaus Altmann

Practice seminar

Submod: 0280bA2.3.2

Akt: 04.09.2023 12:00

Wed, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Module: Basismodul Diskrete Mathematik II (0280bA3.2)

Discrete Mathematics II - Extremal Comb.

LV: 19208601

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4 SWS

Tibor Szabo

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 025/026 Seminarraum)

Tue, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

References

The material is selected from several textbooks:

N. Alon and J. Spencer, The Probabilistic Method

L. Babai and P. Frankl, Linear Algebra Methods in Combinatorics

R. Diestel, Graph Theory

S. Jukna, Extremal Combinatorics

J. Matoušek, Using the Borsuk-Ulam Theorem

J. van Lint and R. Wilson, A Course in Combinatorics

D. West, Introduction to Graph Theory

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Tutorial Discrete Mathematics II - Extremal Comb.

LV: 19208602

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2 SWS

Tibor Szabo

Silas Rathke

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Tue, 16:00 - 18:00 (A6/SR 007/008 Seminarraum)

Diskrete Mathematik II - Optimierung

LV: 19234401

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4 SWS

Ralf Borndörfer

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Description

This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

Contents

Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness 
Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
Shortest Paths: nonnegative weights, general weights, all pairs
Network Flows: Max-Flow-Min-Cut Theorem, augmenting Paths, minimum cost flows, transport and allocation problems
Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
Foundations of linear optimization: Farkas Lemma, Duality Theorem
Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
Interior points and ellipsoid method: basics

Audience

This course is aimed at mathematics students with previous knowledge of discrete mathematics, linear algebra and analysis. Some exercises require the use of a computer.

References

M. Grötschel, Lineare Optimierung, one of the scripts

V. Chvátal, Linear Programming, Freeman 1983

Additional

Garey&Johnson, Computers and Intractability, 1979 (Complexity Theory)

Bertsimas&Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

Korte&Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

Additional information

Credit

This course can be chosen as Discrete Mathematics II (DM II).

If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module.

Language

This lecture is in English.

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Übung zu Optimierung I

LV: 19234402

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (A3/SR 115)

Module: Basismodul Diskrete Geometrie I (0280bA3.3)

Discrete Geometrie I

LV: 19202001

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4 SWS

No lecturers

Lecture

Submod: 0084cB3.2.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (KöLu24-26/SR 006 Neuro/Mathe)

Tue, 10:00 - 12:00 (T9/SR 006 Seminarraum)

Description

polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Polytope theory
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes, shellability
shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
graphs, diameters, Hirsch (ex-)conjecture
Geometry of linear programming
linear programs, simplex algorithm, LP-duality
Combinatorial geometry / Geometric combinatorics
Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
Arrangements, zonotopes, zonotopal tilings, oriented matroids
Examples, examples, examples
regular polytopes, centrally symmetric polytopes
extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
combinatorial optimization and 0/1-polytopes

References

G.M. Ziegler "Lectures in Polytopes"
J. Matousek "Lectures on Discrete Geometry"
Further literature will be announced in class.

Additional information

Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

No lecturers

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

T9/SR 006 Seminarraum

No lecturers

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Discrete Geometrie I

LV: 19202002

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2 SWS

Sophie Rehberg

Practice seminar

Submod: 0084cB3.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 032 Seminarraum)

Module: Aufbaumodul Diskrete Geometrie III (0280bA3.6)

Advanced Module: Discrete Geometry III

LV: 19205901

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2 SWS

Georg Loho

Lecture

Submod: 0280bA3.6.1

Akt: 22.09.2023 14:00

Tue, 14:00 - 16:00 (A6/SR 031 Seminarraum)

Description

This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):

1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or

2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or

3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or

4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

References

Will be announced in class.

Additional information

The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.

Requirements: Preferably Discrete Geometry I and II.

Additional appointments

Appointment series

A6/SR 031 Seminarraum

Georg Loho

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Advanced Module: Discrete Geometry III

LV: 19205902

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2 SWS

Georg Loho

Practice seminar

Submod: 0280bA3.6.2

Akt: 22.09.2023 14:00

Thu, 10:00 - 12:00 (A3/SR 115)

Module: Basismodul Topologie II (0280bA4.2)

Basic Module: Topology II

LV: 19206201

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4 SWS

Pavle Blagojevic

Lecture

Submod: 0280bA4.2.1

Akt: 04.09.2023 12:00

Thu, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Description

Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

References

Literatur

Hatcher, Allen: Algebraic Topology; Cambridge University Press.
http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

Additional appointments

Appointment series

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 19.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Ex.: Basic Module: Topology II

LV: 19206202

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2 SWS

Pavle Blagojevic

Practice seminar

Submod: 0280bA4.2.2

Akt: 04.09.2023 12:00

Tue, 08:00 - 10:00 (A6/SR 031 Seminarraum)

Module: Research Module Topology (0280bA4.5)

Master Seminar Topology

LV: 19223811

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2 SWS

Elmar Vogt

Georg Lehner

Seminar

Submod: 0280bA4.5.1

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 009 Seminarraum)

Description

The seminar will cover advanced topics from topology and homotopy theory. We assume basic knowledge of topology as taught in Topology I and II.

Detailed Information can be found on the Homepage of the seminar.

References

Literatur wird auf der Homepage angegeben.
Literature will be given on the homepage.

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Elmar Vogt

Georg Lehner

einmal, ab 19.10.2023, 16:00 - 18:00 (16 Termine)

Module: Introductory Module Numerical Analysis II (0280bA5.1)

Basic Module: Numeric II

LV: 19202101

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4 SWS

Ana Djurdjevac

Lecture

Submod: 0084cB3.4.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 032 Seminarraum)

Mon, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Description

Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ana Djurdjevac

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Ana Djurdjevac

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Basic Module: Numeric II

LV: 19202102

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2 SWS

No lecturers

Practice seminar

Submod: 0084cB3.4.2

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 025/026 Seminarraum)

Module: Aufbaumodul Numerik IV (0280bA5.3)

Numerics IV: Modeling, Simulation, and Optimization

LV: 19206401

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2 SWS

Christof Schütte

Lecture

Submod: 0280bA5.3.1

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 009 Seminarraum)

Description

Inhalt:

Abstract:

Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

It covers a broad spectrum of research activities, ranging from the design of mathematical models for real-world processes, via efficient numerical simulation algorithms, to the solution of optimization problems for finding optimal scenarios or controls for the process under consideration. This lecture will give an overview over the techniques used in MSO and its application in different areas (life science, mobility, energy, sustainability, …). The lecture will be complemented by several pilot projects in which student groups will develop MSO solutions for realistic (but not too complex) application problems.

Zielpublikum:
Master Mathematik

References

Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)K.
Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Christof Schütte

einmal, ab 20.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Numerics IV: Modeling, Simulation, and Optimization

LV: 19206402

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2 SWS

Christof Schütte

Practice seminar

Submod: 0280bA5.3.2

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (A3/SR 115)

Module: Ergänzungsmodul Ausgewählte Themen (0280bA7.1)

Basic Module: Algebra I

LV: 19202501

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB3.3.1

Akt: 04.09.2023 12:00

Mon, 12:00 - 16:00 (A3/Hs 001 Hörsaal)

Description

Content

Affine algebraic varieties
Rings, ideals, and modules
Noetherian rings
Local rings and localization
Primary decompositione
Finite and integral extensions
Dimension theory
Regular rings

Target Group

Students with the prerequisites mentioned below.

Prerequisites

Linear Algebra I+II
Algebra and Number Theory

References

Literature

Atiyah, M.F.; Macdonald, I.G.: Einführung in die kommutative Algebra. Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. 1969 ix+128 Seiten (This book is the best introduction to the subject with brief and clear descriptions.)
Further literature will be announced in the course.

Additional information

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexander Schmitt

einmal, ab 23.10.2023, 12:00 - 16:00 (15 Termine)

Practice seminar for Basic Module: Algebra I

LV: 19202502

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2 SWS

Marwan Benyoussef

Practice seminar

Submod: 0084cB3.3.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (KöLu24-26/SR 006 Neuro/Mathe)

Probability Theory III

LV: 19208001

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4 SWS

Felix Höfling

Lecture

Submod: 0280bA7.1.1

Akt: 15.09.2023 05:29

Thu, 10:00 - 12:00 (T9/046 Seminarraum)

Wed, 08:00 - 10:00 (T9/046 Seminarraum)

Description

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

Markov jump processes; Brownian motion; sampling theorems in continuous time; stochastic integral; Itō formula; continuous semimartingales; quadratic variation; martingale representation; stochastic differential equations and diffusion processes, connections with partial differential equations.

Additional appointments

Appointment series

T9/046 Seminarraum

Felix Höfling

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

T9/046 Seminarraum

Felix Höfling

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Tutorial: Probability Theory III

LV: 19208002

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Thu, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Discrete Mathematics II - Extremal Comb.

LV: 19208601

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4 SWS

Tibor Szabo

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 025/026 Seminarraum)

Tue, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

References

The material is selected from several textbooks:

N. Alon and J. Spencer, The Probabilistic Method

L. Babai and P. Frankl, Linear Algebra Methods in Combinatorics

R. Diestel, Graph Theory

S. Jukna, Extremal Combinatorics

J. Matoušek, Using the Borsuk-Ulam Theorem

J. van Lint and R. Wilson, A Course in Combinatorics

D. West, Introduction to Graph Theory

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Tutorial Discrete Mathematics II - Extremal Comb.

LV: 19208602

a.SAP verarbeitet

2 SWS

Tibor Szabo

Silas Rathke

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Tue, 16:00 - 18:00 (A6/SR 007/008 Seminarraum)

Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation

LV: 19225101

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4 SWS

Luigi Delle Site

Lecture

Submod: 0280bA7.1.1

Akt: 04.09.2023 12:00

Wed, 08:00 - 10:00 (A6/SR 009 Seminarraum)

Thu, 08:00 - 10:00 (A6/SR 009 Seminarraum)

Description

Program

Polymer Physics: Structure and Dynamics

(a) Theoretical/analytic approaches
(b) Physical and chemical Modeling
(c) Simulation

Biological Membranes

(a) Theoretical/analytic approaches
(b) Physical and chemical Modeling
(c) Simulation

Introduction to Colloids and Liquid Crystals

Theory and Simulation

Introduction to Hydrodynamic scale for large Biological Systems:

Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

References

Basic Literature:

Introduction to Polymer Physics by M. Doi
Soft Matter Physics by M. Doi
Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

Additional information

Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Luigi Delle Site

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

A6/SR 009 Seminarraum

Luigi Delle Site

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation

LV: 19225102

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2 SWS

Luigi Delle Site

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Mon, 08:00 - 10:00 (A3/SR 115)

Diskrete Mathematik II - Optimierung

LV: 19234401

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4 SWS

Ralf Borndörfer

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Description

This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

Contents

Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness 
Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
Shortest Paths: nonnegative weights, general weights, all pairs
Network Flows: Max-Flow-Min-Cut Theorem, augmenting Paths, minimum cost flows, transport and allocation problems
Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
Foundations of linear optimization: Farkas Lemma, Duality Theorem
Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
Interior points and ellipsoid method: basics

Audience

This course is aimed at mathematics students with previous knowledge of discrete mathematics, linear algebra and analysis. Some exercises require the use of a computer.

References

M. Grötschel, Lineare Optimierung, one of the scripts

V. Chvátal, Linear Programming, Freeman 1983

Additional

Garey&Johnson, Computers and Intractability, 1979 (Complexity Theory)

Bertsimas&Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

Korte&Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

Additional information

Credit

This course can be chosen as Discrete Mathematics II (DM II).

If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module.

Language

This lecture is in English.

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Übung zu Optimierung I

LV: 19234402

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (A3/SR 115)

Cryptography and Security in Distributed Systems

LV: 19303601

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4 SWS

Volker Roth

Lecture

Submod: 0280bA7.1.1

Akt: 04.09.2023 12:00

Wed, 14:00 - 16:00 (T9/SR 006 Seminarraum)

Thu, 12:00 - 14:00 (T9/SR 006 Seminarraum)

Description

This course gives an introduction to cryptography and cryptographic key management, as well as an introduction to cryptographic protocols and their application in the field of security in distributed systems. Relevant mathematical tools will be developed accordingly. In addition, the lecture addresses the importance of implementation details in the context of IT system security.

References

Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, 2008
Lindsay N. Childs, A Concrete Introduction to Higher Algebra. Springer Verlag, 1995.
Johannes Buchmann, Einfuehrung in die Kryptographie. Springer Verlag, 1999.

Weitere noch zu bestimmende Literatur und Primärquellen.

Additional information

Requirements: Participants must have a good mathematical understanding and good knowledge of computer security and networking.

Additional appointments

Appointment series

T9/SR 006 Seminarraum

Volker Roth

wöchentlich, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

T9/SR 006 Seminarraum

Volker Roth

wöchentlich, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Cryptography and Security in Distributed Systems

LV: 19303602

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2 SWS

Volker Roth

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (T9/046 Seminarraum)

Module: Ergänzungsmodul Ausgewählte Forschungsthemen (0280bA7.2)

Stochastics IV:

LV: 19242101

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Luca Donati

Lecture

Submod: 0280bA7.2.1

Akt: 15.09.2023 05:29

Tue, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Description

Content
Stochastic processes are mathematical models used to describe the dynamics of random phenomena
and are widely applied in many disciplines ranging from physics, chemistry, biology, and economics.
During the course, students will learn both the theory underlying stochastic processes and advanced numerical
methods to solve problems with real applications.

Program

The first weeks of the course are devoted to review the basic concepts of stochastic analysis already studied in previous courses. The course continues with the study and application of methods for solving stochastic analysis problems. To this end, various Python notebooks will be presented. Note that Python knowledge is not required for the course.

Introduction to Brownian motion (1 week).
The master equation and the Fokker-Planck equation (1 week).
Stochastic calculus and stochastic differential equations (1 week).
Methods to solve stochastic differential equations (2 weeks).
Methods to solve the Master equation (2 weeks):
1. System size expansion
2. Gillespie algorithm
Methods to solve the Fokker-Planck equations (3 weeks):
1. Markov State Models
2. The Square Root Approximation (SqRA).
Robust Perron Cluster Cluster Analysis (PCCA+) (2 weeks).
Estimating transition rates by Neural Networks (2 weeks).
The Kramers problem (1 week).
The Generalized Langevin equation (1 week).

References

• Risken, H., The Fokker-Planck Equation: Methods of Solution and Applications, 1984.
• Gardiner, C., Stochastic Methods: A Handbook for the Natural and Social Sciences, 2009.
• Oksendal, B., Stochastic Differential Equations: An Introduction with Applications, 2010.
• Lecture notes and suggested readings.

Additional information

Prerequisite: Stochastics I, II, III. ???

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Luca Donati

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Exercise: Stochastics IV

LV: 19242102

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2 SWS

Luca Donati

Practice seminar

Submod: 0280bA7.2.2

Akt: 05.09.2023 10:00

Tue, 12:00 - 14:00 (T9/046 Seminarraum)

Cryptanalysis of Symmetrical Schemes

LV: 19320501

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2 SWS

Marian Margraf

Lecture

Submod: 0280bA7.2.1

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (T9/053 Seminarraum)

Description

The lecture aims at a deeper understanding of cryptographic algorithms, especially which design criteria have to be considered for the development of secure encryption algorithms. For that purpose we will get to know and evaluate different cryptanalytic methods for symmetrical and asymmetrical encryption techniques – e.g. linear and differential cryptanalysis on block ciphers, correlation attacks on stream ciphers and algorithms to solve the factorization problem and the discrete logarithm problem. Weaknesses in the implementation, e.g. to exploit side-channel attacks, will be discussed only peripherally.

Additional appointments

Appointment series

T9/053 Seminarraum

Marian Margraf

wöchentlich, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Cryptanalysis

LV: 19320502

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2 SWS

Marian Margraf

Practice seminar

Submod: 0280bA7.2.2

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (T9/046 Seminarraum)

Module: Ergänzungsmodul Forschungsseminar (0280bA7.5)

Master Seminar Topology

LV: 19223811

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Elmar Vogt

Georg Lehner

Seminar

Submod: 0280bA4.5.1

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 009 Seminarraum)

Description

The seminar will cover advanced topics from topology and homotopy theory. We assume basic knowledge of topology as taught in Topology I and II.

Detailed Information can be found on the Homepage of the seminar.

References

Literatur wird auf der Homepage angegeben.
Literature will be given on the homepage.

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Elmar Vogt

Georg Lehner

einmal, ab 19.10.2023, 16:00 - 18:00 (16 Termine)

Seminar Multiscale Methods in Molecular Simulations

LV: 19226511

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2 SWS

Luigi Delle Site

Seminar

Submod: 0084dB1.1.1

Akt: 21.09.2023 14:00

Fri, 12:00 - 14:00 (A3/SR 115)

Description

The discussion will concerns both, specific computational coding and conceptual developments.

References

Related Basic Literature:

(1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

(2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

(3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science

Additional information

Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

Additional appointments

Appointment series

A3/SR 115

Luigi Delle Site

einmal, ab 20.10.2023, 12:00 - 14:00 (16 Termine)

Seminar Uncertainty Quantification & Inverse Problems

LV: 19227611

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2 SWS

Vesa Kaarnioja

Claudia Schillings

Seminar

Submod: 0280bA7.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A6/SR 009 Seminarraum)

Seminar: Advanced Topics in Dynamical Systems

LV: 19239911

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2 SWS

Bernold Fiedler

Isabelle Schneider

Seminar

Submod: 0084dB1.1.1

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A7/SR 140 Seminarraum (Hinterhaus))

Module: Ergänzungsmodul BMS-Fridays (0280bA7.8)

BMS Fridays

LV: 19223111

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Holger Reich

Seminar

Submod: 0280bA7.8.1

Akt: 04.09.2023 12:00

Fri, 14:00 - 17:00 (T9/Gr. Hörsaal)

Description

The Friday colloquia of BMS represent a common meeting point for Berlin mathematics at Urania Berlin: a colloquium with broad emanation that permits an overview of large-scale connections and insights. In thematic series, the conversation is about “mathematics as a whole,” and we hope to be able to witness some breakthroughs.

Typically, there is a BMS colloquium every other Friday afternoon in the BMS Loft at Urania during term time. BMS Friday colloquia usually start at 2:15 pm. Tea and cookies are served before each talk at 1:00 pm.

More details: https://www.math-berlin.de/academics/bms-fridays

Additional appointments

Appointment series

T9/Gr. Hörsaal

Holger Reich

einmal, ab 20.10.2023, 14:00 - 17:00 (16 Termine)

Module: Complementary Module What is ? (0280bA7.9)

PhD Seminar "What is...?"

LV: 19217311

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2 SWS

Holger Reich

Seminar

Submod: 0280bA7.9.1

Akt: 04.09.2023 12:00

Fri, 12:00 - 14:00 (A3/SR 120)

Description

Content: The "What is ...?" seminar is a 30-minute weekly seminar that concisely introduces terms and ideas that are fundamental to certain fields of mathematics but may not be familiar in others.
The vast mathematical landscape in Berlin welcomes mathematicians with diverse backgrounds to work side by side, yet their paths often only cross within their individual research groups. To encourage interdisciplinary cooperation and collaboration, the "What is ...?" seminar attempts to initiate contact by introducing essential vocabulary and foundational concepts of the numerous fields represented in Berlin. The casual atmosphere of the seminar invites the audience to ask many questions and the speakers to experiment with their presentation styles.
The location of the seminar rotates among the Urania, FU, TU, and HU. On the weeks when a BMS Friday takes place, the "What is ...?" seminar topic is arranged to coincide with the Friday talk acting as an introductory talk for the BMS Friday Colloquium. For a schedule of the talks and their locations, check the website. The website is updated frequently throughout the semester.

Talks and more detailed information can be found here
Homepage: http://www.math.fu-berlin.de/w/Math/WhatIsSeminar

Additional information

The "What is ...?" seminars are usually held before the BMS Friday seminar to complement the topic of the talk.

Audience: Anybody interested in mathematics is invited to attend the "What is ...?" seminars. This includes Bachelors, Masters, Diplom, and PhD students from any field, as well as researchers like Post-Docs.
Requirements: The speakers assume that the audience has at least a general knowledge of graduate-level mathematics.

Additional appointments

Appointment series

A3/SR 120

Holger Reich

einmal, ab 20.10.2023, 12:00 - 14:00 (16 Termine)

Mathematics (0280c_MA120)

Module: Introductory Module: Algebra I (0280cA1.1)

Basic Module: Algebra I

LV: 19202501

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB3.3.1

Akt: 04.09.2023 12:00

Mon, 12:00 - 16:00 (A3/Hs 001 Hörsaal)

Description

Content

Affine algebraic varieties
Rings, ideals, and modules
Noetherian rings
Local rings and localization
Primary decompositione
Finite and integral extensions
Dimension theory
Regular rings

Target Group

Students with the prerequisites mentioned below.

Prerequisites

Linear Algebra I+II
Algebra and Number Theory

References

Literature

Atiyah, M.F.; Macdonald, I.G.: Einführung in die kommutative Algebra. Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. 1969 ix+128 Seiten (This book is the best introduction to the subject with brief and clear descriptions.)
Further literature will be announced in the course.

Additional information

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexander Schmitt

einmal, ab 23.10.2023, 12:00 - 16:00 (15 Termine)

Practice seminar for Basic Module: Algebra I

LV: 19202502

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2 SWS

Marwan Benyoussef

Practice seminar

Submod: 0084cB3.3.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (KöLu24-26/SR 006 Neuro/Mathe)

Module: Introductory Module: Differential Geometry I (0280cA1.3)

Differential Geometry I

LV: 19202601

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4 SWS

Konrad Polthier

Lecture

Submod: 0084cB3.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A3/SR 119)

Thu, 12:00 - 14:00 (A3/SR 119)

Description

Topics of the lecture will be:

curves and surfaces in Euclidean space,
metrics and (Riemannian) manifolds,
surface tension, notions of curvature,
vector fields, tensors, covariant derivative
geodesic curves, exponential map,
Gauß-Bonnet theorem, topology,
connection to discrete differential geometry.

This course is a BMS course and will be held in English on request.

Prerequisits:

Analysis I, II, III and Linear Algebra I, II

References

Literature

W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

Additional information

For further information, see Lecture Homepage.

Additional appointments

Appointment series

A3/SR 119

Konrad Polthier

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Konrad Polthier

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Differential Geometry I

LV: 19202602

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2 SWS

Konrad Polthier

Eric Zimmermann

Practice seminar

Submod: 0084cB3.5.2

Akt: 22.09.2023 16:00

Fri, 08:00 - 10:00 (A3/SR 115)

Fri, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Module: Introductory Module: Discrete Geometry I (0280cA1.5)

Discrete Geometrie I

LV: 19202001

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4 SWS

No lecturers

Lecture

Submod: 0084cB3.2.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (KöLu24-26/SR 006 Neuro/Mathe)

Tue, 10:00 - 12:00 (T9/SR 006 Seminarraum)

Description

polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Polytope theory
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes, shellability
shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
graphs, diameters, Hirsch (ex-)conjecture
Geometry of linear programming
linear programs, simplex algorithm, LP-duality
Combinatorial geometry / Geometric combinatorics
Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
Arrangements, zonotopes, zonotopal tilings, oriented matroids
Examples, examples, examples
regular polytopes, centrally symmetric polytopes
extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
combinatorial optimization and 0/1-polytopes

References

G.M. Ziegler "Lectures in Polytopes"
J. Matousek "Lectures on Discrete Geometry"
Further literature will be announced in class.

Additional information

Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

No lecturers

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

T9/SR 006 Seminarraum

No lecturers

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Discrete Geometrie I

LV: 19202002

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2 SWS

Sophie Rehberg

Practice seminar

Submod: 0084cB3.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 032 Seminarraum)

Module: Introductory Module: Discrete Mathematics II (0280cA1.8)

Discrete Mathematics II - Extremal Comb.

LV: 19208601

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4 SWS

Tibor Szabo

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 025/026 Seminarraum)

Tue, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

References

The material is selected from several textbooks:

N. Alon and J. Spencer, The Probabilistic Method

L. Babai and P. Frankl, Linear Algebra Methods in Combinatorics

R. Diestel, Graph Theory

S. Jukna, Extremal Combinatorics

J. Matoušek, Using the Borsuk-Ulam Theorem

J. van Lint and R. Wilson, A Course in Combinatorics

D. West, Introduction to Graph Theory

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Tutorial Discrete Mathematics II - Extremal Comb.

LV: 19208602

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2 SWS

Tibor Szabo

Silas Rathke

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Tue, 16:00 - 18:00 (A6/SR 007/008 Seminarraum)

Diskrete Mathematik II - Optimierung

LV: 19234401

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4 SWS

Ralf Borndörfer

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Description

This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

Contents

Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness 
Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
Shortest Paths: nonnegative weights, general weights, all pairs
Network Flows: Max-Flow-Min-Cut Theorem, augmenting Paths, minimum cost flows, transport and allocation problems
Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
Foundations of linear optimization: Farkas Lemma, Duality Theorem
Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
Interior points and ellipsoid method: basics

Audience

This course is aimed at mathematics students with previous knowledge of discrete mathematics, linear algebra and analysis. Some exercises require the use of a computer.

References

M. Grötschel, Lineare Optimierung, one of the scripts

V. Chvátal, Linear Programming, Freeman 1983

Additional

Garey&Johnson, Computers and Intractability, 1979 (Complexity Theory)

Bertsimas&Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

Korte&Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

Additional information

Credit

This course can be chosen as Discrete Mathematics II (DM II).

If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module.

Language

This lecture is in English.

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Übung zu Optimierung I

LV: 19234402

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (A3/SR 115)

Module: Introductory Module: Numerical Analysis II (0280cA1.11)

Basic Module: Numeric II

LV: 19202101

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4 SWS

Ana Djurdjevac

Lecture

Submod: 0084cB3.4.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 032 Seminarraum)

Mon, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Description

Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ana Djurdjevac

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Ana Djurdjevac

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Basic Module: Numeric II

LV: 19202102

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2 SWS

No lecturers

Practice seminar

Submod: 0084cB3.4.2

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 025/026 Seminarraum)

Module: Introductory Module: Stochastic Processes III (0280cA1.16)

Probability Theory III

LV: 19208001

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Felix Höfling

Lecture

Submod: 0280bA7.1.1

Akt: 15.09.2023 05:29

Thu, 10:00 - 12:00 (T9/046 Seminarraum)

Wed, 08:00 - 10:00 (T9/046 Seminarraum)

Description

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

Additional appointments

Appointment series

T9/046 Seminarraum

Felix Höfling

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

T9/046 Seminarraum

Felix Höfling

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Tutorial: Probability Theory III

LV: 19208002

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Thu, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Module: Introductory Module: Topology II (0280cA1.18)

Basic Module: Topology II

LV: 19206201

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4 SWS

Pavle Blagojevic

Lecture

Submod: 0280bA4.2.1

Akt: 04.09.2023 12:00

Thu, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Description

Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

References

Literatur

Hatcher, Allen: Algebraic Topology; Cambridge University Press.
http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

Additional appointments

Appointment series

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 19.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Ex.: Basic Module: Topology II

LV: 19206202

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2 SWS

Pavle Blagojevic

Practice seminar

Submod: 0280bA4.2.2

Akt: 04.09.2023 12:00

Tue, 08:00 - 10:00 (A6/SR 031 Seminarraum)

Module: Advanced Module: Algebra III (0280cA2.1)

Advanced Module: Algebra III

LV: 19222301

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Klaus Altmann

Lecture

Submod: 0280bA2.3.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 009 Seminarraum)

Description

Course contents: a selection of the following topics

properties of morphisms (proper, projective, smooth)
divisors
(quasi-)coherent sheaves
cohomology
Hilbert functions

References

G.R. Kempf: Algebraic varieties. London Mathematical Society Lecture Note
Series. 172. Cambridge: Cambridge University Press. 1993. x, 163 p.

A. Schmitt: Homological algebra, lecture notes.

J.L. Taylor: Several complex variables with connections to algebraic
geometry and Lie groups. Graduate Studies in Mathematics. 46. Providence,
RI: American Mathematical Society. 2002. xvi, 507 p.

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Klaus Altmann

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Advanced Module: Algebra III

LV: 19222302

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Klaus Altmann

Practice seminar

Submod: 0280bA2.3.2

Akt: 04.09.2023 12:00

Wed, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Module: Advanced Module: Discrete Geometry III (0280cA2.3)

Advanced Module: Discrete Geometry III

LV: 19205901

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Georg Loho

Lecture

Submod: 0280bA3.6.1

Akt: 22.09.2023 14:00

Tue, 14:00 - 16:00 (A6/SR 031 Seminarraum)

Description

This is the third in a series of three courses on discrete geometry. This advanced course will cover a selection of the following topics (depending on the interests of the audience):

1. Oriented Matroids along the lines of the book Oriented Matroids by Björner, Las Vergnas, Sturmfels, White, and Ziegler; and/or

2. Triangulations along the lines of the book Triangulations by de Loera, Rambau, and Santos; and/or

3. Discriminants and tropical geometry along the lines of the book Discriminants, Resultants, and multidimensional determinants by Gelfand, Kapranov, and Zelevinsky; and/or

4. Combinatorics and commutative algebra along the lines of the book Combinatorics and commutative algebra by Stanley.

References

Will be announced in class.

Additional information

Additional appointments

Appointment series

A6/SR 031 Seminarraum

Georg Loho

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Advanced Module: Discrete Geometry III

LV: 19205902

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2 SWS

Georg Loho

Practice seminar

Submod: 0280bA3.6.2

Akt: 22.09.2023 14:00

Thu, 10:00 - 12:00 (A3/SR 115)

Module: Advanced Module: Numerical Analysis IV (0280cA2.6)

Numerics IV: Modeling, Simulation, and Optimization

LV: 19206401

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Christof Schütte

Lecture

Submod: 0280bA5.3.1

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 009 Seminarraum)

Description

Inhalt:

Abstract:

Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

Zielpublikum:
Master Mathematik

References

Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)K.
Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Christof Schütte

einmal, ab 20.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Numerics IV: Modeling, Simulation, and Optimization

LV: 19206402

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Christof Schütte

Practice seminar

Submod: 0280bA5.3.2

Akt: 04.09.2023 12:00

Tue, 10:00 - 12:00 (A3/SR 115)

Module: Advanced Module: Stochastic Processes IV (0280cA2.8)

Stochastics IV:

LV: 19242101

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Luca Donati

Lecture

Submod: 0280bA7.2.1

Akt: 15.09.2023 05:29

Tue, 14:00 - 16:00 (A6/SR 009 Seminarraum)

Description

Program

Introduction to Brownian motion (1 week).
The master equation and the Fokker-Planck equation (1 week).
Stochastic calculus and stochastic differential equations (1 week).
Methods to solve stochastic differential equations (2 weeks).
Methods to solve the Master equation (2 weeks):
1. System size expansion
2. Gillespie algorithm
Methods to solve the Fokker-Planck equations (3 weeks):
1. Markov State Models
2. The Square Root Approximation (SqRA).
Robust Perron Cluster Cluster Analysis (PCCA+) (2 weeks).
Estimating transition rates by Neural Networks (2 weeks).
The Kramers problem (1 week).
The Generalized Langevin equation (1 week).

References

Additional information

Prerequisite: Stochastics I, II, III. ???

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Luca Donati

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Exercise: Stochastics IV

LV: 19242102

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Luca Donati

Practice seminar

Submod: 0280bA7.2.2

Akt: 05.09.2023 10:00

Tue, 12:00 - 14:00 (T9/046 Seminarraum)

Module: Specialisation Module: Master’s Seminar Numerical Analysis (0280cA3.6)

Seminar Uncertainty Quantification & Inverse Problems

LV: 19227611

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Vesa Kaarnioja

Claudia Schillings

Seminar

Submod: 0280bA7.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A6/SR 009 Seminarraum)

Research Seminar Numerical Analysis of stochastic and deterministic partial differential equations

LV: 19246816

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Claudia Schillings

Research Seminar

Submod: 0280cA3.6.1

Akt: 04.09.2023 12:00

Thu, 12:00 - 14:00 (A3/SR 115)

Module: Specialisation Module: Master’s Seminar Partial Differential Equations (0280cA3.7)

Sobolev- and BV-spaces

LV: 19247111

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Marita Thomas

Seminar

Submod: 0084dB1.1.1

Akt: 04.09.2023 12:00

Tue, 16:00 - 18:00 (A3/ 024 Seminarraum )

Module: Specialisation Module: Master’s Seminar Stochastic Processes (0280cA3.8)

Masterseminar Stochastics

LV: 19208111

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Nicolas Perkowski

Seminar

Submod: 0084dB1.1.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 007/008 Seminarraum)

Description

Content: The seminar covers advanced topics of stochastics.

Detailed Information can be found on the Homepage of the seminar.

References

Literatur wir in der Vorbesprechung bekanntgegeben.

Literature will be announced in the preliminary discussion

Additional information

Prerequisites: Stochastics I and II.
Target Group: BMS Students, Master students and advanced Bachelor students.

Additional appointments

Appointment series

A6/SR 007/008 Seminarraum

Nicolas Perkowski

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

Module: Specialisation Module: Master’s Seminar Topology (0280cA3.9)

Master Seminar Topology

LV: 19223811

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Elmar Vogt

Georg Lehner

Seminar

Submod: 0280bA4.5.1

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 009 Seminarraum)

Description

The seminar will cover advanced topics from topology and homotopy theory. We assume basic knowledge of topology as taught in Topology I and II.

Detailed Information can be found on the Homepage of the seminar.

References

Literatur wird auf der Homepage angegeben.
Literature will be given on the homepage.

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Elmar Vogt

Georg Lehner

einmal, ab 19.10.2023, 16:00 - 18:00 (16 Termine)

Module: Complementary Module: Selected Topics A (0280cA4.1)

Discrete Geometrie I

LV: 19202001

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No lecturers

Lecture

Submod: 0084cB3.2.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (KöLu24-26/SR 006 Neuro/Mathe)

Tue, 10:00 - 12:00 (T9/SR 006 Seminarraum)

Description

polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Polytope theory
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes, shellability
shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
graphs, diameters, Hirsch (ex-)conjecture
Geometry of linear programming
linear programs, simplex algorithm, LP-duality
Combinatorial geometry / Geometric combinatorics
Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
Arrangements, zonotopes, zonotopal tilings, oriented matroids
Examples, examples, examples
regular polytopes, centrally symmetric polytopes
extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
combinatorial optimization and 0/1-polytopes

References

G.M. Ziegler "Lectures in Polytopes"
J. Matousek "Lectures on Discrete Geometry"
Further literature will be announced in class.

Additional information

Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

No lecturers

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

T9/SR 006 Seminarraum

No lecturers

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Discrete Geometrie I

LV: 19202002

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2 SWS

Sophie Rehberg

Practice seminar

Submod: 0084cB3.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 032 Seminarraum)

Basic Module: Numeric II

LV: 19202101

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Ana Djurdjevac

Lecture

Submod: 0084cB3.4.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 032 Seminarraum)

Mon, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Description

Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ana Djurdjevac

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Ana Djurdjevac

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Basic Module: Numeric II

LV: 19202102

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2 SWS

No lecturers

Practice seminar

Submod: 0084cB3.4.2

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 025/026 Seminarraum)

Basic Module: Algebra I

LV: 19202501

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Alexander Schmitt

Lecture

Submod: 0084cB3.3.1

Akt: 04.09.2023 12:00

Mon, 12:00 - 16:00 (A3/Hs 001 Hörsaal)

Description

Content

Affine algebraic varieties
Rings, ideals, and modules
Noetherian rings
Local rings and localization
Primary decompositione
Finite and integral extensions
Dimension theory
Regular rings

Target Group

Students with the prerequisites mentioned below.

Prerequisites

Linear Algebra I+II
Algebra and Number Theory

References

Literature

Atiyah, M.F.; Macdonald, I.G.: Einführung in die kommutative Algebra. Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. 1969 ix+128 Seiten (This book is the best introduction to the subject with brief and clear descriptions.)
Further literature will be announced in the course.

Additional information

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexander Schmitt

einmal, ab 23.10.2023, 12:00 - 16:00 (15 Termine)

Practice seminar for Basic Module: Algebra I

LV: 19202502

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2 SWS

Marwan Benyoussef

Practice seminar

Submod: 0084cB3.3.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (KöLu24-26/SR 006 Neuro/Mathe)

Differential Geometry I

LV: 19202601

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Konrad Polthier

Lecture

Submod: 0084cB3.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A3/SR 119)

Thu, 12:00 - 14:00 (A3/SR 119)

Description

Topics of the lecture will be:

curves and surfaces in Euclidean space,
metrics and (Riemannian) manifolds,
surface tension, notions of curvature,
vector fields, tensors, covariant derivative
geodesic curves, exponential map,
Gauß-Bonnet theorem, topology,
connection to discrete differential geometry.

This course is a BMS course and will be held in English on request.

Prerequisits:

Analysis I, II, III and Linear Algebra I, II

References

Literature

W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

Additional information

For further information, see Lecture Homepage.

Additional appointments

Appointment series

A3/SR 119

Konrad Polthier

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Konrad Polthier

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Differential Geometry I

LV: 19202602

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Konrad Polthier

Eric Zimmermann

Practice seminar

Submod: 0084cB3.5.2

Akt: 22.09.2023 16:00

Fri, 08:00 - 10:00 (A3/SR 115)

Fri, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Basic Module: Topology II

LV: 19206201

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Pavle Blagojevic

Lecture

Submod: 0280bA4.2.1

Akt: 04.09.2023 12:00

Thu, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Description

Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

References

Literatur

Hatcher, Allen: Algebraic Topology; Cambridge University Press.
http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

Additional appointments

Appointment series

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 19.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Ex.: Basic Module: Topology II

LV: 19206202

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Pavle Blagojevic

Practice seminar

Submod: 0280bA4.2.2

Akt: 04.09.2023 12:00

Tue, 08:00 - 10:00 (A6/SR 031 Seminarraum)

Probability Theory III

LV: 19208001

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Felix Höfling

Lecture

Submod: 0280bA7.1.1

Akt: 15.09.2023 05:29

Thu, 10:00 - 12:00 (T9/046 Seminarraum)

Wed, 08:00 - 10:00 (T9/046 Seminarraum)

Description

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

Additional appointments

Appointment series

T9/046 Seminarraum

Felix Höfling

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

T9/046 Seminarraum

Felix Höfling

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Tutorial: Probability Theory III

LV: 19208002

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Thu, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Discrete Mathematics II - Extremal Comb.

LV: 19208601

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Tibor Szabo

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 025/026 Seminarraum)

Tue, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

References

The material is selected from several textbooks:

N. Alon and J. Spencer, The Probabilistic Method

L. Babai and P. Frankl, Linear Algebra Methods in Combinatorics

R. Diestel, Graph Theory

S. Jukna, Extremal Combinatorics

J. Matoušek, Using the Borsuk-Ulam Theorem

J. van Lint and R. Wilson, A Course in Combinatorics

D. West, Introduction to Graph Theory

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Tutorial Discrete Mathematics II - Extremal Comb.

LV: 19208602

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2 SWS

Tibor Szabo

Silas Rathke

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Tue, 16:00 - 18:00 (A6/SR 007/008 Seminarraum)

Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation

LV: 19225101

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4 SWS

Luigi Delle Site

Lecture

Submod: 0280bA7.1.1

Akt: 04.09.2023 12:00

Wed, 08:00 - 10:00 (A6/SR 009 Seminarraum)

Thu, 08:00 - 10:00 (A6/SR 009 Seminarraum)

Description

Program

Polymer Physics: Structure and Dynamics

(a) Theoretical/analytic approaches
(b) Physical and chemical Modeling
(c) Simulation

Biological Membranes

(a) Theoretical/analytic approaches
(b) Physical and chemical Modeling
(c) Simulation

Introduction to Colloids and Liquid Crystals

Theory and Simulation

Introduction to Hydrodynamic scale for large Biological Systems:

Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

References

Basic Literature:

Introduction to Polymer Physics by M. Doi
Soft Matter Physics by M. Doi
Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

Additional information

Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Luigi Delle Site

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

A6/SR 009 Seminarraum

Luigi Delle Site

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation

LV: 19225102

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2 SWS

Luigi Delle Site

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Mon, 08:00 - 10:00 (A3/SR 115)

Diskrete Mathematik II - Optimierung

LV: 19234401

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Ralf Borndörfer

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Description

This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

Contents

Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness 
Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
Shortest Paths: nonnegative weights, general weights, all pairs
Network Flows: Max-Flow-Min-Cut Theorem, augmenting Paths, minimum cost flows, transport and allocation problems
Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
Foundations of linear optimization: Farkas Lemma, Duality Theorem
Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
Interior points and ellipsoid method: basics

Audience

This course is aimed at mathematics students with previous knowledge of discrete mathematics, linear algebra and analysis. Some exercises require the use of a computer.

References

M. Grötschel, Lineare Optimierung, one of the scripts

V. Chvátal, Linear Programming, Freeman 1983

Additional

Garey&Johnson, Computers and Intractability, 1979 (Complexity Theory)

Bertsimas&Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

Korte&Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

Additional information

Credit

This course can be chosen as Discrete Mathematics II (DM II).

If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module.

Language

This lecture is in English.

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Übung zu Optimierung I

LV: 19234402

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (A3/SR 115)

Module: Complementary Module: Selected Topics B (0280cA4.2)

Discrete Geometrie I

LV: 19202001

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4 SWS

No lecturers

Lecture

Submod: 0084cB3.2.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (KöLu24-26/SR 006 Neuro/Mathe)

Tue, 10:00 - 12:00 (T9/SR 006 Seminarraum)

Description

polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Polytope theory
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes, shellability
shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
graphs, diameters, Hirsch (ex-)conjecture
Geometry of linear programming
linear programs, simplex algorithm, LP-duality
Combinatorial geometry / Geometric combinatorics
Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
Arrangements, zonotopes, zonotopal tilings, oriented matroids
Examples, examples, examples
regular polytopes, centrally symmetric polytopes
extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
combinatorial optimization and 0/1-polytopes

References

G.M. Ziegler "Lectures in Polytopes"
J. Matousek "Lectures on Discrete Geometry"
Further literature will be announced in class.

Additional information

Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

Additional appointments

Appointment series

KöLu24-26/SR 006 Neuro/Mathe

No lecturers

einmal, ab 18.10.2023, 10:00 - 12:00 (16 Termine)

T9/SR 006 Seminarraum

No lecturers

einmal, ab 17.10.2023, 10:00 - 12:00 (16 Termine)

Practice seminar for Discrete Geometrie I

LV: 19202002

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2 SWS

Sophie Rehberg

Practice seminar

Submod: 0084cB3.2.2

Akt: 04.09.2023 12:00

Fri, 10:00 - 12:00 (A6/SR 032 Seminarraum)

Basic Module: Numeric II

LV: 19202101

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4 SWS

Ana Djurdjevac

Lecture

Submod: 0084cB3.4.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 032 Seminarraum)

Mon, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

Description

Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ana Djurdjevac

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Ana Djurdjevac

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

Practice seminar for Basic Module: Numeric II

LV: 19202102

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2 SWS

No lecturers

Practice seminar

Submod: 0084cB3.4.2

Akt: 04.09.2023 12:00

Thu, 16:00 - 18:00 (A6/SR 025/026 Seminarraum)

Basic Module: Algebra I

LV: 19202501

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4 SWS

Alexander Schmitt

Lecture

Submod: 0084cB3.3.1

Akt: 04.09.2023 12:00

Mon, 12:00 - 16:00 (A3/Hs 001 Hörsaal)

Description

Content

Affine algebraic varieties
Rings, ideals, and modules
Noetherian rings
Local rings and localization
Primary decompositione
Finite and integral extensions
Dimension theory
Regular rings

Target Group

Students with the prerequisites mentioned below.

Prerequisites

Linear Algebra I+II
Algebra and Number Theory

References

Literature

Atiyah, M.F.; Macdonald, I.G.: Einführung in die kommutative Algebra. Addison-Wesley Publishing Co., Reading, Mass-London-Don Mills, Ont. 1969 ix+128 Seiten (This book is the best introduction to the subject with brief and clear descriptions.)
Further literature will be announced in the course.

Additional information

Homepage: Professor Alexander Schmitt

Additional appointments

Appointment series

A3/Hs 001 Hörsaal

Alexander Schmitt

einmal, ab 23.10.2023, 12:00 - 16:00 (15 Termine)

Practice seminar for Basic Module: Algebra I

LV: 19202502

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2 SWS

Marwan Benyoussef

Practice seminar

Submod: 0084cB3.3.2

Akt: 04.09.2023 12:00

Wed, 16:00 - 18:00 (KöLu24-26/SR 006 Neuro/Mathe)

Differential Geometry I

LV: 19202601

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4 SWS

Konrad Polthier

Lecture

Submod: 0084cB3.5.1

Akt: 04.09.2023 12:00

Tue, 12:00 - 14:00 (A3/SR 119)

Thu, 12:00 - 14:00 (A3/SR 119)

Description

Topics of the lecture will be:

curves and surfaces in Euclidean space,
metrics and (Riemannian) manifolds,
surface tension, notions of curvature,
vector fields, tensors, covariant derivative
geodesic curves, exponential map,
Gauß-Bonnet theorem, topology,
connection to discrete differential geometry.

This course is a BMS course and will be held in English on request.

Prerequisits:

Analysis I, II, III and Linear Algebra I, II

References

Literature

W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001

Additional information

For further information, see Lecture Homepage.

Additional appointments

Appointment series

A3/SR 119

Konrad Polthier

einmal, ab 17.10.2023, 12:00 - 14:00 (16 Termine)

A3/SR 119

Konrad Polthier

einmal, ab 19.10.2023, 12:00 - 14:00 (16 Termine)

Practice seminar for Differential Geometry I

LV: 19202602

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2 SWS

Konrad Polthier

Eric Zimmermann

Practice seminar

Submod: 0084cB3.5.2

Akt: 22.09.2023 16:00

Fri, 08:00 - 10:00 (A3/SR 115)

Fri, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Basic Module: Topology II

LV: 19206201

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4 SWS

Pavle Blagojevic

Lecture

Submod: 0280bA4.2.1

Akt: 04.09.2023 12:00

Thu, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 007/008 Seminarraum)

Description

Content: Homology, cohomology and applications, CW-complexes, basic notions of homotopy theory

References

Literatur

Hatcher, Allen: Algebraic Topology; Cambridge University Press.
http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Lück, Wolfgang: Algebraische Topologie, Homologie und Mannigfaltigkeiten; Vieweg.

Additional appointments

Appointment series

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 19.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 007/008 Seminarraum

Pavle Blagojevic

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Ex.: Basic Module: Topology II

LV: 19206202

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2 SWS

Pavle Blagojevic

Practice seminar

Submod: 0280bA4.2.2

Akt: 04.09.2023 12:00

Tue, 08:00 - 10:00 (A6/SR 031 Seminarraum)

Probability Theory III

LV: 19208001

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4 SWS

Felix Höfling

Lecture

Submod: 0280bA7.1.1

Akt: 15.09.2023 05:29

Thu, 10:00 - 12:00 (T9/046 Seminarraum)

Wed, 08:00 - 10:00 (T9/046 Seminarraum)

Description

Stochastic analysis is the study of stochastic processes that evolve in continuous time. We will treat the following subjects, among others:

Additional appointments

Appointment series

T9/046 Seminarraum

Felix Höfling

einmal, ab 19.10.2023, 10:00 - 12:00 (16 Termine)

T9/046 Seminarraum

Felix Höfling

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

Tutorial: Probability Theory III

LV: 19208002

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Thu, 08:00 - 10:00 (A7/SR 140 Seminarraum (Hinterhaus))

Discrete Mathematics II - Extremal Comb.

LV: 19208601

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4 SWS

Tibor Szabo

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Wed, 12:00 - 14:00 (A6/SR 025/026 Seminarraum)

Tue, 14:00 - 16:00 (A6/SR 025/026 Seminarraum)

References

The material is selected from several textbooks:

N. Alon and J. Spencer, The Probabilistic Method

L. Babai and P. Frankl, Linear Algebra Methods in Combinatorics

R. Diestel, Graph Theory

S. Jukna, Extremal Combinatorics

J. Matoušek, Using the Borsuk-Ulam Theorem

J. van Lint and R. Wilson, A Course in Combinatorics

D. West, Introduction to Graph Theory

Additional appointments

Appointment series

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 18.10.2023, 12:00 - 14:00 (16 Termine)

A6/SR 025/026 Seminarraum

Tibor Szabo

einmal, ab 17.10.2023, 14:00 - 16:00 (16 Termine)

Tutorial Discrete Mathematics II - Extremal Comb.

LV: 19208602

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2 SWS

Tibor Szabo

Silas Rathke

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Tue, 16:00 - 18:00 (A6/SR 007/008 Seminarraum)

Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation

LV: 19225101

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4 SWS

Luigi Delle Site

Lecture

Submod: 0280bA7.1.1

Akt: 04.09.2023 12:00

Wed, 08:00 - 10:00 (A6/SR 009 Seminarraum)

Thu, 08:00 - 10:00 (A6/SR 009 Seminarraum)

Description

Program

Polymer Physics: Structure and Dynamics

(a) Theoretical/analytic approaches
(b) Physical and chemical Modeling
(c) Simulation

Biological Membranes

(a) Theoretical/analytic approaches
(b) Physical and chemical Modeling
(c) Simulation

Introduction to Colloids and Liquid Crystals

Theory and Simulation

Introduction to Hydrodynamic scale for large Biological Systems:

Examples are e.g. Cellular processes, Red Blood Cells in Capillary Flow, etc. (Theory and Simulation)

References

Basic Literature:

Introduction to Polymer Physics by M. Doi
Soft Matter Physics by M. Doi
Biomembrane Frontiers: Nanostructures, Models, and the Design of Life (Handbook of Modern Biophysics) by von Thomas Jue, Subhash H. Risbud, Marjorie L. Longo, Roland Faller (Editors)

Additional information

Audience: Master students of Mathematics and Physics interested in mathematical theory and computational modeling of Soft Matter Systems.

Requirements: Basic Knowledge of statistical physics and of dynamics, computer programming

Additional appointments

Appointment series

A6/SR 009 Seminarraum

Luigi Delle Site

einmal, ab 18.10.2023, 08:00 - 10:00 (16 Termine)

A6/SR 009 Seminarraum

Luigi Delle Site

einmal, ab 19.10.2023, 08:00 - 10:00 (16 Termine)

Practice seminar for Soft Matter: Mathematical Aspects, Physical Modeling and Computer Simulation

LV: 19225102

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2 SWS

Luigi Delle Site

Practice seminar

Submod: 0280bA7.1.2

Akt: 04.09.2023 12:00

Mon, 08:00 - 10:00 (A3/SR 115)

Diskrete Mathematik II - Optimierung

LV: 19234401

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4 SWS

Ralf Borndörfer

Lecture

Submod: 0280bA3.2.1

Akt: 04.09.2023 12:00

Mon, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Wed, 14:00 - 16:00 (A6/SR 032 Seminarraum)

Description

This lecture starts the optimization branch of discrete mathematics. It deals with algorithmic graph theory and linear optimization.

Contents

Complexity: complexity measures, run time of algorithms, the classes P and NP, NP-completeness 
Matroids and Independence Systems: independence systems, matroids, trees, forests, oracles, optimization over independence systems
Shortest Paths: nonnegative weights, general weights, all pairs
Network Flows: Max-Flow-Min-Cut Theorem, augmenting Paths, minimum cost flows, transport and allocation problems
Polyhedra: faces, dimension formula, projections of polyhedra, transformation, polarity, representation theorems
Foundations of linear optimization: Farkas Lemma, Duality Theorem
Simplex algorithm: basis, degeneration, basis exchange, revised simplex algorithm, bounds, dual simplex algorithm, post-optimization, numerics
Interior points and ellipsoid method: basics

Audience

This course is aimed at mathematics students with previous knowledge of discrete mathematics, linear algebra and analysis. Some exercises require the use of a computer.

References

M. Grötschel, Lineare Optimierung, one of the scripts

V. Chvátal, Linear Programming, Freeman 1983

Additional

Garey&Johnson, Computers and Intractability, 1979 (Complexity Theory)

Bertsimas&Tsitsiklis, Introduction to Linear Optimization, 97 (Linear Programming)

Korte&Vygen, Combinatorial Optimization, 2006 (Flows, Shortest Paths, Matchings)

Additional information

Credit

This course can be chosen as Discrete Mathematics II (DM II).

If Discrete Mathematics II - Extreme Combinatorics is taken at the same time, one of the two courses can be chosen as DM II and the other as a supplementary module.

Language

This lecture is in English.

Additional appointments

Appointment series

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 16.10.2023, 14:00 - 16:00 (16 Termine)

A6/SR 032 Seminarraum

Ralf Borndörfer

einmal, ab 18.10.2023, 14:00 - 16:00 (16 Termine)

Übung zu Optimierung I

LV: 19234402

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2 SWS

No lecturers

Practice seminar

Submod: 0280bA3.2.2

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (A3/SR 115)

Module: Complementary Module: Selected Topics C (0280cA4.3)

Discrete Geometrie I

LV: 19202001

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4 SWS

No lecturers

Lecture

Submod: 0084cB3.2.1

Akt: 04.09.2023 12:00

Wed, 10:00 - 12:00 (KöLu24-26/SR 006 Neuro/Mathe)