Mathematics

• Gesamtes Lehrangebot der Mathematik

  E17oA1.1
  • 19000546 Mentoring
    Mentoring (Ulrike Seyferth)
    Schedule: Mo 14.04. 10:00-12:00, Mo 14.04. 10:00-12:00 (Class starts on: 2025-04-14)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    The mentoring program offers events and counseling services primarily (but not only!) for first-year students. All offers are voluntary and are based on your needs and wishes!

    If you have questions or wishes, please contact us!

    Your mentors in mathematics, computer science and bioinformatics

  • 19200170 Begrüßungs- und Abschlussveranstaltung
    Introductory presentation for first-semester students in Mathematics (Marita Thomas)
    Schedule: -
    Location: keine Angabe
    

    Additional information / Pre-requisites

    Target group:
    Newly enrolled in Mathematics (first semester)

    Comments

    Am Montag, den 14.10.2024, ab 10:15 Uhr findet eine Begrüßungs- und Einführungsveranstaltung für Studienanfänger*innen der Mathematik statt.

    Die Veranstaltung soll den Neuimmatrikulierten einen Überblick über den Aufbau in den verschiedenen Studiengängen und Hinweise für eine effiziente Anlage des Studiums geben. Einige Hochschullehrer des Fachbereichs, darunter die Studiengangsverantwortlichen und die Dozenten der Anfängervorlesungen werden an der Veranstaltung teilnehmen.

    Anschließend übernehmen die studentischen Mentor*innen der Mathematik, die den Studienanfänger*innen mit Rat und Tat zur Seite stehen.

    Weitere Informationen

  • 19200810 Proseminar
    Undergraduate Seminar: History + Contextualization of Mathematics (Anina Mischau)
    Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    This proseminar, specially designed for teacher training students, focuses on the discovery and development of mathematics as part of culture and society. From the point of view of "becoming mathematics", the main focus will be on the intra-mathematical development of selected mathematical topics and findings, their historical and cultural contextualisation and the actors involved in this development. In addition, some of these topics and findings will be examined as examples of where and to what extent they have found their way into other areas and contexts, e.g. in art, music, architecture or other scientific disciplines. In the second part of the proseminar, students will prepare small projects independently in group work on a mathematical topic of their choice and present them in the course.

    Suggested reading

    ... wird im Seminar bekannt gegeben.

  • 19201401 Lecture
    Linear Algebra I (Niels Lindner)
    Schedule: Di 12:00-14:00, Fr 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    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.

     

    Suggested reading

    • 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

  • 19201402 Practice seminar
    Practice seminar for Linear Algebra I (Niels Lindner)
    Schedule: Di 14:00-16:00, Mi 12:00-14:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: 1.1.26 Seminarraum E1 (Arnimallee 14)
    
  • 19201441 Zentralübung
    Large tutorial for Linear Algebra I (Tillmann Kleiner)
    Schedule: Fr 14:00-16:00 (Class starts on: 2025-04-25)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19202301 Lecture
    Computational Sciences (Sebastian Matera)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-07)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Comments

    The main focus of the module is on learning working methods. 1-3 problems of interdisciplinary relevance are selected and scientific theory, algorithmics, numerics and efficiency are rigorously practiced on these examples. In the computer exercises, students work in teams to develop, test and optimize implementations of the problems. Examples of suitable problems are e.g.:

    • Wave phenomena and spectral analysis methods: Waves and oscillations in physics, the Fourier and Laplace transforms, discretization, DFT, FFT, implementation, stability analysis, duration analysis, code optimization, hardware acceleration

    • Gravitation, electrostatics and computational procedures: gravitation problems and Coulomb‘s law, periodic systems and convergence, Ewald summation, error analysis, Particle Mesh Ewald, efficient implementation, hardware acceleration

    • Thermal conductivity equation, Poisson’s equation and solution methods: thermal conductivity equation, Poisson’s equation, parabolic PDEs, PDEs, analytical solutions for special cases, domain decomposition / finite element approximation, solution using algebraic methods, implementation, convergence analysis, code optimization, hardware acceleration

    • Data analysis and dimensional reduction: examples of correlated high-dimensional signals, Rayleigh quotient and optimality principle, eigenvalue problem, singular value decomposition and usual solution methods, Nyström approximation and sparse sampling, efficient implementation

  • 19202312 Project Seminar
    Project Seminar for Computational Sciences (Sebastian Matera)
    Schedule: Mo 16:00-18:00, Mi 16:00-18:00 (Class starts on: 2025-04-07)
    Location: A6/030 Rechnerpoolraum (Arnimallee 6)
    
  • 19202801 Lecture
    Analysis I (Pavle Blagojevic)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

    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:

    1. fundamentals, elementary logic, ordered pairs, relations, functions, domain and range of a function, inverse functions (injectivity, surjectivity)
    2. numbers, induction, calculations in R, C
    3. 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
    4. sequences and series, limits, cauchy sequences, convergence criteria, series and basic principles of convergence
    5. topological aspects of R, open, closed, and compact real sets
    6. sequences of functions, series of functions, power series
    7. properties of functions, boundedness, monotony, convexity
    8. continuity, limits and continuity of functions, uniform continuity, intermediate value theorems, continuity and compactness
    9. differentiability, concept of the derivative, differentiation rules, mean value theorem, local and global extrema, curvature, monotony, convexity
    10. elementary functions, rational functions, root functions, exponential functions, angular functions, hyperbolic functions, real logarithm, inverse trigonometric functions, curve sketching
    11. beginnings of integral calculus

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

    Suggested reading

    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.

  • 19202802 Practice seminar
    Tutorial: Analysis I (Pavle Blagojevic)
    Schedule: Di 14:00-16:00, Mi 10:00-12:00, Mi 14:00-16:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19202841 Zentralübung
    Large tutorial for Analysis I (Pavle Blagojevic)
    Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    
  • 19203533 Professional Internship
    Internship Mathematics (Luigi Delle Site)
    Schedule: -
    Location: keine Angabe
    

    Additional information / Pre-requisites

    at least 6 weeks (240 hours) not at university

    Comments

    Contents:
    Internships have an important orientation function for the progress of studies and for the future professional orientation of students. The internship itself serves to get to know a selected field of activity locally and to test the technical and key competences acquired so far in the concrete everyday working life. The events that accompany the internship offer the opportunity - through intensive preparation and reflection - to make the practical phase effective. The students deal with questions of career orientation and application and have the opportunity to exchange ideas about the concrete work process. In addition, they learn to define specialist knowledge in connection with professional requirements and to deal with the relationship between studies and business experience.
    Further information about the internship can be found here: Internship
    Information about the internship report: Internship report

    Target group:
    Mandatory module for students in the Bachelor's programme Mathematics.

  • 19203599 Miscellaneous
    Miscellaneous for Internship Mathematics (Luigi Delle Site)
    Schedule: -
    Location: keine Angabe
    

    Comments

    Achtung: Um das Modul "Berufspraktikum" abschliessen zu können, müssen Sie sich sowohl zu dieser Veranstaltung als auch zur Veranstaltung Berufspraktikum anmelden. Nur wenn Sie sich zu beidem angemeldet haben, ist das Modul komplett!

  • 19203611 Seminar
    Proseminar/Seminar: das Buch der Beweise (Giulia Codenotti)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Comments

    Inhalt: Vorträge zu Gitterproblemen in 2 (und 3) Dimensionen. Weitere Informationen finden Sie auf der Homepage des Proseminars.

  • 19204726 Methods Tutorial
    Peer Instruction (Alexandra Rezmer, Benedikt Weygandt)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    Zusätzliches Übungsangebot im Format der Methode Peer Instruction: Dabei werden passend zur jeweils ausgewählten Vorlesung vertiefende SC-Fragen vorgestellt, zu denen in Kleingruppen diskutiert wird. Diese Methode führt zu einem tragfähigen Verständnis zentraler mathematischer Begriffe und Sätze. 

    Suggested reading

    Bauer, T. (2019). Peer Instruction als Instrument zur Aktivierung von Studierenden in mathematischen Übungsgruppen. Mathematische Semesterberichte, 66, 219-241. https://doi.org/10.1007/s00591-018-0225-8

    Bauer, T. (2019). Verständnisaufgaben zur Analysis 1 und 2. Springer Spektrum. https://doi. org/10.1007/978-3-662-59703-3.

    Mazur, E. (2017). Peer instruction: Interaktive Lehre praktisch umgesetzt. Springer Spektrum. https://doi.org/10.1007/978-3-662-54377-1

  • 19205401 Lecture
    Basic module: Topology I (Christian Haase)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-04-16)
    Location: Mo A6/SR 031 Seminarraum (Arnimallee 6), Mi 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    
    Course Overview This is a beginning course from the series of three courses Topology I—III:

    1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
    2. Groups acting on topological spaces
    3. Gluing constructions, simplicial complexes
    4. Homotopies between continuous maps, degree of a map, fundamental group.
    5. Seifert-van Kampen Theorem.
    6. Covering spaces.
    7. Simplicial homology
    8. Combinatorial applications

    Suggested reading

    Literature:

    1. M. A. Armstron: Basic Topology, Springer UTM
    2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
    3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
    4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
    5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
    6. Klaus Jänich: Topologie, Springer-Verlag
    7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
    8. James R. Munkres: Topology, Prentice Hall

  • 19205402 Practice seminar
    Exercise for Basic Module: Topology I (Sofia Garzón Mora)
    Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    
  • 19206011 Seminar
    Discrete Mathematics Masterseminar (Tibor Szabo)
    Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

     

     

    Comments

    Content:
    The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
    Target audience:
    BMS students, Master students, or advanced Bachelor students.
    Prerequisites:
    Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

     

  • 19207101 Lecture
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

    Requirements: basic courses in analysis, basic course numerical mathematics

    Literature:

    Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
    https://doi.org/10.3390/atmos14101523

    T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

    J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

    Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000

  • 19207102 Practice seminar
    Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19211014 Advanced graduate seminar
    Advanced Seminar Nonlinear Dynamics (Bernold Fiedler, Isabelle Schneider)
    Schedule: Di 14:00-18:00 (Class starts on: 2025-04-15)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    In cooperation with Dr. Wolfrum (WIAS Berlin), lecturers present recent topics on dynamical systems.

  • 19211601 Lecture
    Analysis II (Marita Thomas)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Content

    This is the continuation of the Analysis I course taught in the previous winter term. Central topics of the course are integration in one space dimension and differential calculus of several variables. 

    Suggested reading

    • 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.

  • 19211602 Practice seminar
    Practice seminar for Analysis II (Marita Thomas)
    Schedule: Mi 14:00-16:00, Do 16:00-18:00 (Class starts on: 2025-04-16)
    Location: 1.1.53 Seminarraum E2 (Arnimallee 14)
    
  • 19211641 Zentralübung
    Large tutorial for Analysis II (André-Alexander Zepernick)
    Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19211701 Lecture
    Linear Algebra II (Alexander Schmitt)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-04-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Contents:

    • Determinants
    • Eigenvalues and eigenvectors: diagonalizability, trigonalizability, set of Cayley-Hamilton, Jordanian normal form
    • Bilinear forms
    • Vectorräume with scalar product: Euclidean, unitary vectorräume, orthogonal projection, isometries, self-adjusted images, Gram-Schmidt orthonormalization methods, major axis transformation

    Prerequisites:
    Linear Algebra I
    Literature:

    Will be mentioned in the lecture.

  • 19211702 Practice seminar
    Practice seminar for Linear Algebra II (Alexander Schmitt)
    Schedule: Do 08:00-10:00, Do 10:00-12:00, Do 16:00-18:00, Fr 08:00-10:00, Fr 10:00-12:00 (Class starts on: 2025-04-17)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    
  • 19211741 Zentralübung
    Mentoring for Linear Algebra II (Jan Sevenster)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19211901 Lecture
    Computer-oriented Mathematics II (Robert Gruhlke)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Additional information / Pre-requisites

    Studierende der Mathematik (Monobachelor und Lehramt) und Bioinformatik, sowie Numerikinteressierte aus Physik, Informatik und anderen Natur- und Geisteswissenschaften.

    Comments

    Inhalt:

    Die Auswahl der behandelten numerischen Verfahren enthält Polynominterpolation, Newton-Cotes-Formeln zur numerische Integration und Euler-Verfahren für lineare Differentialgleichungen.

  • 19211902 Practice seminar
    Practice seminar for Computer-oriented Mathematics II (Robert Gruhlke)
    Schedule: Di 08:00-10:00, Di 16:00-18:00, Mi 16:00-18:00, Do 08:00-10:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    
  • 19211941 Zentralübung
    Practice seminar for Computer-oriented Mathematics II (Claudia Schillings)
    Schedule: Fr 14:00-16:00 (Class starts on: 2025-04-25)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    
  • 19212001 Lecture
    Numerics I (Claudia Schillings)
    Schedule: Mo 10:00-12:00, Mi 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-14)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Numerical methods for: iterative solution of nonlinear systems of equations (fixpoint and Newton methods), curve fitting, interpolation, numerical quadrature, and numerics of ODE systems.

    Suggested reading

    Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 1. Springer, Berlin, 2005.

    Aus dem FU-Netz auch online verfügbar.

    Link

  • 19212002 Practice seminar
    Practice seminar for Numerics I (N.N.)
    Schedule: Di 08:00-10:00, Di 12:00-14:00 (Class starts on: 2025-04-15)
    Location: T9/049 Seminarraum (Takustr. 9)
    
  • 19212801 Lecture
    Theory of Functions (Nicolas Perkowski)
    Schedule: Di 14:00-16:00, Do 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Function theory is a classical field of mathematics, which deals with the properties of complex-differentiable functions on the complex number plane and has connections to algebra, analysis, number theory and geometry.

    The concept of complex differentiability restricts real-differentiable functions from R2 to R2 to angle-preserving images. We will discover that complex-differentiable functions are quite rigid objects, but they are endowed with many amazing analytical, geometric, and visual properties.

    A major result discussed in this lecture is Cauchy's integral theorem which states that the integral of any complexly differentiable function along a closed path in the complex plane is zero. We will see many nice consequences of this result, e.g. Cauchy's integral formula, the residual theorem and a proof of the fundamental theorem of algebra, as well as modern graphical representation methods.

    Suggested reading

    Literatur:

    E. Freitag and R. Busam 'Complex analysis', (Springer) 2nd Edition 2009 (the original German version is called 'Funktionentheorie')

  • 19212802 Practice seminar
    Practice seminar for Theory of Functions (Julian Kern)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    
  • 19213101 Lecture
    Geometry (Giulia Codenotti)
    Schedule: Di 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-04-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Inhalt

    Diese Vorlesung für das Bachelorstudium soll als natürliche Fortsetzung von Lineare Algebra I und II Fundamente legen für Vorlesungen/Zyklen wie Diskrete Geometrie, Algebraische Geometrie und Differenzialgeometrie.

    Sie behandelt grundlegende Modelle der Geometrie, insbesondere

    euklidische, affine, sphärische, projektive und hyperbolische Geometrie,Möbiusgeometrie, Polarität und Dualität Strukturgruppen, Messen (Längen, Winkel, Volumina), explizite Berechnungen und Anwendungen, Beispiele sowie Illustrationsthemen;

    Dabei werden weitere Bezüge hergestellt, zum Beispiel zur Funktionentheorie und zur Numerik.

    Suggested reading

    Literatur

    1. Marcel Berger. Geometry I
    2. David A. Brannan, Matthew F. Esplen, and Jeremy J. Gray. Geometry
    3. Gerd Fischer. Analytische Geometrie
    4. V.V. Prasolov und V.M. Tikhomirov. Geometry

  • 19213102 Practice seminar
    Practice seminar for Geometry (Giulia Codenotti)
    Schedule: Mo 10:00-12:00, Mo 16:00-18:00 (Class starts on: 2025-04-14)
    Location: A3/SR 119 (Arnimallee 3-5)
    
  • 19213910 Proseminar
    Proseminar/Seminar on Number Theory: Geometry of Numbers (Niels Lindner)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Nötige Vorkenntnisse: Lineare Algebra und eine gewisse Vertrautheit mit den Grundbegriffen der Algebra, etwa "Gruppe", "Ring", "Körper", "Ideal", "Normalteiler", etc.

    Comments

    This proseminar/seminar deals with Minkowski's "geometry of numbers", which does not only open up a geometric perspective on algebraic number theory, but also enables interesting applications in discrete geometry and combinatorial optimization. More precisely, we will dive into the following topics:

    * Minkowski's classical convex body theorems

    * Gaussian integers, Fermat's two-squares theorem, Legendre's four-squares theorem

    * Algebraic number fields, finiteness of the class number, Dirichlet's unit theorem

    * Linear equations over the integers: Hermite and Smith normal forms

    * Basics of lattice theory

    * Lattice basis reduction and the LLL algorithm

    * The shortest vector problem

    * Dense sphere packings

    * Khinchine's flatness theorem

    * Integer linear programming in fixed dimension

    The purpose of this list is to offer a coarse thematic overview. The precise seminar topics will be fixed later, together with the participants.

    Further information will be provided on the Whiteboard homepage of the seminar at the beginning of the lecture period.

  • 19214210 Proseminar
    Proseminar Wissenschaftskommunikation der Mathematik (Anna Maria Hartkopf)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-28)
    Location: A6/030 Rechnerpoolraum (Arnimallee 6)
    
  • 19214501 Lecture
    Basic Module: Algebra II (Holger Reich)
    Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisits: Comutitive algebra

    Comments

    The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

    Possible topics include: 
    - categories and functors
    - additive and abelian categories
    - cohomology
    - sheaf theory
    - ringed spaces
    - schemes
    - separated and proper morphisms
    - blowing up
    - embeddings into projective spaces, divisors, invertible sheaves 
    - Riemann-Roch -Gröbner bases.

    Suggested reading

    For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten

  • 19214502 Practice seminar
    Practice seminar for Basic Module: Algebra II (Georg Lehner)
    Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19214701 Lecture
    Discrete Mathematics I (Ralf Borndörfer)
    Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Target group:

    BMS students, Master and Bachelor students

    Whiteboard:

    You need access to the whiteboard in order to receive information and participate in the exercises.

    Large tutorial:

    Participation is recommended, but non-mandatory.

    Exams:

    1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
    2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

    Comments

    Content:

    Selection from the following topics:

    • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)

    Suggested reading

    • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
    • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
    • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
    • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
    • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.

  • 19214702 Practice seminar
    Practice seminar for Discrete Mathematics I (Silas Rathke)
    Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Comments

    Content:

    Selection from the following topics:

    • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
    • Discrete Structures (graphs, set systems, designs, posets, matroids)
    • Graph Theory (trees, matchings, connectivity, planarity, colorings)
    • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)

  • 19214741 Zentralübung
    Large tutorial for Discrete Mathematics I (Ralf Borndörfer)
    Schedule: Mi 08:00-10:00 (Class starts on: 2025-04-16)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    
  • 19214901 Lecture
    Basic Module: Discrete Geometrie II (Georg Loho)
    Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

    Comments

    Inhalt:

    This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

    The material will be a selection of the following topics:
    Linear programming and some applications

     

    • Linear programming and duality
    • Pivot rules and the diameter of polytopes

    Subdivisions and triangulations

    • Delaunay and Voronoi
    • Delaunay triangulations and inscribable polytopes
    • Weighted Voronoi diagrams and optimal transport

    Basic structures in convex geometry

     

    • convexity and separation theorems
    • convex bodies and polytopes/polyhedra
    • polarity
    • Mahler’s conjecture
    • approximation by polytopes

    Volumes and roundness

    • Hilbert’s third problem
    • volumes and mixed volumes
    • volume computations and estimates
    • Löwner-John ellipsoids and roundness
    • valuations

    Geometric inequalities

    • Brunn-Minkowski and Alexandrov-Fenchel inequality
    • isoperimetric inequalities
    • measure concentration and phenomena in high-dimensions

    Geometry of numbers

    • lattices
    • Minkowski's (first) theorem
    • successive minima
    • lattice points in convex bodies and Ehrhart's theorem
    • Ehrhart-Macdonald reciprocity

    Sphere packings

    • lattice packings and coverings
    • the Theorem of Minkowski-Hlawka
    • analytic methods

    Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

    Suggested reading

    The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.

  • 19214902 Practice seminar
    Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19215001 Lecture
    Constructive Combinatorics (Tibor Szabo)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Basic Bachelor Algebra, Probability, and Disrete Mathematics.

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

    Suggested reading

    A script will be provided.

  • 19215002 Practice seminar
    Constructive Combinatorics exercises (Tibor Szabo)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Comments

    Abstract:
    Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
    The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
    Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
    For further details please check Prof. Szabó's homepage.

  • 19215201 Lecture
    Basic Module: Numerics III (Volker John)
    Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisites

    Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

    Comments

    The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

     

    Suggested reading

    • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
    • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)

  • 19215202 Practice seminar
    Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
    Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Homepage:Wiki der Numerik II

  • 19215301 Lecture
    Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    Content:

    Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

    Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

     

    This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

    The course will cover a selection from the following topics

    1. Conservation laws and governing equations,

    2. Numerical methods for geophysical flow simulations,

    3. Dynamical systems and bifurcation theory,

    4. Data-based characterization of atmospheric flows

     

    This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

    Suggested reading

    Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

    Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

     

  • 19215302 Practice seminar
    Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    
  • 19215601 Lecture Cancelled
    Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Additional information / Pre-requisites

    <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

    Comments

    Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

    Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

    Suggested reading

    L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

    Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).

  • 19215602 Practice seminar Cancelled
    Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    

    Comments

    Am 23. April findet keine Übung statt.

  • 19216201 Lecture
    Markov chains and markov models (Marcus Weber)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Master students of Mathematics and Physics

    Comments

    Markov chains are a universal tool to model real-world processes, including financial markets, reaction kinetics and molecular dynamics.
    
    Topics:

    • Introduction to the theory of Markov chains
    • Estimation of Markov chains from data
    • Estimation uncertainty
    • Transition path theory
    • Analysis of Markov chains
    • Spectral analysis
    • Discretization of continuous Markov processes

  • 19216202 Practice seminar
    Practice seminar for Markov chains and markov models (Marcus Weber)
    Schedule: Di 12:00-14:00 (Class starts on: 2025-04-22)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Markov chains are a universal tool to model real-world processes, including financial markets, reaction kinetics and molecular dynamics.
    
    Topics:

    • Introduction to the theory of Markov chains
    • Estimation of Markov chains from data
    • Estimation uncertainty
    • Transition path theory
    • Analysis of Markov chains
    • Spectral analysis
    • Discretization of continuous Markov processes

  • 19217311 Seminar
    PhD Seminar "What is...?" (Holger Reich)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-18)
    Location: A7/SR 031 (Arnimallee 7)
    

    Additional information / Pre-requisites

    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.

    Comments

    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

  • 19219011 Seminar
    Seminar of IRTG 2544 "Stochastische Analysis in Interaktion" (Nicolas Perkowski)
    Schedule: Mi 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    PhD student seminar of IRTG 2544 "Stochastic Analysis in Interaction".

  • 19219701 Lecture
    Algebra with Probability in Combinatorics (Tibor Szabo)
    Schedule: Do 08:00-10:00 (Class starts on: 2025-04-17)
    Location: T9/049 Seminarraum (Takustr. 9)
    

    Comments

    In this lecture specialized topics of Combinatorics and Graph Theory are presented.

  • 19221001 Lecture
    Analysis 1 (Mathematics for Physicists I) (Rupert Klein)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-04-17)
    Location: 1.3.14 Hörsaal A (Arnimallee 14)
    

    Comments

    Content:
    Physics often uses the language of mathematics to describe nature. The course "Mathematics for Physicists" is intended to provide the necessary basics and tools from mathematics. The first part deals with sets and figures, bodies, real numbers, functions, sequences and limits, series, convergence criteria, continuity, derivations, differentiation rules, mean value theorem, Taylor series, Riemann integral, basic functions and main theorem, integration methods, inauthentic integrals, trigonometric series.

    Target group:
    Physics and meteorology students from the 1st semester onwards

    Requirements:
    Some school mathematics and interest

    Suggested reading

    Literatur:
    Kerner / von Wahl: Mathematik für Physiker, Springer Verlag.
    Fischer/Kaul: Mathematik für Physiker 1, Vieweg.

  • 19221002 Practice seminar
    Practice seminar for Analysis 1 (Mathematics for Physicists I) (Rupert Klein)
    Schedule: Di 14:00-16:00, Mi 12:00-14:00, Do 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    
  • 19221101 Lecture
    Mathematics for Geoscientists II (Niels Lindner)
    Schedule: Do 08:00-10:00 (Class starts on: 2025-04-17)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    General information
    Following the lecture "Mathematik für GeowissenschaftlerInnen I", this lecture extends the spectrum of mathematical tools helping us to describe and analyze processes in nature.
    Content: Separation of variables for functions of multiple variables; second order differential equations; systems of linear differential equations; linear systems of equations; vectors and matrices; scalar product and norm; functions of multiple variables; partial derivatives; gradient and Hessian matrix; simple partial differential equations from mathematical physics.

    Suggested reading

    Literatur wird in der Vorlesung bekannt gegeben

  • 19221102 Practice seminar
    Practice seminar for Mathematics for Geoscientists II (Niels Lindner)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: KöLu24-26/SR 017 (vorrang Schülerlabor) (Königin-Luise-Str. 24 / 26)
    

    Comments

    Inhalt: Separationsansatz für Funktionen mehrerer Veränderlicher; Differentialgleichungen 2. Ordnung; Systeme linearer Differentialgleichungen; Gleichungssysteme; Vektoren und Matrizen; Skalarprodukt und Norm; Funktionen mehrerer Veränderlicher; partielle Ableitungen; Gradient und Hessesche Matrix; einfache partielle Differentialgleichungen der mathematischen Physik.
    Literatur wird in der Vorlesung bekannt gegeben

  • 19222601 Lecture
    Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Zielgruppe: Students who are interested in stochastics and numerics
    Voraussetzungen: Stochastik I + II, Numerik I + II

    Comments

    Inhalt der Veranstaltung:
    The lecture will cover the following topics (not exhaustive)

    • Brownian motion 
    • Numerical discretization of stochastic differential equations
    • Monte Carlo methods
    • Representations of random fields
    • Modelling with stochastic differential equations
    • Applications

    Suggested reading

    Literatur:

    1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
    2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
    3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
    4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
    5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014

  • 19222602 Practice seminar
    Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19223111 Seminar
    BMS Fridays (Holger Reich)
    Schedule: Fr 14:00-17:00 (Class starts on: 2025-04-25)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

    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

  • 19223614 Advanced graduate seminar
    Advanced Seminar Topological Combinatorics (Pavle Blagojevic)
    Schedule: -
    Location: keine Angabe
    

    Comments

    In this seminar we treat current research problems in discrete and computational geometry that can be approached using methods from algebraic topology. The aim of the seminar is to make advances in research and introduce students to potential research topics.
    All seminars take place in the seminar room of the "Villa", Arnimallee 2, 14195 Berlin.

  • 19223901 Lecture
    Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
    Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

    Suggested reading

    The following books will be relevant:

    • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
    • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
    • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
    • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.

  • 19223902 Practice seminar
    Übung zu UQ and QMC (Claudia Schillings)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19224301 Lecture
    Basics of Mathematics Education
    Schedule: Mo 12:00-14:00 (Class starts on: 2025-04-28)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

    Comments

    The lecture deals with fundamental topics of mathematics education, which are taken up again and deepened in the seminars. It takes place on 8 dates as a double lesson.

  • 19224911 Seminar
    Basics of Mathematics Education 2 (Tablu Othmann)
    Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    In this seminar material didactic questions, i.e. for the respective topic characteristic possibilities, difficulties and hurdles for learning are treated. This seminar is offered on several parallel dates, some of which focus on different topics. Please select one of the seminars offered.

  • 19225011 Seminar
    Basics of Mathematics Education 2 (Tablu Othmann)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    In this seminar material didactic questions, i.e. for the respective topic characteristic possibilities, difficulties and hurdles for learning are treated. This seminar is offered on several parallel dates, some of which focus on different topics. Please select one of the seminars offered.

  • 19225501 Lecture
    Professional Mathematical Knowledge for Primary School Teachers II (Ulrike Bücking, Maren-Wanda Wolf)
    Schedule: Do 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2025-04-17)
    Location: Hs A (Raum B.006, 200 Pl.) (Arnimallee 22)
    

    Additional information / Pre-requisites

    Studien- und Prüfungsordnung Grundschulpädagogik (BA)

    Comments

    Die LV MatheProfi II besteht wöchentlich aus zwei Vorlesungen (insgesamt 12 Vorlesungen) bis zum 6.6.25 und wöchentlich einem Tutorium (Übung, Teilnahmepflicht bis zum Semesterende) sowie selbstständiger Arbeit im Umfang von ca. 6 h pro Woche (90 h gesamt). Zusätzlich bieten wir zu Ihrer Unterstützung eine Zentralübung an.

    In diesem Semester wird die elementare Geometrie fortgeführt. Außerdem werden Stochastik (insbesondere Wahrscheinlichkeitsrechnung), Graphentheorie und (grundschulrelevante) Körper im Raum thematisiert.

    Die Anmeldung zu dieser Veranstaltung im Whiteboard (ehemals KVV) ist unbedingt erforderlich: https://kvv.imp.fu-berlin.de, hier werden die Tutoriumsplätze verteilt! Weitere Informationen erfolgen hierzu per Mail, sofern Sie über das CampusManagement zur LV angemeldet sind.

    Suggested reading

    Literatur (online über FU Account):

    Holland, G. (1974). Geometrie für Lehrer und Studenten. Band 1. Hannover: Hermann Schroedel Verlag. (nicht online verfügbar)

    Helmerich, M. A., & Lengnink, K. (2016). Einführung Mathematik Primarstufe – Geometrie. Heidelberg : Springer Spektrum.

    Benölken, R. & Gorski, H.-J. & Müller-Philipp, S. (2008). Leitfaden Geometrie : Springer Spektrum.

    Büchter A, & Henn, H. (2005). Elementare Stochastik : eine Einführung in die Mathematik der Daten und des Zufalls. Berlin u.a. : Springer.

  • 19225541 Zentralübung
    Large tutorial for Professional Mathematical Knowledge for Primary School Teachers II (Jan-Hendrik de Wiljes)
    Schedule: Mo 10:00-12:00, Do 12:00-14:00 (Class starts on: 2025-04-14)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    
  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

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

    Comments

    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.

    Suggested reading

    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

  • 19226611 Seminar
    Seminar Quantum Computational Methods (Luigi Delle Site)
    Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

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

    Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

    Comments

    The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
    In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
    Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

    Suggested reading

    Related Basic Literature:
    (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
    (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
    (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871

  • 19227611 Seminar
    Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Comments

    The seminar covers advanced topics of uncertainty quantification and inverse problems.

  • 19229601 Lecture Cancelled
    Stochastic dynamics in fluids (Felix Höfling)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Target audience: M.Sc. Computational Sciences/Mathematik/Physik

    Requirements: some advanced course on either statistical physics or stochastic processes

    Comments

    The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

    The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

    Keywords:

    • Brownian motion, diffusion, and stochastic processes in fluids
    • harmonic analysis of correlation functions
    • Zwanzig-Mori projection operator formalism
    • mode-coupling approximations, long-time tails
    • critical dynamics and transport anomalies

    Suggested reading

    • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
    • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

    Further literature will be given during the course.

  • 19229602 Practice seminar Cancelled
    Exercises to Stochastic processes in fluids (Felix Höfling)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    
  • 19230015 Advanced seminar
    Mathematics Education - Selected Topics (N.N.)
    Schedule: Mi 11:00-14:00 (Class starts on: 2025-04-23)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    The course discusses the objectives of a school-based treatment of various contents of analysis lessons, the course on analytical geometry and stochastics in upper secondary school. Selected examples are used to develop concepts for didactic analysis and reduction of individual teaching units and to discuss conclusions for teaching and with regard to the Central Abitur.

    The use of digital media (computer algebra systems, interactive whiteboards, teaching software) in the upper secondary school is demonstrated with examples. In a block seminar, first experiences with the interactive whiteboard are gained and its use in the classroom is discussed.

  • 19230115 Advanced seminar
    Mathematics Education - Selected Topics (Karin Bergmann)
    Schedule: Di 12:00-15:00 (Class starts on: 2025-04-15)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    In der Veranstaltung werden Zielvorstellungen einer schulischen Behandlung verschiedener Inhalte des Analysisunterrichts, des Kurses zur Analytischen Geometrie und der Stochastik in der Sekundarstufe II erörtert. An ausgewählten Beispielen werden über die didaktische Analyse und Reduktion Konzepte einzelner Unterrichtseinheiten erarbeitet und Folgerungen für den Unterricht und in Hinblick auf das Zentralabitur diskutiert.

    Der Einsatz von digitalen Medien (Computeralgebrasysteme, interaktive Whiteboards, Unterrichtssoftware) in der gymnasialen Oberstufe wird an Beispielen aufgezeigt. In einem Blockseminar an einem Samstag (Termin n.V.) werden Erfahrungen am interaktiven Whiteboard/Panel gesammelt und dessen Einsatz im Unterricht diskutiert.

  • 19230215 Advanced seminar
    Mathematics Education - Selected Topics (Thorsten Scheiner)
    Schedule: Termine siehe LV-Details (Class starts on: 2025-05-23)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    In line with the Science Council's demand for consideration of the growing importance of media literacy, according to which teachers should be enabled to prepare students for the competent use of information and communication technologies and to make digital media available for teaching and learning processes in schools, this seminar will focus on the following topics discuss the functions and effects of digital media in teaching and learning processes, analysing the possibilities of Internet and software use in mathematics lessons and demonstrate the advantages and disadvantages of using these digital tools using selected examples.

    The focus is on the practical handling of the possibilities of the Internet and selected programs (spreadsheet and dynamic geometry software). This is to take place in the form of intensive small group work. Afterwards, it is necessary to question the use of the respective tool with regard to achieving the goals of mathematics teaching and to work out examples for a problem-adequate application.

    Forms of active participation: active participation in discussions, working on tasks, presentations of projects. The module examination takes the form of an exam (60 min).

  • 19230410 Proseminar
    Proseminar: Exploring randomness (Julian Kern)
    Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
    Location: A3/SR 115 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    The date in the first lecture week is cancelled. Instead, there will be an additional block date at the end of the semester on which all talks will be presented. The date will be discussed in the first meeting of the proseminar.

    Target group: Bachelor students (mono and combined)
    Prerequisites: None (topics will be adapted to previous knowledge)

    Comments

    Content: Students work independently and in groups on a project and present their results. The basis for assessment are not the research results, but the research process itself. At the end, the results are presented in the form of talks. A list of possible topics is discussed on the first date and adapted to the students' previous knowledge. All topics are from the field of probability theory.

    Suggested reading

    Keine

  • 19230515 Advanced seminar
    Mathematics Education - Development, Evaluation and Research (Brigitte Lutz-Westphal)
    Schedule: Di 09:00-12:00 (Class starts on: 2025-04-15)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    In this seminar we will deal with a current field of research in mathematics education. Innovative teaching concepts (e.g. research-based/self-organized/dialogical learning) form the main focus of the seminar and are developed in a theoretical and practical context.

    On the basis, methods and results of mathematics education research, own questions for learning and teaching mathematics are formulated, discussed and concretely developed. The students gain an insight into the methods of mathematics education research.

    Individual meetings may be held in blocks.

    Suggested reading

    Ruf, Urs & Gallin, Peter (1998 bzw. spätere Auflagen): Dialogisches Lernen in Sprache und Mathematik, Band 1 und 2

    Ruf, Urs; Keller, Stefan & Winter, Felix (2008): Besser lernen im Dialog

    lerndialoge.ch

  • 19230615 Advanced seminar
    Mathematics Education - Development, Evaluation and Research (Benedikt Weygandt)
    Schedule: Mo 09:00-12:00, Fr 14:00-14:30 (Class starts on: 2025-04-11)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    In this seminar we will deal with a current field of research in mathematics education. Innovative teaching concepts (e.g. research-based/self-organized/dialogical learning) form the main focus of the seminar and are developed in a theoretical and practical context.

    On the basis, methods and results of mathematics education research, own questions for learning and teaching mathematics are formulated, discussed and concretely developed. The students gain an insight into the methods of mathematics education research.

    Individual meetings may be held in blocks.

  • 19230815 Advanced seminar
    Mathematics Education - Development, Evaluation and Research (Thorsten Scheiner)
    Schedule: So Sa 10:00-18:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-05-30)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    Titel des Seminars: Stärkenbasierter Mathematikunterricht: Individuelle Förderung und positive Lernkultur

    Seminarbeschreibung: Dieses Seminar zielt darauf ab, Lehramtsstudierende darin zu befähigen, die mathematischen Stärken ihrer Schüler:innen zu erkennen und gezielt zu fördern. Mithilfe praxisorientierter Analysewerkzeuge und der Reflexion realer Schülerbeispiele lernen die Teilnehmer:innen, wie sie ein unterstützendes und motivierendes Lernumfeld gestalten können, das die individuellen Potenziale aller Schüler:innen entfaltet. Ein besonderer Schwerpunkt liegt dabei auf der Förderung einer positiven Lernatmosphäre, die wesentlich zur Entwicklung einer positiven mathematischen Identität und Selbstwirksamkeit beiträgt.

    Das Seminar findet als Blockveranstaltung an zwei Wochenenden statt (siehe Termine).

    Aktive Teilnahmeformen umfassen das Lesen fachlicher Texte, das Verfassen schriftlicher Aufgaben, die Analyse von Schülerarbeiten, das Üben von Wahrnehmungsfähigkeiten sowie die engagierte Teilnahme an den Seminareinheiten. Zusätzlich erstellen die Teilnehmenden ein Reflexionsportfolio.

    Modulprüfung: Hausarbeit  

  • 19231011 Seminar
    Practical Teaching Studies in Mathematics - Preparatory Seminar (Alexandra Rezmer)
    Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Refer to German description. Courses of Mathematis Education are part of the German teacher-training and held in German only.

  • 19231111 Seminar
    Practical Teaching Studies in Mathematics - Preparatory Seminar (N.N.)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-28)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Refer to German description. Courses of Mathematis Education are part of the German teacher-training and held in German only.

  • 19231211 Seminar Cancelled
    Practical Teaching Studies in Mathematics - Preparatory Seminar
    Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Refer to German description. Courses of Mathematis Education are part of the German teacher-training and held in German only.

  • 19233011 Seminar
    Elective Module - Gender & Diversity (Anina Mischau)
    Schedule: Sa 09:00-16:30, zusätzliche Termine siehe LV-Details (Class starts on: 2025-05-03)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Refer to German description. Courses of Mathematics Education are part of the German teacher-training and held in German only.

  • 19233115 Advanced seminar
    X-Student Research Group (Jan-Hendrik de Wiljes)
    Schedule: Do 09:00-12:00 (Class starts on: 2025-04-17)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Refer to German description. Courses of Mathematics Education are part of the German teacher-training and held in German only.

  • 19233511 Seminar
    Geometric Group Theory (Georg Lehner)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Additional information / Pre-requisites

    Aimed at: Bachelor and masters students
    
    Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.

    Comments

    Groups are best understood as symmetries of mathematical objects. Whereas finite groups can often be completely understood by their actions on vector spaces, this approach will often fail with infinite groups, such as free groups or hyperbolic groups. Geometric group theory tries to construct natural geometric objects (topological spaces such as manifolds or graphs for example) that these groups act on and allows one to classify the complexity these groups can have.
    
    In this seminar, we will follow Clara Löh's book on the subject. Topics will include Cayley graphs, free groups and their subgroups, quasi-isometry classes of groups, growth types of groups, hyperbolic groups and the Banach-Tarski theorem.

    Suggested reading

    Clara Löh - Geometric Group Theory

  • 19234501 Lecture
    Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
    Location: T9/053 Seminarraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Prerequisites: Basic knowledge of stochastics, and numerical methods

    Comments

    Content:

    Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

    - Basic of stochastic processes:

    Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

    - Model reduction techniques for stochastic dynamics:

    averaging technique, effective dynamics, Markov state modeling

    - Machine learning techniques using/for stochastic dynamics: 

    dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

    Suggested reading

    1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

    2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

    3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

    4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

    5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

    6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.

  • 19234502 Practice seminar
    Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
    Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

  • 19234810 Proseminar
    Women in the History of Mathematics and Computer Science (Anina Mischau)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    For mathematicians and computer scientists in a monobachelor's degree, creditable as ABV!

    Comments

    The seminar focuses on the development and rediscovery of the life stories and the work of some important mathematicians and computer scientists in the 19th and 20th centuries. The life and work of Sophie Germaine (1776-1831), Ada Lovelace (1815-1852), Sonja Kovalevskaya (1850-1891), Emmy Noether (1882-1935), Ruth Moufang (1905-1977), Grace Murray Hopper (1906-1992) and other female scientists are examined.

    The seminar is not about highlighting these women as an exception, because it would only set them on their exotic status. Rather, it is about a historical contextualization of their life and work. This not only enables an exemplary examination of social and cultural inclusion and exclusion processes along the gender category, but also the development of new perspectives on the traditional cultural history of both disciplines. The seminar is based on the approach of researching or discovering learning, i.e. the students will independently prepare and present individual seminar topics in group work. These presentations will then be discussed in the seminar. Through the use of observation sheets, a feedback culture is also to be tested that will be helpful in dealing with pupils and/or colleagues in later professional life.

  • 19236220 Course
    Mathematical Pupil Society (7th grade) (Maik Pickl)
    Schedule: Mi 16:00-18:00 (Class starts on: 2025-04-30)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    The Mathematical Pupil Society "Leonhard Euler" (MSG) is an extra-curricular, free institution for the promotion of mathematically interested and talented secondary school students based at the Institute for Mathematics at Humboldt University Berlin in cooperation with other Berlin universities, currently the Technische Universität Berlin, Freie Universität Berlin and Hochschule für Technik und Wirtschaft.

    Since 1970, the Mathematical Pupil Society "Leonhard Euler" has been supporting mathematically interested and talented students. In more than 20 weekly courses, the approx. 250 participants from grades 5 to 12 gain exciting insights into various areas of mathematics beyond the subject matter of the school. The focus is on problem-oriented work, scientific methods and training for mathematical competitions.

    The members of the MSG meet weekly for two hours for regular circular work. The circles take place in the premises of Berlin universities and some Berlin schools -- especially here at the FU Berlin at the Institute of Mathematics (c/o Prof. Günter M. Ziegler); they are led by staff of the universities, by students of Berlin universities, by (partly former) teachers of Berlin schools and other mathematics enthusiasts.

  • 19236320 Course
    Mathematical Pupil Society (8th grade) (Kerstin Hanff)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-08)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    The Mathematical Pupil Society "Leonhard Euler" (MSG) is an extra-curricular, free institution for the promotion of mathematically interested and talented secondary school students based at the Institute for Mathematics at Humboldt University Berlin in cooperation with other Berlin universities, currently the Technische Universität Berlin, Freie Universität Berlin and Hochschule für Technik und Wirtschaft.

    Since 1970, the Mathematical Pupil Society "Leonhard Euler" has been supporting mathematically interested and talented students. In more than 20 weekly courses, the approx. 250 participants from grades 5 to 12 gain exciting insights into various areas of mathematics beyond the subject matter of the school. The focus is on problem-oriented work, scientific methods and training for mathematical competitions.

    The members of the MSG meet weekly for two hours for regular circular work. The circles take place in the premises of Berlin universities and some Berlin schools -- especially here at the FU Berlin at the Institute of Mathematics (c/o Prof. Günter M. Ziegler); they are led by staff of the universities, by students of Berlin universities, by (partly former) teachers of Berlin schools and other mathematics enthusiasts.

  • 19236420 Course
    Mathematical School Society (9th grade) (Nils Heumann)
    Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    The Mathematical Pupil Society "Leonhard Euler" (MSG) is an extra-curricular, free institution for the promotion of mathematically interested and talented secondary school students based at the Institute for Mathematics at Humboldt University Berlin in cooperation with other Berlin universities, currently the Technische Universität Berlin, Freie Universität Berlin and Hochschule für Technik und Wirtschaft.

    Since 1970, the Mathematical Pupil Society "Leonhard Euler" has been supporting mathematically interested and talented students. In more than 20 weekly courses, the approx. 250 participants from grades 5 to 12 gain exciting insights into various areas of mathematics beyond the subject matter of the school. The focus is on problem-oriented work, scientific methods and training for mathematical competitions.

    The members of the MSG meet weekly for two hours for regular circular work. The circles take place in the premises of Berlin universities and some Berlin schools -- especially here at the FU Berlin at the Institute of Mathematics (c/o Prof. Günter M. Ziegler); they are led by staff of the universities, by students of Berlin universities, by (partly former) teachers of Berlin schools and other mathematics enthusiasts.

  • 19236520 Course
    Mathematical Pupil Society (10th grade) (Felix Funk)
    Schedule: Mi 16:00-18:00 (Class starts on: 2025-04-30)
    Location: Virtueller Raum 01
    

    Comments

    The Mathematical Pupil Society "Leonhard Euler" (MSG) is an extra-curricular, free institution for the promotion of mathematically interested and talented secondary school students based at the Institute for Mathematics at Humboldt University Berlin in cooperation with other Berlin universities, currently the Technische Universität Berlin, Freie Universität Berlin and Hochschule für Technik und Wirtschaft.

    Since 1970, the Mathematical Pupil Society "Leonhard Euler" has been supporting mathematically interested and talented students. In more than 20 weekly courses, the approx. 250 participants from grades 5 to 12 gain exciting insights into various areas of mathematics beyond the subject matter of the school. The focus is on problem-oriented work, scientific methods and training for mathematical competitions.

    The members of the MSG meet weekly for two hours for regular circular work. The circles take place in the premises of Berlin universities and some Berlin schools -- especially here at the FU Berlin at the Institute of Mathematics (c/o Prof. Günter M. Ziegler); they are led by staff of the universities, by students of Berlin universities, by (partly former) teachers of Berlin schools and other mathematics enthusiasts.

  • 19236620 Course
    Mathematical Pupil Society (11th grade) (Simon Hergersberg)
    Schedule: Di 16:00-18:00 (Class starts on: 2025-04-29)
    Location: A7/SR 031 (Arnimallee 7)
    

    Comments

    The Mathematical Pupil Society "Leonhard Euler" (MSG) is an extra-curricular, free institution for the promotion of mathematically interested and talented secondary school students based at the Institute for Mathematics at Humboldt University Berlin in cooperation with other Berlin universities, currently the Technische Universität Berlin, Freie Universität Berlin and Hochschule für Technik und Wirtschaft.

    Since 1970, the Mathematical Pupil Society "Leonhard Euler" has been supporting mathematically interested and talented students. In more than 20 weekly courses, the approx. 250 participants from grades 5 to 12 gain exciting insights into various areas of mathematics beyond the subject matter of the school. The focus is on problem-oriented work, scientific methods and training for mathematical competitions.

    The members of the MSG meet weekly for two hours for regular circular work. The circles take place in the premises of Berlin universities and some Berlin schools -- especially here at the FU Berlin at the Institute of Mathematics (c/o Prof. Günter M. Ziegler); they are led by staff of the universities, by students of Berlin universities, by (partly former) teachers of Berlin schools and other mathematics enthusiasts.

  • 19237901 Lecture
    Discovering Mathematics II (Christian Haase)
    Schedule: Mi 10:00-12:00, Mi 14:00-16:00, Do 16:00-18:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    
  • 19237902 Practice seminar
    Practice seminar for Discovering Mathematics II (Christian Haase)
    Schedule: Mi 12:00-14:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
    Location: A7/SR 031 (Arnimallee 7)
    
  • 19237941 Zentralübung
    Large tutorial for Discovering Mathematics II (Christian Haase)
    Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-28)
    Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
    

    Comments

    In der Zetralübung ist Anwesenheit Pflicht.

  • 19238601 Lecture
    Professional Mathematical Knowledge for Primary School Teachers I.1 (Ulrike Bücking, Jan-Hendrik de Wiljes)
    Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
    Location: , Gr. Hörsaal (Raum B.001), Hs A (Raum B.006, 200 Pl.)
    

    Additional information / Pre-requisites

    Studien- und Prüfungsordnung Grundschulpädagogik (BA)

    Comments

    Englische Übersetzung fehlt im MVS!

    Suggested reading

    Literatur (online über FU Account):
    Padberg, F., & Büchter, A. (2015). Einführung Mathematik Primarstufe - Arithmetik (Mathematik Primarstufe und Sekundarstufe I II). Berlin, Heidelberg: Springer Spektrum. [es gibt auch eine neuere Auflage von 2019]
     

  • 19238641 Zentralübung
    Large tutorial for Professional Mathematical Knowledge for Primary School Teachers I.1 (Ulrike Bücking, Maren-Wanda Wolf)
    Schedule: Mi 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-16)
    Location: Hs A (Raum B.006, 200 Pl.) (Arnimallee 22)
    
  • 19239711 Seminar
    Advanced Dynamical Systems (Bernold Fiedler)
    Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in delay equations. Dates only by arrangement.

  • 19239911 Seminar
    Advanced Differential Equations (Bernold Fiedler)
    Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in dynamical systems. Dates only by arrangement.

  • 19240701 Lecture
    Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
    Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    

    Additional information / Pre-requisites

    Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

    Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

    Comments

    Prpgram:

    -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

  • 19240702 Practice seminar
    Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
    Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
    Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    
  • 19241301 Lecture
    Partial Differential Equations I (André Erhardt)
    Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Comments

    • Basic differential equations (Laplace,- heat and wave equations)
    • Representation formulas
    • Solution methods
    • Introduction to Hilbert space methods

    This can serve as the basis for a BSc and/or MSc project.  

    Suggested reading

    L.C. Evans, Partial Differential Equations
     

  • 19241302 Practice seminar
    Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
    Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
    Location: 0.1.01 Hörsaal B (Arnimallee 14)
    
  • 19241710 Proseminar
    Proseminar Mathematics Panorama (Anna Maria Hartkopf)
    Schedule: Termine siehe LV-Details (Class starts on: 2025-09-24)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Detaillierte Informationen finden Sie auf der Webseite zum Seminar Panorama der Mathematik.

    Inhalt: Im Seminar Panorama der Mathematik sollen in Absprache mit den Teilnehmern ausgewählte Themen aus der älteren und jüngeren Geschichte der Mathematik herausgegriffen und untersucht werden. Denkbare Themen sind zum Beispiel die Entwicklung von Algorithmen wie Newton-Verfahren, Gauss-Elimination, Matrix-Multiplikation, Simplex-Verfahren etc., die Entwicklung von Bereichen der Mathematik wie Invariantentheorie, Mengenlehre, Topologie o.ä.. Dabei sollen auch moderne Aspekte berücksichtigt werden, etwa aktuelle Anwendungen, Forschungsstand, Ergebnisse aus der jüngeren Vergangenheit.

    Suggested reading

    1. Hans Wußing, 6000 Jahre Mathematik: Eine kulturgeschichtliche Zeitreise;
    2. Band 1: Von den Anfängen bis Leibniz und Newton, Band 2: Von Euler bis zur Gegenwart, Springer 2009
    3. Heinz-Wilhelm Alten et al., 4000 Jahre Algebra, Springer 2008
    4. Christoph J. Scriba, 5000 Jahre Geometrie, Springer 2009
    5. Heinz-Niels Jahnke, Geschichte der Analysis: Texte zur Didaktik der Mathematik, Spektrum 1999
    6. Richard Courant und Herbert Robbins, Was ist Mathematik?, Springer 2010
    7. Phillip J. Davis, Reuben Hersh, The Mathematical Experience, Mariner Books 1999
    8. Knoebel, Arthur; Laubenbacher, Reinhard; Lodder, Jerry; Pengelley, David
    9. Mathematical masterpieces, Springer 2007
    10. Laubenbacher, Reinhard; Pengelley, David, Mathematical expeditions. Chronicles by the explorers, Springer 1999
    11. sowie abhängig vom Thema

  • 19242101 Lecture
    Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
    Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Prerequisite: Stochastics I, II, III. 
    Recommended: Functional Analysis.

    Comments

    Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

    • Ito calculus for Gaussian random measures;
    • semilinear stochastic PDEs in one dimension;
    • Schauder estimates;
    • Gaussian hypercontractivity;
    • paraproducts and paracontrolled distributions;
    • local existence and uniqueness for semilinear SPDEs in higher dimensions;
    • properties of solutions

    Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

    Suggested reading

    Literature
    There will be lecture notes.

  • 19242102 Practice seminar
    Exercise: Stochastics IV (Guilherme de Lima Feltes)
    Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    
  • 19243001 Lecture
    Partial Differential Equations III (Erica Ipocoana)
    Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Voraussetzungen: Partielle Differentialgleichungen I und II

    Comments

    The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

     

    Suggested reading

    Wird in der Vorlesung bekannt gegeben / to be announced.

  • 19243002 Practice seminar
    Tutorial Partial Differential Equations III (Erica Ipocoana)
    Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
    Location: A3/SR 119 (Arnimallee 3-5)
    
  • 19244601 Lecture
    Methods of Molecular Simulations (Felix Höfling)
    Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Exercises will be computer based

    Comments

    This course teaches molecular simulation algorithms and techniques, in particular:

    • Molecular dynamics algorithm and integrators
    • Monte Carlo sampling
    • Thermostats and barostats
    • Electrostatic treatment
    • Implicit vs. explicit solvent methods

    Suggested reading

    It is recommended to get access to or a hard copy of at least one of the following books:

    • Allen & Tildesley: Computer simulation of liquids, 2nd ed. (Oxford Univ. Press, 2017)
    • Frenkel & Smit: Understanding molecular simulation, 2nd ed. (Acad. Press, London, 2002)
    • Tuckerman: Statistical Mechanics: Theory and Molecular Simulation (Oxford Univ. Press, 2010)
    • Rapaport: The art of molecular dynamics simulations, 2nd ed. (Cambridge Univ. Press, 2004)

  • 19244602 Practice seminar
    Lecture for Methods of Molecular Simulations (Felix Höfling)
    Schedule: Do 10:00-12:00 (Class starts on: 2025-04-24)
    Location: A3/SR 120 (Arnimallee 3-5)
    
  • 19245610 Proseminar
    Proseminar Mathematik - Lehramt (Brigitte Lutz-Westphal)
    Schedule: Mo 08:00-10:00 (Class starts on: 2025-04-14)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Der Titel dieses Seminares ist „Was genau soll ich unterrichten? Schulmathematik neu entdeckt“.

    Dabei werden wir ausgewählte Lehrplanthemen gründlich durchdenken und das dafür benötigte Fachwissen genauer beleuchten. Eine solche „Sachanalyse“ ist die Basis für jegliche Unterrichtsplanung, wie sie in den späteren Fachdidaktik-Modulen Stück für Stück erarbeitet wird. Eine aktive Mitarbeit in den Seminarsitzungen wird erwartet. (Die Themen dieses Proseminars eigenen sich evtl. nicht als Themen für die in der Fachwissenschaft anzufertigende Bachelorarbeit!)

     

    Comments

    Dieses Proseminar richtet sich ausdrücklich an Lehramtsstudierende bereits ab dem 2. Fachsemester Mathematik.
    Es folgt einem neuen Konzept, das wir erproben wollen, um schon zu Beginn des Lehramtsstudiums bereits den Blick stärker in Richtung Schule und Unterricht wenden zu können. Auch höhere Semester sind willkommen.

    Achtung, das Seminar beginnt erst am Montag, den 28.04.! Am Montag 14.04. finden wegen des Dies Academicus keine Lehrveranstaltungen statt und am Montag 21.04. ist ein Feiertag.

    Suggested reading

    Literatur wird im Seminar bekannt gegeben.

  • 19245910 Proseminar
    Undergraduate Seminar: XSRG (Jan-Hendrik de Wiljes)
    Schedule: Do 09:00-12:00 (Class starts on: 2025-04-17)
    Location: Virtueller Raum 02
    

    Additional information / Pre-requisites

    Voraussetzungen: Mindestens 2-3 Anfangsvorlesungen in Mathematik, insbesondere Lineare Algebra, sollten besucht worden sein. Es wird nicht so sehr um die dort vermittelten Inhalte gehen, sondern vielmehr darum, mathematisches Arbeiten an der Hochschule (Definition, Satz, Beweis, Problemlösen) kennengelernt zu haben.

    Comments

    Hinweise

    • Wichtig: Dieses Proseminar dient nur als Platzhalter-Veranstaltung für die X-Student Research Group, die als Präsenzveranstaltung Do 9‒12 Uhr in Raum 024/A3 stattfindet. 
    • XSRGs sind studentische Forschungsgruppen, weitere Infos zu diesem Format unter: https://www.berlin-university-alliance.de/commitments/teaching-learning/sturop/research-groups/index.html 
    • Teilnahme: Insgesamt gibt es 15 Plätze. Um einen Platz zu erhalten, muss man am ersten Veranstatlungstermin physisch anwesend sein. Bei mehr als 15 Personen entscheidet das Los.
    • Die erfolgreiche Teilnahme an dem XSRG-Modul gibt 5 LP (unbenotet, nur pass/fail). Anschließend kann beim jeweiligen Prüfungsbüro ein Antrag gestellt werden, um dieses Modul im ABV-Bereich (alle Studiengänge) anzurechnen. Je nach Studiengang wurde die XSRG in der Vergangenheit beispielsweise auch schon als fachdidaktisches Wahlmodul oder mathematisches Proseminar angerechnet. 
    • Bei Fragen gerne im Vorfeld an weygandt@math.fu-berlin.de und jan.dewiljes@math.fu-berlin.de wenden.

     

    XSRG „Mathematiklehre bottom-up denken“

    Was passiert eigentlich, wenn Studierende Hochschullehre reflektieren und lernförderlich (um)gestalten?

    Es ist immer einfach, bestehende Konzepte zu kritisieren ‒ aber davon alleine ändert sich ja nichts! Daher wollen wir euch die einmalige Gelegenheit geben, eure Erfahrungen, Expertise und Perspektive als Lernende in die Weiterentwicklung guter Hochschullehre einzubringen. 

    Lassen wir uns dafür mal auf ein ‒ vielleicht verrücktes? ‒ Gedankenexperiment ein:

    • Was würde herauskommen, wenn Studierende eine für sie selbst sinnvolle und gute Mathe-Vorlesung gestalten? Oder gleich ein ganzes Modul?
    • Welche Art von Tutorien haltet ihr für sinnvoll? Welche Tätigkeiten (denken, nachrechnen, diskutieren ...) sollten in den jeweiligen Veranstaltungen (VL, Übung, Zentralübung...) in welchem Format (frontal, einzeln, Gruppe ...) passieren?
    • Und was ist mit dem Material: Wie sollten Übungsaufgaben aussehen? Skripte? Klausuren?

    Ablauf

    Zur Inspiration beginnen wir mit einer kurzen Einführung in die Hochschulmathematikdidaktik und u.a. auch einem Besuch beim University:Future Festival.

    Anschließend widmen wir uns in Kleingruppen unterschiedlichen Mathematik-Veranstaltungen aus euren Studiengängen. Infrage kommt alles von Mathematik entdecken über Analysis I, Mathematik für Physiker*innen I, die Nebenfachvorlesung im Medizinstudium bis hin zu Höherer Topologie VIII ‒ wichtig ist, dass ihr damit Erfahrungen gemacht habt!

    Die von euch erarbeiteten Ideen, Ansätze und Konzepte können wir anschließend auch mit Hochschullehrenden diskutieren und ausprobieren! 

     

    Suggested reading

    Die Literatur wird bei der Vorbesprechung bekanntgegeben. Zur Einstimmung kann man bereits etwas in einem der Bände der Reihe Winning Ways for Your Mathematical Plays von Berlekamp, Conway und Guy schmökern.

    Unbedingt zur Seminarvorbereitung lesen:

    M. Lehn: Wie halte ich einen Seminarvortrag?

  • 19246021 Projekt
    Mathematical modeling in discussions of societal challenges (Sarah Wolf, Anina Mischau, Joshua Wiebe)
    Schedule: Mi 13:00-17:00 (Class starts on: 2025-04-16)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Additional information / Pre-requisites

    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

     

    Comments

    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.

    Schwerpunkte im Bereich Mathematik für Schulen:

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

    Schwerpunkte im Bereich mathematische Forschung:

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

    Suggested reading

    Wird in der ersten Sitzung bekannt gegeben.

  • 19247111 Seminar
    Variational methods & Gamma-convergence (Marita Thomas)
    Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

  • 19247620 Course
    Mathematics Teacher Training Course 13 (Ralph-Hardo Schulz, Gabriella Artisi, Karin Bergmann, Sabine Giese, Melanie Carola Schnapka, Volker Schulze)
    Schedule: -
    Location: keine Angabe
    
  • 19248101 Lecture
    Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

    Comments

    Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
     

    Leitidee der Veranstaltung
    Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

    Inhaltliche Schwerpunkte
    Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

    Methodische Konzeption
    Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

    Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
    Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

    Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
     

    Überblick über die wöchentliche Struktur der Veranstaltung 

    • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
    • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
    • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

     

    Lernziele
    Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

    Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

    • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
    • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
    • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
    • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
    • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

     

    Formalia & Organisatorisches
    a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
    b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

    • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
    • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
    • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

    c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
     

  • 19248102 Practice seminar
    Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
    Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    
  • 19254707 Integrierte Veranstaltung
    Mathematisches Professionswissen für das Lehramt an Grundschulen I.2 - Quereinstieg (Christine Scharlach)
    Schedule: Mo 12:00-14:00, Di 12:00-14:00, Mi 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Studien- und Prüfungsordnung

    Comments

    Die LV MatheProfi I.2 besteht wöchentlich aus einer Integrierten Veranstaltung mit drei Terminen (Teilnahmepflicht) und einem Tutorium (Übung) sowie weiterer selbstständiger Arbeit im Umfang von ca. 8 h pro Woche (mit Prüfungsvorbereitung 180 h gesamt). Inhaltlich liegt der Schwerpunkt des ersten Teils weiter im Bereich der Arithmetik ("Zahlen und Operationen"), im zweiten Teil dann im Bereich der Geometrie ("Raum und Form").

    Bitte melden Sie sich im Campus Management an.

    Suggested reading

    Literatur (online über FU Account):
    Padberg, F., & Büchter, A. (2015). Einführung Mathematik Primarstufe - Arithmetik (Mathematik Primarstufe und Sekundarstufe I+II). Berlin, Heidelberg: Springer Spektrum. [neuere Auflage von 2019]

    Padberg, F., & Büchter, A. (2015). Vertiefung Mathematik Primarstufe — Arithmetik/Zahlentheorie (2. Aufl. ed.). Berlin [u.a.]: Springer Spektrum.

    Padberg, F.,  Wartha, S., und Büchter, A. Didaktik Der Bruchrechnung. Mathematik Primarstufe und Sekundarstufe I+II. (5. Aufl. 2017 ed.), Berlin, Heidelberg: Springer , 2017.

    Holland, G. (1974). Geometrie für Lehrer und Studenten. Band 1. Hannover: Hermann Schroedel Verlag. (nicht online verfügbar)

    Helmerich, M. A., & Lengnink, K. (2016). Einführung Mathematik Primarstufe – Geometrie. Heidelberg : Springer Spektrum.

  • 19254741 Zentralübung
    Zentralübung zu Mathematisches Professionswissen für das Lehramt an Grundschulen I.2 - Quereinstieg (Christine Scharlach, Wiebke Neumann)
    Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    
  • 19320501 Lecture
    Cryptanalysis of Symmetrical Schemes (Marian Margraf)
    Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
    Location: 1.4.03 Seminarraum T2 (Arnimallee 14)
    

    Comments

    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.

  • 19320502 Practice seminar
    Practice seminar for Cryptanalysis (Marian Margraf)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    
  • 19322701 Lecture
    Cryptoanalysis of Asymmetrical Schemes (Marian Margraf)
    Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Comments

    Cryptoanalysis of asymmetrical schemes

    The lecture deals with different asymmetrical cryptanalytics, in particular with the supposed hard problems of these processes. Some of the contents are

    • RSA and the problem of factorization
    • DSA and the discrete logarithm problem
    • Merkel-Hellman and the knapsack and grid problem
    • McEliece and the problem of decoding
    • Matsumoto-Imai and the multivariate Polynomial System

    Knowledge in the areas of IT security and cryptography is obligatory.

  • 19322702 Practice seminar
    Practice seminar for Cryptoanalysis of Asymmetrical Schemes (Marian Margraf)
    Schedule: Mi 16:00-18:00 (Class starts on: 2025-04-16)
    Location: T9/K40 Multimediaraum (Takustr. 9)