Mathematics

• Analysis I

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  • 19202801 Lecture
    Analysis I (Marita Thomas)
    Schedule: Di 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-15)
    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

    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 (Marita Thomas)
    Schedule: Mi 12:00-14:00, Mi 14:00-16:00, Mi 16:00-18:00, Fr 08:00-10:00 (Class starts on: 2024-10-16)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

• Analysis II

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  • 19211601 Lecture
    Analysis II (Isabelle Schneider)
    Schedule: Di 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Suggested reading

     

  • 19211602 Practice seminar
    Practice seminar for Analysis II (Isabelle Schneider)
    Schedule: Mi 10:00-12:00, Do 16:00-18:00, Fr 10:00-12:00 (Class starts on: 2024-10-16)
    Location: A3/SR 115 (Arnimallee 3-5)
    

• Analysis III

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  • 19201301 Lecture
    Analysis III (Holger Reich)
    Schedule: Di 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

    Comments

    Contents

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

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

    These basics are indispensable for a successful study of mathematics.

    Suggested reading

    Literatur

    • T. Bröcker: Analysis II und Analysis III, Bibliographisches Institut, Mannheim, 1992
    • H. Amann, J. Escher: Analysis 3, Birkhäuser Verlag, 2008.
    • S. Hildebrandt: Analysis 2, Springer Verlag, 2003.
    • K. Königsberger: Analysis 2, Springer Verlag, 2004.

  • 19201302 Practice seminar
    Practice seminar for Analysis III (Holger Reich, Georg Lehner)
    Schedule: Di 14:00-16:00 (Class starts on: 2024-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

• Linear Algebra I

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  • 19201401 Lecture
    Linear Algebra I (Alexander Schmitt)
    Schedule: Mo 08:00-10:00, Mi 08:00-10:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-16)
    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 (Alexander Schmitt)
    Schedule: Mo 10:00-12:00, Mo 16:00-18:00, Mi 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2024-10-14)
    Location: A3/SR 119 (Arnimallee 3-5)
    

• Linear Algebra II

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  • 19211701 Lecture
    Linear Algebra II (N.N.)
    Schedule: Mi 12:00-14:00, Fr 08:00-10:00 (Class starts on: 2024-10-16)
    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 (N.N.)
    Schedule: Mo 10:00-16:00 (Class starts on: 2024-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Computer-Oriented Mathematics I

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  • 19200501 Lecture
    Computerorientated Mathematics I (5 LP) (Ralf Kornhuber, Claudia Schillings)
    Schedule: Fr 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-18)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

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

    Homepage: All current information on lectures and lectures

    Suggested reading

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

  • 19200502 Practice seminar
    Practice seminar for Computerorientated Mathematics I (5 LP) (André-Alexander Zepernick)
    Schedule: Mo 12:00-14:00, Mo 14:00-16:00, Di 08:00-10:00, Di 16:00-18:00, Mi 10:00-12:00, Do 14:00-16:00, Fr 08:00-10:00 (Class starts on: 2024-10-21)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Probability and Statistics I

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  • 19200601 Lecture
    Stochastics I (Ana Djurdjevac)
    Schedule: Mo 14:00-16:00, Mi 12:00-14:00 (Class starts on: 2024-10-14)
    Location: T9/SR 006 Seminarraum (Takustr. 9)
    

    Additional information / Pre-requisites

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

    Comments

    Inhalt:

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

    Suggested reading

    Literatur:

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

  • 19200602 Practice seminar
    Tutorial: Stochastics I (N.N.)
    Schedule: Mo 12:00-14:00, Di 08:00-10:00 (Class starts on: 2024-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Academic Work in Mathematics

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  • 19202211 Seminar
    Seminar Discrete Mathematics I (Tibor Szabo)
    Schedule: Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-08)
    Location: T9/046 Seminarraum (Takustr. 9)
    

    Comments

    This seminar will carry out a more specific study of some of the concepts of enumerative combinatorics and discrete structures that were introduced in the lecture Discrete Mathematics I.

  • 19203311 Seminar Cancelled
    Proseminar/Seminar Gruppentheorie (N.N.)
    Schedule: -
    Location: keine Angabe
    

    Additional information / Pre-requisites

    Participants should feel comfortable with the contents of 'Linear algebra 1', and perhaps 'Linear algebra 2'. If there are interested students who have already done the 'Algebra und Zahlentheorie' module, we will also be able to find interesting topics for them.

    Comments

    In this (pro)seminar we will recapitulate the basics of group theory and study a few deeper properties and theorems. Possible topics are: solvable groups, nilpotent groups, representations of finite groups, the theorem of Schur-Zassenhaus, the theorems of P. Hall.

  • 19208111 Seminar
    Masterseminar Stochastics (Nicolas Perkowski, N.N.)
    Schedule: Termine siehe LV-Details (Class starts on: 2024-10-16)
    Location: A6/SR 009 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

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

    Comments

    Content: The seminar covers advanced topics of stochastics.

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

    Suggested reading

    Literatur wir in der Vorbesprechung bekanntgegeben.

    Literature will be announced in the preliminary discussion

  • 19226511 Seminar
    Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
    Schedule: Fr 12:00-14:00 (Class starts on: 2024-10-18)
    Location: A7/SR 031 (Arnimallee 7)
    

    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

  • 19239711 Seminar
    Infinite-Dimensional Dynamics (Bernold Fiedler, Isabelle Schneider)
    Schedule: Do 16:00-18:00 (Class starts on: 2024-10-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in delay equations.

  • 19239911 Seminar
    Nonlinear Dynamics (Bernold Fiedler, Isabelle Schneider)
    Schedule: Do 14:00-16:00 (Class starts on: 2024-10-17)
    Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    

    Comments

    Students present recent papers on topics in dynamical systems.

  • 19247111 Seminar
    Topics in measure and integration theory (Marita Thomas)
    Schedule: Di 16:00-18:00 (Class starts on: 2024-10-15)
    Location: A3/SR 119 (Arnimallee 3-5)
    

    Comments

    This seminar builds upon the Analysis III course to deepen topics in measure and integration theory. Topics are, for example: covering theorems, Lebesgue-, Hausdorff- and Radon measures, Radon Nikodym derivatives. 

• Special topics in Mathematics

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  • 19202001 Lecture
    Discrete Geometrie I (Georg Loho)
    Schedule: Di 10:00-12:00, Mi 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-15)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

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

    Comments

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

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

     

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

     

     

     

     

     

     

     

     

     

    Suggested reading

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

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Georg Loho)
    Schedule: Mo 16:00-18:00, Fr 10:00-12:00 (Class starts on: 2024-10-14)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

• Special topics in Pure Mathematics

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  • 19236101 Lecture
    Mathematisches Panorama (Sarah Wolf, Anina Mischau)
    Schedule: Di 12:00-14:00 (Class starts on: 2024-10-15)
    Location: T9/SR 005 Übungsraum (Takustr. 9)
    

    Comments

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

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

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

    Suggested reading

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

  • 19236102 Practice seminar
    Übung zu: Mathematisches Panorama (Anina Mischau, Sarah Wolf)
    Schedule: Mi 14:00-16:00, Do 12:00-14:00, Do 16:00-18:00 (Class starts on: 2024-10-16)
    Location: A3/ 024 Seminarraum (Arnimallee 3-5)
    

• Functional Analysis

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  • 19201901 Lecture
    Functional Analysis (Pavle Blagojevic)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2024-10-15)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Content:
    Functional analysis is the branch of mathematics dealing with the study of normalized (or general topological) vector spaces and continuous images between them. Analysis, topology and algebra are linked.
    The lecture deals with Banach and Hilbert spaces, linear operators and functional as well as spectral theory of compact operators.

    Target group: Students from the 3rd/4th semester on.

    Requirements: Good command of the material of the lectures Analysis I/II and Linear Algebra I/II.

    Suggested reading

    Literatur:

    • Dirk Werner: Funktionalanalysis, 7. Auflage, Springer-Verlag 2011, ISBN 978-3-642-21016-7

  • 19201902 Practice seminar
    Tutorial: Functional Analysis (Pavle Blagojevic, N.N.)
    Schedule: Do 16:00-18:00 (Class starts on: 2024-10-17)
    Location: A3/019 Seminarraum (Arnimallee 3-5)
    

    Comments

    Inhalt:
    Die Funktionalanalysis ist der Zweig der Mathematik, der sich mit der Untersuchung von normierten (oder allgemeiner topologischen) Vektorräumen und stetigen Abbildungen zwischen ihnen befasst. Hierbei werden Analysis, Topologie und Algebra verknüpft.
    Die Vorlesung behandelt Banach- und Hilberträume, lineare Operatoren und Funktionale sowie Spektraltheorie kompakter Operatoren.
    
    Zielgruppe: Studierende vom 4. Semester an.
    
    Voraussetzungen: Sicheres Beherrschen des Stoffs der Vorlesungen Analysis I/II und Lineare Algebra I/II.
    
    Literatur:

     

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

     

• Algebra and Number Theroy

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  • 19200701 Lecture
    Algebra and Theory of Numbers (Kivanc Ersoy)
    Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2024-10-14)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

    Subject matter:
    Selected topics from:

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

  • 19200702 Practice seminar
    Practice seminar for Algebra and Theory of Numbers (N.N.)
    Schedule: Fr 10:00-12:00 (Class starts on: 2024-10-18)
    Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    

• Mathematical Project

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  • 19246021 Projekt
    Mathematical modeling in discussions of societal challenges (Sarah Wolf, Anina Mischau, Joshua Wiebe)
    Schedule: Mi 13:00-17:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-16)
    Location: A6/SR 032 Seminarraum (Arnimallee 6)
    

    Additional information / Pre-requisites

    Ggf können Veranstaltungen mit Schüler*innen 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 bzw. Aspekten der Wissenschaftskommunikation. So werden z.B. Grundlagen des Kommunikationsformats erarbeitet (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 hergestellt. Praktisch arbeiten die Studierenden in Gruppen an eigenen Modellen und entwerfen Elemente, die in Zusammenhang mit einem Decision Theatre im schulischen Kontext oder mit anderen gesellschaftlichen Zielgruppen verwendet werden können. Das Anwendungsthema ist nachhaltige Mobilität.

    In dem Projektseminar ist ein intensiver Austausch zwischen Studierenden aus dem Monostudiengang und aus dem Lehramtsstudiengang der Mathematik intendiert. Durch das Kennenlernen von und die Mitwirkung in einem aktuellen mathematischen wie didaktischen Forschungsprojekt und durch den Einblick in dessen Abläufe und 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 und Beobachtung von Schüler*innengruppen

    Schwerpunkte im Bereich mathematische Forschung:

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

    Suggested reading

    Wird in den Sitzungen bekannt gegeben.

• Algebra I

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  • 19202501 Lecture
    Basic Module: Algebra I (Alexandru Constantinescu)
    Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-14)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Content

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

    ? Affine algebraic varieties

    ? Rings, ideals, and modules

    ? Noetherian rings

    ? Local rings and localization

    ? Primary decompositione

    ? Finite and integral extensions

    ? Dimension theory

    ? Regular rings

    Target Group
    Students with the prerequisites mentioned below.

    Prerequisites
    ? Linear Algebra I+II ? Algebra and Number Theory
    
    Literature
    ? Atiyah, M.F.; Macdonald, I.G.: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 ix+128 pp. (This book is probably the best entry to the subject. It is short, concise, and clearly written.)
    ? Further literature will be announced in class.

    
    Homepage: Professor Alexander Schmitt

  • 19202502 Practice seminar
    Practice seminar for Basic Module: Algebra I (Alexandru Constantinescu)
    Schedule: Mo 08:00-10:00, Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-09)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

• Numerical Mathematics II

  0084dB3.4
  • 19202101 Lecture
    Basic Module: Numeric II (Volker John)
    Schedule: Mo 10:00-12:00, Mo 14:00-20:00 (Class starts on: 2024-10-14)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

    Comments

    Description: Extending basic knowledge on initial value problems with ordinary differential equations from Numerik I, the course presents methods for stiff problems and multistep methods. In the second part of the course iterative methods for solving linear systems of equations are studied.

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

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

  • 19202102 Practice seminar
    Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
    Schedule: Do 12:00-14:00 (Class starts on: 2024-10-17)
    Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Advanced and Applied Algorithms

  0084dB3.7
  • 19303501 Lecture
    Advanced Algorithms (László Kozma)
    Schedule: Di 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2024-10-15)
    Location: T9/SR 006 Seminarraum (Takustr. 9)
    

    Additional information / Pre-requisites

    Target audience

    All Master and Bachelor students who are interested in algorithms.

    Prerequisites

    Basic familiarity with the design and analysis of algorithms.

    Comments

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

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

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

    Suggested reading

    • Cormen, Leiserson, Rivest, Stein: Introduction to Algorithms, 4th Ed. MIT Press 2022
    • Kleinberg, Tardos: Algorithm Design, Addison-Wesley 2005.
    • Sedgewick, Wayne: Algorithms, 4th Ed., Addison-Wesley 2016

  • 19303502 Practice seminar
    Practice seminar for Advanced Algorithms (László Kozma)
    Schedule: Fr 08:00-10:00, Fr 14:00-16:00 (Class starts on: 2024-10-18)
    Location: T9/046 Seminarraum (Takustr. 9)
    

• Modules w/o courses in this semester

  15 Modules
  • Computer-Oriented Mathematics II 0084dA1.7
  • Numerical Mathematics I 0084dA1.9
  • Higher Analysis 0084dB2.1
  • Current Topics in Mathematics 0084dB2.10
  • Special topics in Applied Mathematics 0084dB2.13
  • Complex Analysis 0084dB2.3
  • Probability and Statistics II 0084dB2.4
  • Elementary Geometry 0084dB2.6
  • Geometry 0084dB2.7
  • Data Structures and Data Abstraction with Applications 0084dB2.8
  • Differential Equations I 0084dB3.1
  • Discrete Mathematics I 0084dB3.2
  • Differential Geometry I 0084dB3.5
  • Topology I 0084dB3.6
  • Visualization 0084dB3.8.