Mathematics
Mathematics
0084d_k120-
Analysis I
0084dA1.1-
19202801
Lecture
Analysis I (Elena Mäder-Baumdicker)
Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
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:- fundamentals, elementary logic, ordered pairs, relations, functions, domain and range of a function, inverse functions (injectivity, surjectivity)
- numbers, induction, calculations in R, C
- arrangement of R, maximum and minimum, supremum and infimum of real sets, supremum / infimum completeness of R, absolute value of a real number, Q is dense in R
- sequences and series, limits, cauchy sequences, convergence criteria, series and basic principles of convergence
- topological aspects of R, open, closed, and compact real sets
- sequences of functions, series of functions, power series
- properties of functions, boundedness, monotony, convexity
- continuity, limits and continuity of functions, uniform continuity, intermediate value theorems, continuity and compactness
- differentiability, concept of the derivative, differentiation rules, mean value theorem, local and global extrema, curvature, monotony, convexity
- elementary functions, rational functions, root functions, exponential functions, angular functions, hyperbolic functions, real logarithm, inverse trigonometric functions, curve sketching
- beginnings of integral calculus
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.
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19202802
Practice seminar
Tutorial: Analysis I (Elena Mäder-Baumdicker)
Schedule: Mi 12:00-14:00, Mi 14:00-16:00, Fr 08:00-10:00, Fr 10:00-12:00 (Class starts on: 2025-10-15)
Location: Mi A3/SR 119 (Arnimallee 3-5), Fr A3/SR 119 (Arnimallee 3-5), Fr A6/SR 025/026 Seminarraum (Arnimallee 6)
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19202801
Lecture
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Analysis II
0084dA1.2-
19211601
Lecture
Analysis II (Pavle Blagojevic)
Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
Comments
Content
- Additions to Analysis I. Non-authentic integrals
- Uniform convergence of function sequences. Power series. Sentence of Taylor.
- Elements of topology. Standardized and metric spaces. Open quantities. Convergence. Completed quantities. Consistency. Compactness
- Differential calculus of several variables. Partial, total and continuous differentiability. Block via the inverse function. Block of implicit functions.
- Iterated integrals.
- Ordinary differential equations. Basic terms, elementary solvable differential equations, existential and unambiguous results for systems.
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.
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19211601
Lecture
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Analysis III
0084dA1.3-
19201301
Lecture
Analysis III (Marita Thomas)
Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
Comments
Contents
The lecture Analysis III is the final lecture of the cycle Analysis I-III.
- ODEs
- 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
- H. Amann, J. Escher: Analysis 2, Birkhäuser Verlag, 2008.
- H. Amann, J. Escher: Analysis 3, Birkhäuser Verlag, 2008.
- O. Forster: Analysis 2, Springer Verlag, 2012.
- O. Forster: Analysis 3, Vieweg+Teubner, 2012.
- H. Heuser: Lehrbuch der Analysis 2, Vieweg+Teubner, 2012.
- S. Hildebrandt: Analysis 2, Springer Verlag, 2003.
- J. Jost: Postmodern Analysis, Springer Verlag, 2008.
- K. Königsberger: Analysis 2, Springer Verlag, 2004.
- W. Rudin: Principles of Mathematical Analysis, International Series in Pure & Applied Mathematics, 1976.
und für geschichtlich Interessierte:
- O. Becker: Grundlagen der Mathematik, Verlag Karl Alber, Freiburg, 1964.
- E. Hairer, G. Wanner: Analysis by its History, Springer, 2000.
- V.J. Katz: A History of Mathematics, Harper Collins, New York, 1993.
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19201302
Practice seminar
Practice seminar for Analysis III (Marita Thomas, Sven Tornquist)
Schedule: Di 14:00-16:00, Mi 10:00-12:00 (Class starts on: 2025-10-14)
Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
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19201301
Lecture
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Linear Algebra I
0084dA1.4-
19201401
Lecture
Linear Algebra I (Georg Loho)
Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2025-10-15)
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
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19201402
Practice seminar
Practice seminar for Linear Algebra I (Georg Loho, Jan-Hendrik de Wiljes)
Schedule: Mo 10:00-12:00, Mo 16:00-18:00, Mi 10:00-12:00, Do 08:00-10:00, Do 12:00-14:00, Fr 10:00-12:00 (Class starts on: 2025-10-15)
Location: Mo A3/SR 115 (Arnimallee 3-5), Mo A6/SR 009 Seminarraum (Arnimallee 6), Mi A6/SR 009 Seminarraum (Arnimallee 6), Do A6/SR 007/008 Seminarraum (Arnimallee 6), Do A6/SR 032 Seminarraum (Arnimallee 6), Fr A6/SR 031 Seminarraum (Arnimallee 6)
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19201401
Lecture
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Linear Algebra II
0084dA1.5-
19211702
Practice seminar
Practice seminar for Linear Algebra II (Marcus Weber)
Schedule: Di 08:00-10:00, Di 14:00-16:00, Mi 12:00-14:00, Do 16:00-18:00, Fr 08:00-10:00 (Class starts on: 2025-10-14)
Location: A3/019 Seminarraum (Arnimallee 3-5)
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19211702
Practice seminar
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Computer-Oriented Mathematics I
0084dA1.6-
19200501
Lecture
Computerorientated Mathematics I (5 LP) (Claudia Schillings)
Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
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)
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19200502
Practice seminar
Practice seminar for Computerorientated Mathematics I (5 LP) (N.N.)
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: 2025-10-13)
Location: A6/SR 031 Seminarraum (Arnimallee 6)
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19200501
Lecture
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Numerical Mathematics I
0084dA1.9-
19212001
Lecture
Numerics I (Volker John)
Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-13)
Location: A7/SR 031 (Arnimallee 7)
Comments
Numerical methods for: iterative solution of nonlinear systems of equations (fixpoint and Newton methods), curve fitting, interpolation, numerical quadrature, and numerics for initial value problems and two point boundary value problems with ODEs. The course is taught in German.
Suggested reading
Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 1. Springer, Berlin, 2005.
Aus dem FU-Netz auch online verfügbar.
Es wird ein Vorlesungsskript geben.
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19212002
Practice seminar
Practice seminar for Numerics I (N.N.)
Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
Location: A7/SR 031 (Arnimallee 7)
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19212001
Lecture
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Academic Work in Mathematics
0084dB1.1-
19226511
Seminar
Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
Location: SR A9
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
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19240317
Seminar / Undergraduate Course
Advancing mathematics with AI (Georg Loho)
Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
Location: A3/SR 120 (Arnimallee 3-5)
Comments
The course will probably be held in German.
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19247111
Seminar
Ordinary Differential Equations (Marita Thomas)
Schedule: Di 16:00-18:00 (Class starts on: 2025-10-14)
Location: A6/SR 009 Seminarraum (Arnimallee 6)
Comments
Ordinary differential equations arise in many applications from physics, chemistry, biology or economics. This seminar extends the topics that were covered in the Analysis III course, e.g., eigenvalue problems and stability theory will be addressed.
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19226511
Seminar
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Special topics in Mathematics
0084dB2.11-
19202001
Lecture
Discrete Geometrie I (Christian Haase)
Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
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.
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19202002
Practice seminar
Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
Location: A6/SR 031 Seminarraum (Arnimallee 6)
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19202001
Lecture
-
Special topics in Pure Mathematics
0084dB2.12-
19236101
Lecture
Mathematisches Panorama (Anina Mischau, Sarah Wolf)
Schedule: Mi 12:00-14:00 (Class starts on: 2025-10-15)
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.
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
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19236102
Practice seminar
Übung zu: Mathematisches Panorama (Anina Mischau)
Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-24)
Location: A6/SR 007/008 Seminarraum (Arnimallee 6)
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19236101
Lecture
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Functional Analysis
0084dB2.2-
19201901
Lecture
Functional Analysis (Dirk Werner)
Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
Location: A3/019 Seminarraum (Arnimallee 3-5)
Comments
Content:
Functional analysis is the branch of mathematics dealing with the study of normed (or general topological) vector spaces and continuous mappings between them. Thus, analysis, topology and algebra are linked.
The course deals with Banach and Hilbert spaces, linear operators and functionals as well as spectral theory of compact operators.Target group: Students from the 3rd/4th semester on.
Requirements: Good command of the material of the courses Analysis I/II and Linear Algebra I/II.
Suggested reading
Literatur:
- Dirk Werner: Funktionalanalysis, 8. Auflage, Springer-Verlag 2018
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19201902
Practice seminar
Tutorial: Functional Analysis (Dirk Werner)
Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
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
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19201901
Lecture
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Probability and Statistics II
0084dB2.4-
19212901
Lecture
Stochastics II (Felix Höfling)
Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
Additional information / Pre-requisites
Prerequisite: Stochastics I and Analysis I — III.
Comments
Contents:
- Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
- Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
- martingales in discrete time: convergence, stopping theorems, inequalities;
- Markov chains in discrete and continuous time: recurrence and transience, invariant measures.
Suggested reading
- Klenke: Wahrscheinlichkeitstheorie
- Durrett: Probability. Theory and Examples.
Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
Further literature will be given during the lecture. -
19212902
Practice seminar
Practice seminar for Stochastics II (Felix Höfling)
Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
Location: A6/SR 031 Seminarraum (Arnimallee 6)
Comments
Inhalt
- This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
More precisely, the course will cover the following aspects of probability theory: - Measure theory and the Lebesgue integral
- Convergence of random variables and 0-1 laws
- Generating functions: branching processes and characteristic functions
- Markov chains
- Introduction to martingales
- This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
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19212901
Lecture
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Algebra and Number Theroy
0084dB2.5-
19200701
Lecture
Algebra and Theory of Numbers (Alexander Schmitt)
Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2025-10-15)
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 (Alexander Schmitt)
Schedule: Mi 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-15)
Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
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19200701
Lecture
-
Numerical Mathematics II
0084dB3.4-
19202101
Lecture
Basic Module: Numeric II (Robert Gruhlke)
Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
Comments
Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.
Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS
Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)
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19202102
Practice seminar
Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
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19202101
Lecture
-
Differential Geometry I
0084dB3.5-
19202601
Lecture
Differential Geometry I (Konrad Polthier)
Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
Additional information / Pre-requisites
For further information, see Lecture Homepage.
Comments
Topics of the lecture will be:
- curves and surfaces in Euclidean space,
- metrics and (Riemannian) manifolds,
- surface tension, notions of curvature,
- vector fields, tensors, covariant derivative
- geodesic curves, exponential map,
- Gauß-Bonnet theorem, topology,
- connection to discrete differential geometry.
This course is a BMS course and will be held in English on request.
Prerequisits:
Analysis I, II, III and Linear Algebra I, II
Suggested reading
Literature
- W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
- M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
- J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
- C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001
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19202602
Practice seminar
Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
Location: A6/SR 031 Seminarraum (Arnimallee 6)
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19202601
Lecture
-
-
Computer-Oriented Mathematics II 0084dA1.7
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Probability and Statistics I 0084dA1.8
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Higher Analysis 0084dB2.1
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Current Topics in Mathematics 0084dB2.10
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Special topics in Applied Mathematics 0084dB2.13
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Complex Analysis 0084dB2.3
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Elementary Geometry 0084dB2.6
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Geometry 0084dB2.7
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Data Structures and Data Abstraction with Applications 0084dB2.8
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Mathematical Project 0084dB2.9
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Differential Equations I 0084dB3.1
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Discrete Mathematics I 0084dB3.2
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Algebra I 0084dB3.3
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Topology I 0084dB3.6
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Advanced and Applied Algorithms 0084dB3.7
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Visualization 0084dB3.8.
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