COURSES GIVEN IN WINTERTERM 1999/2000

(Deutsch)
The following courses are planned.

LECTURES

MATHEMATIK FÜR PHYSIKER I
Date:
Mo 11:45-13:15 (46/280) Lecture
Tu 10-11:30 (13/222) Lecture
Mo 10-11:30 (46/280) Lecture
Course language:
German.
Contents:
The students should learn the basic mathematical tools needed by a physicist. This includes linear algebra (vector spaces, linear mappings, determinants, linear endomorphisms, euclidean and unitarian spaces, spectral theory, basics of multilinear algebra) and calculus in one and several variables (series, continous, differentiable and analytical functions, implicit functions, local extrema, differentiation and integration, computation of integrals).
Literature:
Jänich, K.: Lineare Alegbra. 7. Aufl. 1998 Springer-Verlag ISBN 3-540-64535-7.
Bröcker, Th.: Analysis, Band 1. 2. korr. Aufl. 1995 Spektrum Akademischer Verlag ISBN 3-86025-417-0.
Forster, O.: Analysis 1. Vieweg Verlag.
Heuser, H.: Lehrbuch der Analysis, Teil 1. Teubner Verlag.
Lecturer
Klaus Wirthmüller

LINEARE ALGEBRA I
Date:
Mo 11:45-13:30 (46/220) Lecture
Th 10:00-11:30 (46/220) Lecture
Mo 15:30-17:00 (48/438) Tutorial
Th 15:30-17:00 (13/222) Tutorial
Tu 08:15-09:45 (13/370) Exampleclass
Tu 11:45-13:15 (44/482) Exampleclass
We 11:45-13:15 (44/482) Exampleclass
We 13:45-15:15 (11/260) Exampleclass
Course language:
German.
Contents:
Theory of vector spaces and linear operators.
Literature:
G. Fischer, Lineare Algebra, Vieweg Verlag (1998)
K. Jaenich, Linear Algebra, Springer Verlag (1981)
W. Klingenberg, Lineare Algebra und Geometrie, Springer Verlag (1990)
M. Koecher, Lineare Algebra und analytische Geometrie, Springer Verlag (1983)
B. Brieskorn, Lineare Algebra und analytische Geometrie I, Vieweg Verlag (1983)
H.-D. Ebbinghaus, et al., Zahlen, Springer Verlag
Lecturer
Gert-Matin Greuel
Assistent:
Thomas Keilen

EINFÜHRUNG IN DIE FUNKTIONENTHEORIE
Date:
Th 11:45-13:30 (24/102) Lecture
(tba) Exampleclass
Course language:
German.
Contents:
Introduction to complex analysis, power series, analytical functions, Cauchy integrals, holomorphy, Laurent series, residues.
Literature:
W. Fischer / I. Lieb, Funktionentheorie, Vieweg 1980.
R. Remmert, Funktionentheorie I, Springer 1984.
K. Jänich, Funktionentheorie, 3. Aufl., Springer 1993.
E. Freitag / R. Busam, Funktionentheorie, Springer 1991.
Lecturer
Jörg Zintl
Assistent:
Christian Schick

ALGEBRAIC GEOMETRY I
Date:
Mo 10:00-11:30 (48/210) Lecture
We 08:15-09:45 (48/438) Lecture
Fr 10:00-11:30 (11/201) Exampleclass
Course language:
English.
Contents:
Introduction to basic concepts of algebraic geometry (affine and projective varieties, local aspects, etc., up to dimension theory).
Literature:
R. Hartshorne: Algebraic Geometry, Springer 1977.
H. Grauert und R. Remmert: Coherent Analytic Sheaves, Springer 1984.
D. Cox, J. Little and D. O´Shea: Ideals, Varieties and Algorithms, Springer 1996.
Lecturer
Günther Trautmann
Assistent:
Hans Georg Freiermuth

COMMUTATIVE ALGEBRA
Date:
Th 10:00-11:30 (48/438) Lecture
Mo 13:45-15:15 (11/260) Exampleclass
Course language:
English.
Contents:
Commutative rings, modules, chain conditions, normalization, localization, completion, regular rings, Hilbert polynomial, dimension theory.
Literature:
D. Eisenbud: Commutative Algebra with a View Toward Algebraic Geometry, Springer 1996.
M. F. Atiyah, I. G. Macdonald: Introduction to Commutative Algebra. Addison-Wesley 1969.
H. Matsumura: Commutative Algebra. A. Benjamin 1970.
H. Matsumura: Commutative Ring Theory. CUP 1986.
Lecturer
Gerhard Pfister
Assistent:
Anne Frühbis-Krüger

SINGULARITY THEORY
Date:
Mo 11:45-13:15 (11/260) Lecture
Mo 10:00-11:30 (48/438) Exampleclass
Course language:
English.
Contents:
Deformation theory: proof of the existence of the versal deformation of an isolated singularity. This requires Standardbases for powerseries rings, Grauert`s division theorem, Grauert`s Approximationstheorem.
Literature:
Script: Theo De Jong, Gerhard Pfister: Local Analytic Geometry.
Lecturer
Gerhard Pfister
Assistent:
Anne Frühbis-Krüger

ALGEBRAIC TOPOLOGY
Date:
Tu 10:00-11:30 (48/438) Lecture
Th 11:45-13:15 (48/438) Lecture
Mi 11:45-13:15 (13/370) Exampleclass
Course language:
English.
Contents:
Homological algebra; homology; homotopy invariance of homology; excision; Mayer-Vietoris sequence; Eilenberg-Steenrod axioms; Lefschetz fixed point theorem; Künneth theorem; cohomology; orientation; products; duality on manifolds.
Literature:
K. Jänich: Topologie.
R. Stöcker und H. Zieschang: Algebraische Topologie.
M. J. Greenberg: Lectures on Algebraic Topology.
J. J. Rotman: An Introduction to Algebraic Topology.
E. H. Spanier: Algebraic Topology.
Lecturer
Christoph Lossen
Assistent:
Thomas Bayer

EINFÜHRUNG IN DIE COMPUTERALGEBRA
Date:
Tu 11:45-13:15 (48/438) Lecture
Fr 13:45-15:15 (48/582) Exampleclass
Course language:
German.
Contents:
Elementary introduction to basic concepts and algorithms in Computer Algebra with the aim of solving algebraic systems of equations and visualising their solution sets. "Learning by Doing" - using the Computer Algebra System SINGULAR.
Literature:
D. Cox, J. Little and D. O´Shea, Ideals, Varieties and Algorithms, Springer 1996.
W. V. Vasconcelos, Computational Methods in Commutative Algebra and Algebraic Geometry, Springer 1997.
Lecturer
Gert-Martin Greuel
Assistent:
Eric Westenberger

SEMINARS AND TUTORIALS

TUTORIAL IN ALGEBRAIC GEOMETRY - 1ST YEAR MATHEMATICS INTERNATIONAL
Date:
Th 08:15-09:45 (11/260) Tutorial - Part I
Fr 11:45-13:15 (48/438) Tutorial - Part II
Course language:
English.
Contents:
In part I we will discuss questions which arise during the lectures Algebraic Geometry, Algebraic Topology, and Commutative Algebra. In part II supplements to these lectures will be presented respectively questions arising in Algebraic Geometry will be discussed.
Tutors:
Jörg Zintl, Hans Georg Freiermuth

TUTORIAL IN ALGEBRAIC GEOMETRY - 2ND YEAR MATHEMATICS INTERNATIONAL
Course language:
English.
Contents:
Questions which arise during the lecture Singularity Theory and Algebraic Topology will be discussed.
Tutors:
Anne Frühbis-Krüger

SEMINAR ÜBER SINGULARITÄTENTHEORIE UND COMPUTERALGEBRA
Date:
Tu 15:30-17:00 (48/436) Seminar
Course language:
German.
Contents:
Well chosen chapters from the above fields of mathematics.
Supervisor:
Gert-Martin Greuel, Gerhard Pfister
Coordination:
Thomas Keilen

ALGEBRAISCHE GEOMETRIE
Date:
Mo 13:45-15:15 (48/436) Seminar
Course language:
German, resp. English.
Contents:
Selected topics and constructions in algebraic geometry.
Supervisor:
Günther Trautmann, Jörg Zintl

SEIBERG-WITTEN-INVARIANTEN
Date:
Th 15:30-17:00 (48/438) Seminar
Course language:
German
Contents:
Construction and properties of the moduli space of Seiberg-Witten monopoles, Seiberg-Witten invariants, applications.
Supervisor:
Hans Georg Freiermuth,

OBERSEMINAR ÜBER KOMPLEXE ANALYSIS UND SINGULARITÄTEN
Date:
Mo 15:30-17:00 (48/436)
Course language:
German, resp. English.
Contents:
New papers from the above fields of mathematics will be presented.
Coordination:
Thomas Keilen
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Last modification: 6 July 2001.