Lectures in Mathematics, winter 2003/04

VL 12001	Preliminary course in mathematics			ects:
	Schmitt, Bernhard
	15.9.03-19.9.03, daily from 10.00-13.00, LE HS IV,   Beginn: 15.9.03
UE 12002	by agreement			ects:

VL 12003	Analysis I			ects: 7,5 p.
	Dahlke, Stephan
	Tue 9-11, Wed 12-13, Fri 11-13, HG 4,   Begin: 10-21-2003
UE 12004	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Basic course	> = 1	yes, SS 2004	no

Contents:

We shall be concerned with the basic properties of univariate functions. One central topic will be the differential calculus. Another important issue is the integration of functions (integration by pars, substitution etc.).

Interrelations:	to all parts of pure and applied mathematics
Criteria:	to be announced
Literature:	Forster, Otto: Analysis I, Vieweg Grauert Hans; Lieb, Ingo: Differential- und Integralrechnung I, Springer, 1976 Heuser, Harro: Lehrbuch der Analysis I, Teubner Verlag

VL 12005	Linear Algebra I			ects: 6 p.
	Knöller, Friedrich Wilh.
	Mon 9-11, HG 4, Thu 11-13, HG 4,   Begin: Oct. 20, 2003
UE 12006	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Basic course	> = 1	yes, SS 04	no

Contents:

It is one of the basic courses for beginners in Mathematics or Physics. The main topics will be: - Vector spaces und linear mappings - Determinants and eigen-values - Scalar products and normal forms

Prerequisites:	Concentrated and steady work
Interrelations:	to all parts of Mathematics
Criteria:	to be announced
Literature:	Brieskorn: Lineare Algebra und Analytische Geometrie Fischer: Lineare Algebra Greub: Linear Algebra

VL 12007	Mathematics I			ects: 7,5 p.
	Schlickewei, Hans Peter
	Tue 9-11, HG 5, Thu 13-14, HG 113, Fri 10-12, HG 113,   Begin: 10-21-2003
UE 12008	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Basic course	> = 1	yes, SS 2004	no

Contents:

Algebraic structures; vector spaces and linear maps; matrices, determinants and systems of linear equations; scalar products; eigenvalues. Hint: this course is part one of a 3-semester course ``mathematics for computer scientists''. It belongs to the basic part of the computer science studies (Diplom).

Prerequisites:
Interrelations:	Computer Science
Criteria:	to be announced
Literature:	to be announced

VL 12009	Analysis III			ects: 6 p.
	Gromes, Wolfgang
	Mon 9-11 HG 7, Thu 9-11, HG 6,   Begin: 10-20-2003
UE 12010	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Basic course	> = 3	no	no

Contents:

General Radon-Integrals, especially Lebesgue-Integrals in Rn, theorems of Lebesgue, B. Levi, Fubini, change of variables with applications (for example Fourier series, Fourier transformation, convolution. Integration on submanifolds, theorems of Gauss and Stokes.

Prerequisites:	Analysis, Linear Algebra
Remark:	This course applies to students of Mathematics and Physics
Criteria:	to be announced
Literature:	Forster: Analysis III, Vieweg Heuser: Analysis 2, Teubner

VL 12011	Mathematics III			ects: 6 p.
	Hinz, Jürgen
	Mon 9-11, Thu 11-13, HG 113,   Begin: 10-20-2003
UE 12012	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Basic course	> = 3	no	no

Contents:

Calculus in several real variables, basic concepts and facts of stochastics (= probability theory and statistics)

Prerequisites:	Mathematics I - II
Interrelations:	Computer Science
Criteria:	to be announced
Literature:	to be announced

VL 12013	Complex Analysis			ects: 6 p.
	Upmeier, Harald
	Mon 11-13, HG 7; Thu 11-13, HG 116,   Beginning: 10-20-2003
UE 12014	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Adv. course	> = 4	yes, SS 2004	yes

Contents:

Cauchy-Riemann equations, Cauchy integral theorem, calculus of resdues and applications, Riemann mapping theorem, conformal mappings, harmonic functions

Prerequisites:	Analysis, Linear Algebra
Interrelations:
Criteria:	to be announced
Literature:	script

VL 12015	Logic			ects: 6 p.
	Schwentick, Thomas
	Tue 9-11, HG 7; Fri 11-13, HG 5,   Beginning: 10-21-2003
UE 12016	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics Computer Science	Basic course Theor. Computer Science	> = 3	no	no

Contents:

Mathematical Logic is one of the foundations of Computer Science. Fundamental questions concerning the nature of algorithmic computation were initially asked in Logics and found their answers by logical methods. Digital computers are based on propositional logic. Query languages for relational databases and logical programming languages (Prolog) have their roots in first-order predicate logic. These are only three of many important connections. Remark: The course applies to students of Mathematics (Diploma) and Computer Science (Diploma)

Interrelations:
Criteria:	Active participance in the lab exercises, reaching the required number of exercise points, passing the intermediate tests during the course, passing the final exam
Literature:	Schöning: Logik für Informatiker, Spektrum Akademischer Verlag Ebbinghaus, Flum, Thomas: Mathematical Logic, Spektrum Akademischer Verlag

VL 12017	Introduction to Probability and Statistics (Stochastics 0)			ects: 6 p.
	Wawrzynek,Jerzy
	Thu 14-16, HG 4; Fri 9 - 11, HG 4,   Begin: Oct. 21, 2003
UE 12018	Fr 14-16, HG 4			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Appl. Mathematics	Basic course	> = 3	yes, SS 2004	no

Contents:

The basic concept and facts of stochastics (= probability theory and statistics) will be presented without reference to measure theory.

Prerequisites:	Basic courses in analysis and linear algebra
Interrelations:	Measure theory (Stochastics I)
Criteria:	to be announced at the beginning of the course
Literature:	to be announced at the beginning of the course

VL 12098	Applied Linear Optimization			ects: 3 p.
	Krawczyk,Stanislaw
	Tue 11-13, Fri 9-11, Fri 14 - 16, HG 4,   Begin: Jan. 20, 2004
UE 12018	by agreement,			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Appl. Mathematics	Basic course	> = 3

VL 12019	Functional Analysis			ECTS: 6 P.
	Portenier, Claude
	Mon 9-11, RH Gr. HS (RH 7), Thu 11-13, HG 6,   Begin: 10-20-2003
UE 12020	by agreement			ECTS: 3 P.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Adv. course	> = 4	yes, SS 2004	yes

Contents:

This lecture is intended for all students in mathematics and physics from the 4th semester up. I will present the fundamental concepts and results in functional analysis and apply these methods so some problems in mathematical physics (for example to the classical orthogonal polynomials, to the vibrating string). Moreover, the necessary tools to describe the Dirac formalism will be developed. During the next semester (summer 2004) this material will be deepened. I intend to treat some problems in quantum mechanics, in particular in the spectral theory of unbounded operators using the Dirac formalism.

Prerequisites:
Interrelations:
Criteria:	to be announced
Literature:

VL 12021	Algebra II			ects: 6 p.
	Welker, Volkmar
	Di 9.15-11.00, HG 115, Do 9.15-11.00, HG 4,   Begin: Oct. 21. 2003
UE 12022	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Adv. course	> = 5	possibly a seminar	no

Contents:

In the course we revisit the theory of finite groups that was already considered in Algebra I. Here we take a different point of view. In this course the development of the theory of groups will be driven by the study of group actions and representations. The basic theory of representations of finite groups will be developed.

Prerequisites:	Linear Algebra I, Algebra I
Interrelations:
Criteria:	tba
Literature:	Kurzweil, H., Stellmacher, B.: Theorie der endlichen Gruppen, Springer 1998. Fulton, W., Harris, J.: Representation Theory, Springer 1991.

VL 12023	Algebraic Geometry			ects: 6 p.
	Bauer, Thomas
	Mon 11 - 13, HG 116, Wed 11 - 13, HG 7 ,   Begin: Oct. 20, 2003
UE 12024	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Adv. course	> = 5	no	no

Contents:

Algebraic geometry deals with geometrical objects given as zero sets of (systems of) polynomial equations. The fascination of the subject stems from the interplay of powerful algebraic methods on the one hand, and geometrical intuition on the other hand. The aim of this course is to provide a first introduction to Algebraic Geometry. We will first focus on projective varieties, with applications to elliptic curves and cubic surfaces in three-space. We will also touch more advanced topics such as schemes and cohomology.

Prerequisites:	Algebra I and II
Interrelations:	Complex Functions, Complex Analysis
Criteria:	to be announced
Literature:	K. Hulek: Elementare Algebraische Geometrie. Vieweg. M. Reid: Undergraduate algebraic geometry. Cambridge University Press.

VL 12025	Stochastics II			ects: 6 p.
	Mammitzsch, Volker
	Wed 9 - 11, HG 116; Fr 11 - 13, HG 7 ,   Begin: Oct. 22, 2003
UE 12026	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Appl. Mathematics	Adv. course	> = 5	yes, Stoch. III, SS 2004	no

Contents:

Probability theory will be presented making use of measure theory. There will be treated in detail: - general probability spaces, random variables, - charactertistic functions, - convergence in distribution (incl. Central Limit Theorem), - conditional expections and distributions, - martingales, stopping times.

Prerequisites:	Stochastics I (or equivalent knowledge in measure theory)
Interrelations:	none
Criteria:	to be announced at the beginning of the course
Literature:	to be announced at the beginning of the course

VL 12027	Polytopes			ects: 3 p.
	Welker, Volkmar
	by agreement,   Begin: first week of classes
Subject	Classification	Semester	Continued	Script
Pure Mathematics	Basic course	> = 3	appl. lin. opt. in SS	no

Contents:

Triangles, squares, cubes, tetrahedra etc. all are geometric objects that are subsumed by the name polytope. Polytopes are central objects in pure and applied mathematics. Prominently, I would like to mention linear optimization, whose main goal is to optimize a linear functional over a polytope. In practice the simplex algorithm is used to solve these optimization problems. But there are examples for which the algorithm runs exponentially long - too long. The class introduces that basic concepts of polytope theory and paves are the ground for a solid understanding of the simplex algorithms and the behavior of its time complexity. The course will be continued in SS by a 2 hour class in linear optimization (with 2 hours of recitation). Together with the course the polytopes class serves to fulfill the requirements in linear optimization for students of Wirtschaftsmathematik.

Prerequisites:	Linear Algebra
Interrelations:
Criteria:	no credit
Literature:	Ziegler, G.M.: Lectures on Polytopes, Springer 1995.

VL 12028	Numerical Analysis IIA (finite-dimensional problems)			ects: 6 p.
	Schmitt, Bernhard
	Tue 11-13 HS IV LE, Fri 9-11, HG 109,   Begin: Tue, Oct.21, 2003
UE 12029	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Appl. Mathematics	Adv. course	> = 4		yes

Contents:

Numerical methods for - Eigenvalue problems for matrices - Singular value decompositions of matrices with applications - Linear programming (simplex method) - Fast iteration methods for large linear systems of equations - Robust methods for nonlinear systems of equations

Prerequisites:	Numerical Analysis I, a programming language
Criteria:	to be announced
Literature:	Script, Stoer/Bulirsch: Numerische Mathematik 2; Schaback/ Werner: Numerische Mathematik; Schwarz: Numerische Mathematik; Deuflhard/Hohmann: Numerische Mathematik; Golub/vanLoan: Matrix Computations

VL 12030	Foundations of Life Insurance Mathematics			ects: 3 p.
	Zachow, Ernst-Wilhelm
	Thu 14-18, LE SR IV: 23.10., 30.10., 20.11., 4.12., 8.1., 29.1.,   Begin: Oct. 23, 2003
Subject	Classification	Semester	Continued	Script
Appl. Mathematics	Adv. course	> = 4	yes, SS 04	partly

Contents:

Mathematical methods, models and problems in health insurance (with life time cover).

Prerequisites:	Basic course in probability theory.
Interrelations:	Other courses in insurance mathematics, esp. life insurance mathematics.
Criteria:	to be announced at the beginning of the course. Remark: The subject of this course is allowed for the examinations in the Diplom-Hauptprüfung, the course is also accepted by the DAV/DGVFM (German Actuarial Association).
Literature:	to be announced at the beginning of the course

VL/UE 12097	Combinatorical Optimization II: General Matchings, Branch- and-Bound, and Integer Programming			ects: 3 p.
	Porembski, Marcus
	Fri 11-13, 14-16, LE SR IV : 31.10., 14.11., 28.11., 12.12.,
	16.1., 30.1., 13.2.      Begin: 10-31-2003
Subject	Classification	Semester	Continued	Script
Appl. Mathematics	Adv. course	> = 3	no	no

Contents:

We start with general matching problems. Then branch-and-bound with extensions and applications is described. Finally, different methods of integer programming are discussed.

Prerequisites:	Combinatorical Optimization I
Interrelations:	Business Administration, Economics, Computer Science
Criteria:	To be announced
Literature:	Papdimitrou/Steiglitz: Combinatorial Optimization Cook/Cunningham/Pulleybank/Schrijver: Combinatorial Optimization Nemhauser/Wolsey: Combinatorial Optimization Schrijver: Theory of Linear and Integer Programming Schrijver: Combinatorial Optimization

VL 12048	Mathematics for Humanbiologists and Biologists			ects: 3 p.
	Hinz, Jürgen
	Thu 8-10, LE, Lecture hall, Department of Biology,   Begin: 10-23-2003
UE 12049	by agreement			ects: 3 p.
Subject	Classification	Semester	Continued	Script
Service Lecture	Basic course	> = 1	no	no

Contents:

Mathematical and statistical methods in biology (fundations).

Prerequisites:	School mathematics
Interrelations:	Biology, Physics
Criteria:	to be announced
Literature:	to be announced

SE 12050	Mathematical and statistical methods for pharmacists			ects: 3 P.
	Lohöfer, Helga
	Tue 14.00-15.45, PHCH, Large lecture hall,   Begin: 21/10/2003
UE 12051	Tue 16.00-16.45, PHCH, Small lecture hall, Fri 9.15-10.00, PHCH SR			ects: 3 P.
Subject	Classification	Semester	Continued	Script
Service Lecture	Basic course	> = 1	no	yes

Contents:

Mathematical methods in pharmacy.

Prerequisites:	-
Interrelations:	Chemistry, Physics, Biology
Criteria:	to be announced
Literature:	-

To overview of lectures, to the seminars.