Sorry, all lecture scripts are available in german only.
Papers, related to my studies.
Sorry, all papers are available in german only.
- seminar paper "Der minimale euklidische Algorithmus im Ring der ganzen Gaußschen Zahlen" (Smallest euclidean algorithm in the ring of the whole gaussian numbers)
- term paper "Parsing natürlicher Sprache" (Parsing of natural language)
- diploma thesis "Die Pell'sche Gleichung über Funktionenkörpern" (Pell's equation over function fields)
- master thesis "Einsatz von Optimierungsverfahren in betrieblichen Anwendungen am Beispiel von Re-Use-Szenarios" (Tasks of optimization in regard to re-use scenarios)
lecture script, current version: Aug-25-2004
contents:
- finite automata
- formal languages
- regular languages and finite automata
- context-free languages
graph theory
lecture script, current version: Oct-19-2004
contents:
- graphs
- trees
- algorithms: breadth-first-search, topological sorting, networks
computation
lecture script, current version: Mar-30-2004
contents:
- abstract machines
- LOOP- and WHILE-computation
- partial recursive and primitive recursive functions
- recursive and semi-recursive relations
- basics of complexity theory
automated theory proving
lecture script, current version: Dec-08-2004
contents:
- propositional logic (sequency calculus, tableau-calculus, resolution, Davis-Putnam-method)
- first order logic
- sequqency calculus
- resolution
- logic programming
seminar paper "Der minimale euklidische Algorithmus im Ring der ganzen Gaußschen Zahlen" (Smallest euclidean algorithm in the ring of the whole gaussian numbers)
Let R be a ring. If there exists a map g between R and the natural numbers so that every pair of elements x, y (y not zero) can be written as x=qy+r, while q, r are elements from R and either r=0 or g(r) < g(y), R is called an euclidean ring.
The map g is called euclidean algorithm (euclidean norm).
We will show that every euclidean ring offers a smallest euclidean algorithm.
In this seminar paper we use the ring of the whole gaussian numbers to show and implement a method to create the smallest euclidean algorithm.
Download of the paper (PDF-file, 360 kb)
Download of the implementation (executable jar-file, 30 kb)
You will need a JAVA-Runtime version >= 1.4 to execute the program, visit http://java.sun.com/.
term paper "Parsing natürlicher Sprache" (Parsing of natural language)
In this term paper we give a rough introduction to parsing of natural language.
The first part deals with the possibilities to represent natural language in formal systems, the second part is about some algorithms. We conclude by introducing two real systems to divide natural-language sentences into its syntactical parts.
Download of the paper (PDF-file, 285 kb)
diploma thesis "Die Pell'sche Gleichung über Funktionenkörpern" (Pell's equation over function fields)
Pell's equation is a well-known problem in mathematics since a couple of centuries. Let d a non-square natural number, we try to find all integer solutions of the equation x^2-dy^2=1. The most popular method to solve Pell's equation is based on continued fractions.
In this thesis we analyze Pell's equation over function fields. We try to find solutions A, B of the equation A^2-MB^2=1, while A, B, M are polynomials over a finite field K.
We will show, that every monic non-square M, having an even degree, leads to an infinite number of solutions, which can be derived by using a continued fraction algorithm.
Download of the paper (PDF-file, 455 kb)
Download of the implementation using KANT/KASH (17 kb)
Manual for using the KANT-implementation (in german, ASCII, 6 kb)
Download of the implementation using PARI-GP (15 kb)
Manual for using the PARI-implementation (in german, ASCII, 5 kb)
In order to use the implementation you will need either the algebra-package KANT and the interactive interpreter KASH (http://www.math.tu-berlin.de/~kant/) or the algebra-system PARI with the interpreter GP ( http://pari.math.u-bordeaux.fr/), both are free available.
master thesis "Einsatz von Optimierungsverfahren in betrieblichen Anwendungen am Beispiel von Re-Use-Szenarios" (Tasks of optimization in regard to re-use scenarios)
Consider situations in which someone divdes a set of older devices into their components in order to re-use the components to produce new devices. This provides the chance of saving costs and energy as well as waste avoiding.
Managing the production in such a situation leads to a task of optimization e.g. to minimize the disposal costs or to maximize the (potential) profit.
This paper deals with some exact and non-exact methods to solve tasks of optimization with respect to the refered re-use scenarios. Furthermore, a small library with implementations of the discussed optimization methods is provided.
Download of the paper (PDF-file, 895 kb)
GUI application (runnable JAR-file) to test the re-use library (ZIP-file, 7,3 mb)
some examples to use with the GUI application (ZIP-file, 12 kb)