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Vorlesungsverzeichnis >> Technische Fakultät (TF) >>
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Measure, Topology and Fractal Geometry (MTFGeo)- Dozent/in
- Dr. Wolfgang Degen
- Angaben
- Vorlesung
4 SWS, benoteter Schein, ECTS-Studium, ECTS-Credits: 5, Sprache Deutsch oder Englisch
Zeit und Ort: Fr 12:00 - 14:00, Raum n.V.
Vorbesprechung: 8.10.2014, 14:15 - 14:45 Uhr, Raum Übung 3 / 01.252-128
- Studienfächer / Studienrichtungen
- WF M-BA ab 1 (ECTS-Credits: 5)
WF INF-BA ab 1 (ECTS-Credits: 5)
WF INF-MA ab 1 (ECTS-Credits: 5)
WF M-MA ab 1 (ECTS-Credits: 5)
- ECTS-Informationen:
- Credits: 5
- Prerequisites
- The lecture is suitable for all students of Computer Science and/or Mathematics.
A certificate (Vorlesungsschein) can be acquired by regular attentance
(and a short colloqium if a mark is wished for).
The lecture can also be used for an oral exam in the Master Study.
- Contents
- The first part of the lecture covers the fundamentals of topology:
metric spaces, product spaces, some algebraic topology, etc.
Here the highlights will be some novel methods (invented by the lecturer)
of constructing topologies on possibly dirty and mixolytical real world sets. The next part comprises measure theory. Lebesque is a must since it
belongs to general mathematical education. However, the measures
essential for fractal geometry are the famous Hausdorf measure,
packing measure, and others of that family. Then we have the tools to mathematically analyze concrete fractal
figures, like the Mandelbrot set, the Menger sponge, and so on.
A rather complicated task will be the determination of the "fractal
dimension" of these sets (or figures).
- Literature
- 1. Gerald Edgar: Measure, Topology, and Fractal Geometry, Springer, 2008
2. M.F. Barnsley: Superfractals, Cambridge, 2006 3. C.W. Patty: Foundations of Topology, Prindle,Weber &Schmidt, 1993 4. J. Yeh: Real Analysis. Theory of Measure and Integration, World
Scientific, 2006
- Zusätzliche Informationen
- Erwartete Teilnehmerzahl: 10, Maximale Teilnehmerzahl: 25
Für diese Lehrveranstaltung ist eine Anmeldung erforderlich.
Die Anmeldung erfolgt von Montag, 6.10.2014 bis Sonntag, 30.11.2014 über: mein Campus.
- Institution: Lehrstuhl für Informatik 10 (Systemsimulation)
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