|
|
Vorlesungsverzeichnis >> Technische Fakultät (TF) >>
|
Topology and Fractal Geometry (TopFG)- Verantwortliche/Verantwortlicher
- Dr. Wolfgang Degen
- Angaben
- Vorlesung
2 SWS, benoteter Schein, ECTS-Studium, ECTS-Credits: 2,5, Sprache Deutsch oder Englisch
- Studienfächer / Studienrichtungen
- WF M-BA ab 5 (ECTS-Credits: 5)
WF INF-BA ab 5 (ECTS-Credits: 5)
WF INF-MA ab 5 (ECTS-Credits: 5)
WF M-MA ab 5 (ECTS-Credits: 5)
- Inhalt
- For those who wish to read and know more about the lecture I append the following lines (including an extended set of references):
The fractals are not subsets of general topological spaces, but compact subsets of complete
metric spaces. Recall: if (X,d) is a metric space, and if T(d) is the topology induced by
the metric (or distance) d, we get the topological space (X, T(d)) --- on which we defindoIe certain
so-called Hausdorff measures. Thus the title of the lecture could be extended by the word "Measure" resulting in the title of Gerald Edgar´s book (1).
However, I don´t need to develop the measure thing in the lecture as fully as Edgar.
A novelty of the lecture is the consideration of measures on the Borel sets Bo(T) for quite
general non-metrizable spaces (X,T) some of these being my own invention. The use and utility of this approach for Fractal Geometry is an objective of further exploration.
Fractal Geometry is also a visual art. In this respect I recommend especially the two books of Barnsley (2) and (3). And the book (6) of Patty is currently the best and most comprehensive
introduction to topology I know of.
The prerequisites to understand the lecture are very few since everything will be explained
from scratch.
The first session will be held October 17, 14:15 - 15:30 in room 00.133-128 ("Animationslabor").
- Empfohlene Literatur
- References
(1) Gerald Edgar: Measure, Topology, and Fractal Geometry, Springer, 2008
(2) Barnsley: Superfractals, Cambridge, 2006
(3) Barnsley: Fractals Everywhere, Academic Press, 1993
(4) Falconer: The Geometry of Fractal Sets, Cambridge, 1985
(5) Falconer: Fractal Geometry. Mathematical Foundations and Applications, Wiley, 2006
(6) Patty: Foundations of Topology, PWS, 1993
- ECTS-Informationen:
- Title:
- Topology and Fractal Geometry
- Credits: 2,5
- Prerequisites
- Diese Vorlesung ist geeignet insbesondere fuer Informatiker und Mathematiker, aber auch fuer Hoerer aus anderen Fachbereichen.
Es sind keine speziellen Vorkenntnisse erfordert, da alles
von Grund auf entwickelt wird.
- Literature
- [1] G. Edgar: Measure, Topology, and Fractal Geometry, Springer, 2008[2] M. Barnsley: Superfractals, CUP, 2006
- Zusätzliche Informationen
- Erwartete Teilnehmerzahl: 10, Maximale Teilnehmerzahl: 25
Für diese Lehrveranstaltung ist eine Anmeldung erforderlich.
Die Anmeldung erfolgt von Montag, 9.10.2017 bis Montag, 30.10.2017 über: persönlich beim Dozenten.
- Institution: Lehrstuhl für Informatik 10 (Systemsimulation)
Kurse
|
 |
|
|
UnivIS ist ein Produkt der Config eG, Buckenhof |
|
|