Suchergebnis: Katalogdaten im Frühjahrssemester 2021
Mathematik Master  | ||||||
 WahlfächerFür das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen. | ||||||
| Wahlfächer aus Bereichen der reinen Mathematik | ||||||
| Auswahl: Analysis | ||||||
| Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|---|
| 401-4422-21L | An Introduction to the Calculus of Variations | W | 4 KP | 2V | A. Figalli | |
| Kurzbeschreibung | Calculus of variations is a fundamental tool in mathematical analysis, used to investigate the existence, uniqueness, and properties of minimizers to variational problems. Classic examples include, for instance, the existence of the shortest curve between two points, the equilibrium shape of an elastic membrane, and so on. | |||||
| Lernziel | ||||||
| Inhalt | In the course, we will study both 1-dimensional and multi-dimensional problems. | |||||
| Voraussetzungen / Besonderes | Basic knowledge of Sobolev spaces is important, so some extra additional readings would be required for those unfamiliar with the topic. | |||||
| 401-3378-19L | Entropy in Dynamics | W | 8 KP | 4G | M. Einsiedler | |
| Kurzbeschreibung | Definition and basic property of measure theoretic dynamical entropy (elementary and conditionally). Ergodic theorem for entropy. Topological entropy and variational principle. Measures of maximal entropy. Equidistribution of periodic points. Measure rigidity for commuting maps on the circle group. | |||||
| Lernziel | The course will lead to a firm understanding of measure theoretic dynamical entropy and its applications within dynamics. We will start with the basic properties of (conditional) entropy, relate it to the question of effective coding techniques, discuss and prove the Shannon-McMillan-Breiman theorem that is also known as the ergodic theorem for entropy. Moreover, we will discuss a topological counter part and relate this topological entropy to the measure theoretic entropy by the variational principle. We will use these methods to classify certain natural homogeneous measures, prove equidistribution of periodic points on compact quotients of hyperbolic surfaces, and establish a measure rigidity theorem for commuting maps on the circle group. | |||||
| Skript | Entropy book under construction, available online under https://tbward0.wixsite.com/books/entropy | |||||
| Voraussetzungen / Besonderes | No prior knowledge of dynamical systems will be assumed but measure theory will be assumed and very important. Doctoral students are welcome to attend the course for 2KP. | |||||
Seite
1
von
1
