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240031 Proseminar Matroide (PS) (SoSe 2022)
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Ein Matroid ist eine kombinatorische Struktur, die den Begriff der Unabhängigkeit aus der linearen Algebra verallgemeinert. Matroide besitzen zahlreiche Anwendungen in vielen Bereichen der Kombinatorik, insbesondere der kombinatorischen Optimierung, sowie der Algebra und Geometrie. Ein interessantes Matroid wird durch die Wälder in einem ungerichteten Graphen gebildet. Dieses graphische Matroid taucht dann (implizit) bei der Bestimmung minimaler spannender Bäume in Kruskals Algorithmus auf. Dies ist ein Spezialfall der sogenannten Greedy-Algorithmen.
Im Proseminar werden wir uns mit den Eigenschaften von Matroiden beschäftigen. Neben Austauscheigenschaften und kombinatorischen Charakterisierungen werden wir auch erklären, warum bei Matroiden (und genau dort) der Greedy-Algorithmus immer optimale Lösungen für bestimmte Optimierungsprobleme liefert. Darüber hinaus werden wir Bezüge zur Algebra und diskreten Geometrie besprechen.
Im Laufe des Seminars werden wir uns zahlreiche verschiedene Zugänge zu den zunächst abstrakten Matroiden erarbeiten und dadurch verstehen, weshalb Matroide zentrale Objekte der diskreten Mathematik sind.
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| Frequency | Weekday | Time | Format / Place | Period |
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| Module | Course | Requirements | |
|---|---|---|---|
| 24-B-GEO_ver1 Geometrie (Gym/Ge) | Proseminar | Study requirement
Ungraded examination |
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| 24-B-PX Praxismodul | Proseminar | Study requirement
Ungraded examination |
Student information |
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