Endliche Strukturen
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Endliche Strukturen: (Mathematik für das Lehramt)

Endliche Strukturen: (Mathematik für das Lehramt)


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About the Book

In diesem Band stehen Probleme im Mittelpunkt, die sich zunächst einfach anhören, dann aber eine anspruchsvollere mathematische Bearbeitung verlangen. Sie kommen aus unterschiedlichen Bereichen, doch ist ihnen gemeinsam, dass sie sich auf eine endliche Anzahl von Elementen beziehen. Hierfür werden mathematische Modelle betrachtet und immer wieder die gleichen Fragen gestellt: Hat ein bestimmtes Problem überhaupt eine Lösung? Kann man alle Lösungen systematisch bestimmen? Gibt es dabei einen wirklich effizienten Weg? Das Buch konzentriert sich in fünf Kapiteln auf die grundlegenden algebraischen Strukturen Gruppe, Ring und Körper sowie auf Einblicke in die Galoistheorie, die Codierungstheorie und die Graphentheorie. Am Beispiel endlicher Strukturen wird jeweils aufgezeigt, welche Theorien die Mathematik zur Verfügung stellt, wenn konkrete Fragestellungen wie das Abzählen von Mustern, die Codierung von Nachrichten oder das Aufstellen von Tourenplänen bearbeitet werden sollen.

Table of Contents:
Grundlagen der Wahrscheinlichkeitstheorie und Statistik.- Statistische Modelle.- Schätzmethoden.- Vergleich von Schätzern: Optimalitätstheorie.- Konfidenzintervalle und Hypothesentests.- Optimale Tests und Konfidenzintervalle, Likelihood-Quotienten-Tests und verwandte Methoden.- Lineare Modelle.- A Resultate über benutzte Verteilungsfamilien.- A1 Liste der verwendeten Verteilungen.- B Tabellen.- B1 Exponentielle Familien.- C Verzeichnisse.- Tabellenverzeichnis.- Abbildungsverzeichnis.- Verzeichnis der Beispiele.- Verzeichnis der Aufgaben.

About the Author :
Prof. Dr. Kristina Reiss, Technische Universität München, School of Education Prof. Dr. Gernot Stroth, Universität Halle-Wittenberg, Halle

Review :
Aus den Rezensionen:  “... Der keineswegs oberflächliche Text ist sehr verständlich und ausführlich, Begriffe und Beweise werden immer anschaulich vorbereitet ... Die gelegentlichen Wiederholungen erleichtern die auswählende Lektüre ... Mehr griffige Beispiele hätten belebend gewirkt. Ausführliche Lösungen zu den oft interessanten Aufgaben findet man am Schluss. Der Band ist weitgehend auf der Basis von Schulkenntnissen verständlich, kann also neben Studierenden auch bereits interessierten Schülern zum etwas tieferen Hineinschnuppern in das Fach empfohlen werden.“(Wolfgang Grölz, in: ekz-Informationsdienst, 2011 Vol. 2011/28)  


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Product Details
  • ISBN-13: 9783642171819
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 325
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 3642171818
  • Publisher Date: 03 Feb 2011
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Series Title: Mathematik für das Lehramt


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