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Mathematische Strukturen: Von Der Linearen Algebra Über Ringen Zur Geometrie Mit Garben by Joachim Hilgert

Mathematische Strukturen: Von Der Linearen Algebra Über Ringen Zur Geometrie Mit Garben

by Joachim Hilgert
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Book cover type: Paperback
  • ISBN13: 9783662688922
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 343
  • Original Price: EUR 30.83
  • Language: German
  • Edition: 2. Auflage 2024
  • Item Weight: 499 grams
  • BISAC Subject(s): Geometry / Algebraic

Dieses Buch richtet sich an Studierende der Mathematik, die die Anfängervorlesungen in Analysis und Linearer Algebra gemeistert haben. Es ist gedacht als Orientierungshilfe für die Vielzahl an spezialisierten Fachveranstaltungen in den mittleren und höheren Semestern. Ein wichtiges Anliegen ist die Darstellung von Vergleichsmöglichkeiten und Ähnlichkeiten zwischen mathematischen Disziplinen. Das organisierende Prinzip ist der Begriff der mathematischen Struktur, der sich durch alle Teilgebiete der Mathematik zieht.

Die Inhalte, an denen die verschiedenen Typen von Strukturen exemplarisch erläutert werden, decken curriculare Anforderungen insbesondere aus der Algebra und der Geometrie (differentiell und algebraisch) ab. Die Diskussion von Vergleichsmöglichkeiten enthält aber auch Einführungen in die Kategorientheorie und die Garbentheorie, deren Bedeutung in der modernen Mathematik eine stärkere Verankerung in den Curricula nahelegt.

Das Buch eignet sichinsbesondere auch zum Nachschlagen der dargestellten Strukturen.

Die vorliegende 2. Auflage ist vollständig durchgesehen und um ein Kapitel zu Mannigfaltigkeiten mit Strukturen wie komplex, symplektisch, affin etc. erweitert.

Joachim Hilgert forscht und lehrt am Institut für Mathematik der Universität Paderborn.

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