Elementary Mathematics from a Higher Standpoint

Volume I: Arithmetic, Algebra, Analysis

Autoren: Klein, Felix

  • New translation of the classic volume on arithmetic, algebra, and analysis
  • Invaluable treatise for any mathematics educator
  • Exhibits the connections between geometry and more formalistic mathematics
Weitere Vorteile

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eBook 53,54 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-662-49442-4
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Softcover 69,54 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-662-49440-0
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
Über dieses Buch

​These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom höheren Standpunkte aus”. “Complete” has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English.

The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein’s far-reaching conception of elementarisation, of the “elementary from a higher standpoint”, in its implementation for school mathematics.

This volume I is devoted to what Klein calls the three big “A’s”: arithmetic, algebra and analysis. They are presented and discussed always together with a dimension of geometric interpretation and visualisation - given his epistemological viewpoint of mathematics being based in space intuition. A particularly revealing example for elementarisation is his chapter on the transcendence of e and p, where he succeeds in giving concise yet well accessible proofs for the transcendence of these two numbers. It is in this volume that Klein makes his famous statement about the double discontinuity between mathematics teaching at schools and at universities – it was his major aim to overcome this discontinuity.


Über den Autor

Felix Klein (1849-1925) was a leading German mathematician whose research interests included group theory, complex analysis, and geometry. His work influenced many areas of mathematics and related subjects, ranging from mathematical physics to mathematical didactics.To this day, Felix Klein is considered one of the most important mathematicians of the 19th century. 

Inhaltsverzeichnis (12 Kapitel)

Dieses Buch kaufen

eBook 53,54 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-662-49442-4
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Softcover 69,54 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-662-49440-0
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
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Bibliografische Information

Bibliographic Information
Buchtitel
Elementary Mathematics from a Higher Standpoint
Buchuntertitel
Volume I: Arithmetic, Algebra, Analysis
Autoren
Übersetzt von
Schubring, G.
Copyright
2016
Verlag
Springer-Verlag Berlin Heidelberg
Copyright Inhaber
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-49442-4
DOI
10.1007/978-3-662-49442-4
Softcover ISBN
978-3-662-49440-0
Auflage
1
Seitenzahl
XX, 312
Anzahl der Bilder
125 schwarz-weiß Abbildungen
Zusätzliche Informationen
Original German edition published by Verlag Julius Springer, Berlin, Germany, 1933
Themen