id: 06592110
dt: b
an: 2016e.00555
au: Klein, Felix
ti: Elementary mathematics from a higher standpoint. Volume I: Arithmetic,
algebra, analysis. Translated from the 4th German edition by Gert
Schubring.
so: Berlin: Springer (ISBN 978-3-662-49440-0/pbk; 978-3-662-49442-4/ebook;
978-3-662-49515-5/set). xx, 312~p. (2016).
py: 2016
pu: Berlin: Springer
la: EN
cc: F10 H40 I10
ut:
ci: Zbl 1341.51001; Zbl 1339.26002; Zbl 0006.24206
li: doi:10.1007/978-3-662-49442-4
ab: Publisher’s description: 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.
For Volumes II and III see [Zbl 1341.51001; Zbl 1339.26002]. See the
review of the original German edition in [Zbl 0006.24206].
rv: