Elementary Mathematics from a Higher Standpoint: Volume I: Arithmetic, Algebra, Analysis

by Felix Klein, Gert Schubring (Translator)

These three volumes constitute the first complete English translation of Felix Klein s seminal series Elementarmathematik vom hoheren 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.
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Genres: Mathematics, Algebra

332 pages, Paperback

First published January 1, 1924

Reviews

[Erickson · Rating 5 out of 5]

Very good book, advanced explanations for many things either taken for granted or new perspectives to look at things. Interesting things like impossibility to inscribe heptagon using compass and straightedge, transcendence of e and pi, etc are included with proofs, highly accessible with the presentation style.

Though in my case some topics are not quite understood e.g. Riemann surfaces due to lack of training, nonetheless the book is highly insightful. Recommended for advanced readers or those interested in advanced mathematics.