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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Elementary Mathematics from a Higher Standpoint/ by Felix Klein.
Reminder of title:	Volume I: Arithmetic, Algebra, Analysis /
Author:	Klein, Felix.
Description:	XX, 312 p. 125 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematics—Study and teaching . -
Online resource:	https://doi.org/10.1007/978-3-662-49442-4
ISBN:	9783662494424

Elementary Mathematics from a Higher Standpoint = Volume I: Arithmetic, Algebra, Analysis /
Klein, Felix.

Elementary Mathematics from a Higher StandpointVolume I: Arithmetic, Algebra, Analysis /[electronic resource] :by Felix Klein. - 1st ed. 2016. - XX, 312 p. 125 illus.online resource.

First Part: Arithmetic. I. Calculating with Natural Numbers -- II. The First Extensions of the Notion of a Number -- III. Concerning Special Properties of Integers -- IV. Complex Numbers -- V. Concerning the Modern Development and the General Structure of Mathematics -- Second Part: Algebra. I. Real Equations with Real Unknowns -- II. Equations in the Field of Complex Quantities -- Third Part: I. Logarithmis and Exponential Functions -- The Goniometric Functions -- III. Concerning Infitesimal Calculus Proper -- Supplement: I. Transcendence of the Numbers e and pi -- II. Set Theory -- Appendix -- Index of Names -- Index of Contents.

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. About the Author: 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. .

ISBN: 9783662494424

Standard No.: 10.1007/978-3-662-49442-4doiSubjects--Topical Terms:

1253684
Mathematics—Study and teaching .

LC Class. No.: LC8-6691

Dewey Class. No.: 370

Elementary Mathematics from a Higher Standpoint = Volume I: Arithmetic, Algebra, Analysis /
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505 0 $a First Part: Arithmetic. I. Calculating with Natural Numbers -- II. The First Extensions of the Notion of a Number -- III. Concerning Special Properties of Integers -- IV. Complex Numbers -- V. Concerning the Modern Development and the General Structure of Mathematics -- Second Part: Algebra. I. Real Equations with Real Unknowns -- II. Equations in the Field of Complex Quantities -- Third Part: I. Logarithmis and Exponential Functions -- The Goniometric Functions -- III. Concerning Infitesimal Calculus Proper -- Supplement: I. Transcendence of the Numbers e and pi -- II. Set Theory -- Appendix -- Index of Names -- Index of Contents.
520 $a 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. About the Author: 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. .
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