Overview
- First English translation of the classic volume on precision mathematics and approximation mathematics
- Invaluable treatise for any mathematics educator
- Exhibits the connections between geometry and more formalistic mathematics
- Includes supplementary material: sn.pub/extras
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Table of contents (11 chapters)
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On Functions of a Real Variable and Their Representation in an Orthogonal Coordinate System
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About the Perception of Idealised Structures by Means of Drawings and Models
Keywords
About this book
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.In Volume III, Klein explores the relationship between precision and approximation mathematics. He crosses the various fields of mathematics – from functions in one and two variables to practical geometry to space curves and surfaces – underlining the relation between the exactness of the idealised concepts and the approximations to be considered in applications. Logical procedures are confronted with the way in which concepts arise starting from observations. It is a comparison between properties pertaining only to the theoretical field of abstract mathematics and properties that can be grasped by intuition. The final part, which concerns gestalt relations of curves and surfaces, shows Klein to be the master of the art of description of geometric forms.
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About the author
Bibliographic Information
Book Title: Elementary Mathematics from a Higher Standpoint
Book Subtitle: Volume III: Precision Mathematics and Approximation Mathematics
Authors: Felix Klein
Translated by: Marta Menghini, Anna Baccaglini-Frank
DOI: https://doi.org/10.1007/978-3-662-49439-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Education, Education (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2016
Softcover ISBN: 978-3-662-49437-0Published: 06 July 2016
eBook ISBN: 978-3-662-49439-4Published: 28 June 2016
Edition Number: 1
Number of Pages: XVIII, 259
Number of Illustrations: 156 b/w illustrations