Elementary Mathematics from a Higher Standpoint (eBook)
XVIII, 259 Seiten
Springer-Verlag
978-3-662-49439-4 (ISBN)
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.
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.
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.
First Part: On Functions of a Real Variable and their Representation in an Orthogonal Coordinate System. I. Remarks on the Single Independent Variable x.- II. Functions f (x) of a Real Variable x.- III. The Approximated Representation of Functions.- IV. Further Discussion About the Trigonometric Representation of Functions.- V. Functions of Two Variables. Second Part: Free Geometry of Plane Curve. I. Precision Geometry Considerations in Plane Geometry.- II. Further Considerations of Precision Mathematics on Plane Geometry.- III. Transition to Practical Geometry: a) Geodesy.- IV. Further Considerations on Practical Geometry: b) Drawing Geometry.Third Part: About the Perception of Idealised Structures by Means of Drawings and Models. Name Index.- Subject Index.
Erscheint lt. Verlag | 28.6.2016 |
---|---|
Übersetzer | Marta Menghini, Anna Baccaglini-Frank |
Zusatzinfo | XVIII, 259 p. 156 illus. |
Verlagsort | Berlin |
Sprache | englisch |
Original-Titel | Elementarmathematik vom Höheren Standpunkt aus - Präzisions- und Approximationsmathematik |
Themenwelt | Geisteswissenschaften |
Sozialwissenschaften ► Pädagogik ► Schulpädagogik / Grundschule | |
Schlagworte | Geometry • mathematics education • Multilinear Algebra • Multivariate Calculus • Numerical Mathematics |
ISBN-10 | 3-662-49439-6 / 3662494396 |
ISBN-13 | 978-3-662-49439-4 / 9783662494394 |
Haben Sie eine Frage zum Produkt? |
Größe: 5,2 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich