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Elementary Mathematics from a Higher Standpoint de Felix Klein

Elementary Mathematics from a Higher Standpoint

Autor Felix Klein Traducere de Marta Menghini, Gert Schubring
en Limba Engleză Paperback – 6 iul 2016
This three-part treatment on mathematical knowledge needed by teachers was a pathbreaking book published by the German mathematician Felix Klein between 1924 and 1928 and it is still as relevant as it was 90 years ago. The books pulse with the excitement of the actual lectures they came from and combine geometric intuition with the precision of arithmetic formulas in an inspiring way.
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Specificații

ISBN-13: 9783662495155
ISBN-10: 3662495155
Pagini: 740
Ilustrații: Approx. 740 p. 3 volume-set.
Dimensiuni: 155 x 235 mm
Ediția:1st ed. 2016
Editura: Springer Berlin, Heidelberg
Colecția Springer
Locul publicării:Berlin, Heidelberg, Germany

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

New translation of the three classic volumes Invaluable treatise for any mathematics educator Exhibits the connections between geometry and more formalistic mathematics

Cuprins

First Part: The Simplest Geometric Formations. I. Line-Segment, Area, Volume as Relative Quantities.- II. The Grassmannian Determinant Principle for the Plane.- III. The Grassmannian Principle for Space.- IV. Classification of the Elementary Configurations of Space According to their Behaviour under Transformation of Rectangular Coordinates.- V. Higher Configurations.- Part Two: Geometric Transformations. I. Affine Transformations.- II. Projective Transformations.- III. Higher Point Transformations.- IV. Transformations with Change of Space Element.- V. Theory of the Imaginary.- Part Three: Systematic Discussion of Geometry and its Foundations. I. The Systematic Discussion.- II. Foundations of Geometry.- Final Chapter: Observations about the Teaching of Geometry. I. The Teaching in England.- II. The Teaching in France.- III.The Teaching in Italy.- IV. Teaching in Germany.- Appendix I.- Appendix II.- Index of Names.- Index of Contents.