Elementary Mathematics from a Higher Standpoint - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Mathematics from a Higher Standpoint write by Felix Klein. This book was released on 2016-06-28. Elementary Mathematics from a Higher Standpoint available in PDF, EPUB and Kindle. 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.
Elementary Mathematics from a Higher Standpoint
Elementary Mathematics from a Higher Standpoint - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Mathematics from a Higher Standpoint write by Felix Klein. This book was released on 2016-06-28. Elementary Mathematics from a Higher Standpoint available in PDF, EPUB and Kindle. 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.
Elementary Mathematics from an Advanced Standpoint - Arithmetic - Algebra - Analysis
Elementary Mathematics from an Advanced Standpoint - Arithmetic - Algebra - Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Mathematics from an Advanced Standpoint - Arithmetic - Algebra - Analysis write by Felix Klein. This book was released on 2007-03. Elementary Mathematics from an Advanced Standpoint - Arithmetic - Algebra - Analysis available in PDF, EPUB and Kindle. This book provides a fascinating and inspirational read for anyone with an interest in advanced mathematics, written by the great German mathematician Felix Klein. It is highly recommended for inclusion on the bookshelf of anyone with an interest in the subject.
Elementary Mathematics from a Higher Standpoint
Elementary Mathematics from a Higher Standpoint - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary Mathematics from a Higher Standpoint write by Felix Klein. This book was released on 2016-06-29. Elementary Mathematics from a Higher Standpoint available in PDF, EPUB and Kindle. 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./div This volume II presents a paradigmatic realisation of Klein’s approach of elementarisation for teacher education. It is shown how the various geometries, elaborated particularly since the beginning of the 19th century, are revealed as becoming unified in a new restructured geometry. As Klein liked to stress: “Projective geometry is all geometry”. Non-Euclidean geometry proves to constitute a part of this unifying process. The teaching of geometry is discussed in a separate chapter, which provides moreover important information on the history of geometry teaching and an international comparison.
Elementary mathematics from advanced standpoint
Elementary mathematics from advanced standpoint - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elementary mathematics from advanced standpoint write by Felix Klein. This book was released on 1908. Elementary mathematics from advanced standpoint available in PDF, EPUB and Kindle.
