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Elementary Mathematics From A Higher Standpoint

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Elementary Mathematics From A Higher Standpoint

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Author : Felix Klein
language : en
Publisher: Springer
Release Date : 2016-06-28

Elementary Mathematics From A Higher Standpoint written by Felix Klein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Education categories.

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

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Author : Felix Klein
language : en
Publisher: Springer
Release Date : 2016-06-28

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 A Higher Standpoint Geometry

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Author : Felix Klein
language : en
Publisher:
Release Date : 2016

Elementary Mathematics From A Higher Standpoint Geometry written by Felix Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Education categories.

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. 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. 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 put it: "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. 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. mathematicians of the 19th century. -- Back cover.

Elementary Mathematics From A Higher Standpoint

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Author : Felix Klein
language : en
Publisher: Springer Spektrum
Release Date : 2016-08-24

Elementary Mathematics From A Higher Standpoint written by Felix Klein and has been published by Springer Spektrum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-24 with Education categories.

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. The second volume begins with an analysis of the simplest geometric manifolds such as line segments, and area and volume as relative magnitudes. The second section on geometric transformations examines affine and projective transformations, higher point transformations, transformations with change of space, and the theory of the imaginary. The text concludes with a systematic discussion of geometry and its foundations.

Elementary Mathematics From An Advanced Standpoint

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Author : Felix Klein
language : en
Publisher: Cosimo, Inc.
Release Date : 2007-06-01

Elementary Mathematics From An Advanced Standpoint written by Felix Klein and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-01 with Mathematics categories.

Discusses calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers; algebra-related subjects such as real equations with real unknowns and equations in the field of complex quantities. Also explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 edition. 125 figures.

Elementary Mathematics From A Higher Standpoint Geometry

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Author : Felix Klein
language : en
Publisher:
Release Date : 2016

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. 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.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 put it: "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.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. mathematicians of the 19th century. -- Back cover

Elementary Mathematics From A Higher Standpoint Precision Mathematics And Approximation Mathematics

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Author : Felix Klein
language : en
Publisher:
Release Date : 2016

Elementary Mathematics From A Higher Standpoint Precision Mathematics And Approximation Mathematics written by Felix Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Education categories.

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. 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.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 put it: "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.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. mathematicians of the 19th century. -- Back cover

Elementary Mathematics From The Higher Standpoint

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Author : Ella L. Moulton
language : en
Publisher:
Release Date : 1912

Elementary Mathematics From The Higher Standpoint written by Ella L. Moulton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1912 with categories.

Elementary Mathematics From An Advanced Standpoint Arithmetic Algebra Analysis

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Author : Felix Klein
language : en
Publisher:
Release Date : 1966

Elementary Mathematics From An Advanced Standpoint Arithmetic Algebra Analysis written by Felix Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Mathematics categories.

Elementary Mathematics From An Advanced Standpoint

DOWNLOAD
Author : Felix Klein
language : en
Publisher:
Release Date :

Elementary Mathematics From An Advanced Standpoint written by Felix Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Elementary Mathematics From A Higher Standpoint

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