The Resource Elementary mathematics from a higher standpoint, Volume II, Geometry, Felix Klein ; translated by Gert Schubring
Elementary mathematics from a higher standpoint, Volume II, Geometry, Felix Klein ; translated by Gert Schubring
 Summary
 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 farreaching conception of elementarisation, of the "elementary from a higher standpoint", in its implementation for school mathematics. 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 put it: "Projective geometry is all geometry". NonEuclidean 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. About the Author Felix Klein (18491925) 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
 Language

 eng
 ger
 eng
 Extent
 1 online resource
 Contents

 First Part: The Simplest Geometric Formations. I. LineSegment, 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
 Isbn
 9783662494455
 Label
 Elementary mathematics from a higher standpoint, Volume II, Geometry
 Title
 Elementary mathematics from a higher standpoint
 Title number
 Volume II
 Title part
 Geometry
 Statement of responsibility
 Felix Klein ; translated by Gert Schubring
 Title variation
 Geometry
 Language

 eng
 ger
 eng
 Summary
 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 farreaching conception of elementarisation, of the "elementary from a higher standpoint", in its implementation for school mathematics. 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 put it: "Projective geometry is all geometry". NonEuclidean 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. About the Author Felix Klein (18491925) 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
 Cataloging source
 N$T
 Dewey number
 516
 Index
 no index present
 LC call number
 QA445
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Label
 Elementary mathematics from a higher standpoint, Volume II, Geometry, Felix Klein ; translated by Gert Schubring
 Antecedent source
 unknown
 http://library.link/vocab/branchCode

 net
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 First Part: The Simplest Geometric Formations. I. LineSegment, 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
 Control code
 ocn952706047
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9783662494455
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783662494455
 Quality assurance targets
 unknown
 http://library.link/vocab/recordID
 .b35307596
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)952706047
 springer3662494450
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.deakin.edu.au/portal/Elementarymathematicsfromahigherstandpoint/PeTQFuUa_Ik/" typeof="CreativeWork http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.deakin.edu.au/portal/Elementarymathematicsfromahigherstandpoint/PeTQFuUa_Ik/">Elementary mathematics from a higher standpoint, Volume II, Geometry, Felix Klein ; translated by Gert Schubring</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.library.deakin.edu.au/#Deakin%20University%20Library"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.deakin.edu.au/">Deakin University Library</a></span></span></span></span></div>