Elementary Mathematics from a Higher Standpoint: Volume II: Geometry by Felix Klein (PDF)

Description

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 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Klein’s 3-volume sum is a masterpiece, dedicated to teachers of maths, worldwide, i.e. still applicable today if one just looks at the disastrous mathematical level of our students…The title might be misleading : Klein’s work is by no means “elementary”, but represents a master’s attempt to show the ultimate unity of mathematical knowledge, via teaching mathematics in school and universities, from a higher vista point !Even though the text may appear cryptic at times — either due to Klein’s original, german text or to the translation in english — it’s generally clear, concise and contains plenty of helpful historical informations.N.B. The third volume is a bit of an overkill, as Klein states, more than proves things… And when he does prove, his text is so confused that boredom soon sneaks in…

⭐Klein’s 3-volume sum is a masterpiece, dedicated to teachers of maths, worldwide, i.e. still applicable today if one just looks at the disastrous mathematical level of our students…The title might be misleading : Klein’s work is by no means “elementary”, but represents a master’s attempt to show the ultimate unity of mathematical knowledge, via teaching mathematics in school and universities, from a higher vista point !Even though the text may appear cryptic at times — either due to Klein’s original, german text or to the translation in english — it’s generally clear, concise and contains plenty of helpful historical informations.N.B. The third volume is a bit of an overkill, as Klein states, more than proves things… And when he does prove, his text is so confused that boredom soon sneaks in…

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Free Download Elementary Mathematics from a Higher Standpoint: Volume II: Geometry in PDF format
Elementary Mathematics from a Higher Standpoint: Volume II: Geometry PDF Free Download
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Elementary Mathematics from a Higher Standpoint: Volume II: Geometry 2016 PDF Free Download
Download Elementary Mathematics from a Higher Standpoint: Volume II: Geometry PDF
Free Download Ebook Elementary Mathematics from a Higher Standpoint: Volume II: Geometry