Elementary Mathematics from a Higher Standpoint: Volume II: Geometry
暫譯: 從更高的立場看初等數學：第二卷：幾何學
Klein, Felix, Schubring, Gert
相關主題
商品描述
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.
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.
商品描述(中文翻譯)
這三卷書構成了費利克斯·克萊因（Felix Klein）開創性系列《從更高的角度看基礎數學》（Elementarmathematik vom höheren Standpunkte aus）的第一部完整英文翻譯。「完整」在這裡有兩重意義：首先，現在已經有了第三卷的英文翻譯，而直到今天，唯一的翻譯是中文。其次，第一卷和第二卷的英文版本省略了幾個部分，甚至是原文的擴展部分，而我們現在提供的是一個完整的、修訂過的現代英文翻譯。
這些卷冊最早於1902年至1908年間出版，是克萊因為未來的數學教師提供的課程講義，實現了一種新的教師培訓形式，這種形式至今仍然有效：克萊因引導學生獲得對學校數學更全面和方法論的觀點。這些卷冊使我們能夠理解克萊因對基礎化的深遠構想，即「從更高的角度看基礎」，在學校數學中的實施。
第二卷呈現了克萊因的基礎化方法在教師教育中的範例實現。顯示了自19世紀初以來，發展出來的各種幾何學是如何在一個新的重組幾何中統一的。正如克萊因所強調的：「射影幾何就是所有幾何。」非歐幾何證明是這一統一過程的一部分。幾何教學在一個單獨的章節中進行討論，此外還提供了有關幾何教學歷史的重要信息以及國際比較。
作者簡介
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.
作者簡介(中文翻譯)
費利克斯·克萊因（Felix Klein，1849-1925）是德國著名的數學家，他的研究興趣包括群論、複分析和幾何學。他的工作影響了數學及相關領域的許多方面，從數學物理到數學教學。至今，費利克斯·克萊因被認為是19世紀最重要的數學家之一。
