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Titlebook: Elementary Mathematics from a Higher Standpoint; Volume I: Arithmetic Felix Klein Book 2016 Springer-Verlag Berlin Heidelberg 2016 Algebra.

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發(fā)表于 2025-3-21 16:38:49 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Elementary Mathematics from a Higher Standpoint
副標(biāo)題Volume I: Arithmetic
編輯Felix Klein
視頻videohttp://file.papertrans.cn/308/307391/307391.mp4
概述New translation of the classic volume on arithmetic, algebra, and analysis.Invaluable treatise for any mathematics educator.Exhibits the connections between geometry and more formalistic mathematics.I
圖書(shū)封面Titlebook: Elementary Mathematics from a Higher Standpoint; Volume I: Arithmetic Felix Klein Book 2016 Springer-Verlag Berlin Heidelberg 2016 Algebra.
描述.?These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom h?heren 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 inter
出版日期Book 2016
關(guān)鍵詞Algebra; Analysis; Arithmetic; Infinitesimal Calculus; Mathematics Education
版次1
doihttps://doi.org/10.1007/978-3-662-49442-4
isbn_softcover978-3-662-49440-0
isbn_ebook978-3-662-49442-4
copyrightSpringer-Verlag Berlin Heidelberg 2016
The information of publication is updating

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發(fā)表于 2025-3-21 21:40:51 | 只看該作者
II.?The First Extension of the Notion of Numberake in order the following steps: .1. ..2. ., in connection with the beginnings of operations with letters. .3. ., which leads, then, gradually, to the representation of the .. .It is a matter of indifference in which order we take up the first two points. Let us discuss negative numbers before frac
板凳
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Concerning the Modern Development and the General Structure of Mathematicsde by side independent of one another, now finally mingle. It is difficult to put into vivid language the difference which I have in mind, because none of the current divisions fits the case. You will, however, understand from a concrete example, namely, if I show how one would compile the . in the
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I.?Logarithmic and Exponential Functionspowers of the form . = .., where the exponent . is a positive integer, and extends the notion step by step for ., then for fractional values of ., and finally, if circumstances warrant it, to irrational values of .. In this process the concept of . becomes subordinated to the general concept of powe
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https://doi.org/10.1007/978-94-011-9276-7ake in order the following steps: .1. ..2. ., in connection with the beginnings of operations with letters. .3. ., which leads, then, gradually, to the representation of the .. .It is a matter of indifference in which order we take up the first two points. Let us discuss negative numbers before frac
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https://doi.org/10.1007/978-3-031-16392-0is science which appear in the school curriculum. .1. The first problem of the theory of numbers is that of .: Is one number divisible by another or not? .2. Simple rules can be given which enable us easily to decide as to the ., such as 2, 3, 4, 5, 9, 11, etc. .3. There are ., that is, numbers whic
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