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borovik shadows truth metamathematics elementary mathematics 2010

Type:: E-books
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Size:: 16.0 MB
Uploaded On:: Feb. 7, 2023, 4 p.m.
Added By:: andryold1
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Info Hash:: 7865DF4449A06B6E1AED6AEC7C63BFDC7CA3C74F

Textbook in PDF format From the Preface: This book is an attempt to look at mathematics from a new and somewhat unusual point of view. I have started to systematically record and analyze from a mathematical point of view various difﬁculties experiencing by children in their early learning of mathematics. I hope that my approach will eventually allow me to gain a better understanding of how we—not only children, but adults, too — do mathematics. This explains the title of the book: metamathematics is mathematics applied to study of mathematics. I chase shadows: I am trying to identify and clearly describe hidden structures of elementary mathematics which may intrigue, puzzle, and — like shadows in the night — sometimes scare an inquisitive child. The real life material in my research is limited to stories that my fellow mathematicians have chosen to tell me; they represent tiny but personally signiﬁcant episodes from their childhood. I directed my inquiries to mathematicians for an obvious reason: only mathematicians possess an adequate language which allows them to describe in some depths their experiences of learning mathematics. So far my approach is justiﬁed by the warm welcome it found among my mathematician friends, and I am most grateful to them for their support. For some reason (and the reason deserves a study on its own) my colleagues know what I am talking about!

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Borovik A. Shadows of the Truth. Metamathematics of Elementary Mathematics 2010.pdf 16.0 MB

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borovik shadows truth metamathematics elementary mathematics 2010