But this mathematical language is not mathematics, and there is real substance behind the language itself, just like poems can be translated into other natural languages or algorithms can be written in several programming languages.Ĭalling mathematics a language confuses form with substance or declares that it's all form and no substance. This book is attempting to get rid of that ambiguity by rewriting it in notation that does not allow for ambiguity and present it to computers, who are still very bad at ambiguity. Differential Geometry A First Course in Curves and Surfaces. To be sure, there is a mathematical language, a notation with much ambiguity that is typically ok when conveyed to other humans, because humans are great with ambiguity. This classic work is now available in an unabridged paperback edition.
The style is uneven, sometimes pedantic, sometimes sloppy, sometimes telegram style, sometimes longwinded, etc., depending on my mood when I was writing those particular lines. I oer them to you in the hope that they may help you, and to complement the lectures.
It seems to me like a disrespect to say that mathematics is a language, because it seems to suggest that mathematics on its own has no substance, nothing intrinsic to itself. on manifolds, tensor analysis, and dierential geometry. geometry, the divergence theorem, triangulations, and the Gauss Bonnet theorem. By studying the properties of the curvature of curves on a sur face, we will be led to the rst and second fundamental forms of a surface. In this case, the actual subject of interest appears to be relativity, not mathematics. differential geometry and about manifolds are refereed to doCarmo12,Berger andGostiaux4,Lafontaine29,andGray23.Amorecompletelistofreferences can be found in Section 20.11.
The people who usually do this say this because they are not interested in the mathematics itself, but in some other subject that happens to require mathematics. I have a big problem when people describe mathematics as just "a language".
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