Basic elements of differential geometry and topology

書誌事項

Basic elements of differential geometry and topology

by S.P. Novikov and A.T. Fomenko ; [translated from the Russian by M. Tsaplina]

(Mathematics and its applications, . Soviet series ; v. 60)

Kluwer Academic Publishers, c1990

タイトル別名

Ėlementy different︠s︡ialʹnoĭ geometrii i topologii

Элементы дифференциальной геометрии и топологии

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注記

Translation of: Элементы дифференциальной геометрии и топологии

Originally published: Nauka , c1987

Includes bibliographical references and index

内容説明・目次

内容説明

One service mathematics has rendered the 'Et moi, ..., si j'avait su comment en revenir, je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Matht"natics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics seNe as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

目次

I. Basic Concepts of Differential Geometry.- II. Tensors. Riemannian Geometry.- III. Basic Elements of Topology.- Appendices.- Appendix 1 The Simplest Groups of Transformations of Euclidean and Non-Euclidean Spaces.- Appendix 2 Some Elements of Modern Concepts of the Geometry of the Real World.- Appendix 3 Crystallographic Croups.- Appendix 4 Homology Groups and Methods of their Calculation.- Appendix 5 The Theory of Geodesics, Second Variation and Variational Calculus.- Appendix 6 Basic Geometric Properties of the Lobachevskian Plane.- Appendix 7 Selected Exerices on the Material of the Course.- Additional Material.- References.

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詳細情報

  • NII書誌ID(NCID)
    BA11405642
  • ISBN
    • 0792310098
  • LCCN
    90048303
  • 出版国コード
    ne
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    rus
  • 出版地
    Dordrecht ; Boston
  • ページ数/冊数
    x, 490 p.
  • 大きさ
    25 cm
  • 分類
  • 件名
  • 親書誌ID
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