Application of elementary differential geometry to influence analysis

著者

    • Poon, Yat-Sun
    • Poon, Wai-Yin

書誌事項

Application of elementary differential geometry to influence analysis

Yat-Sun Poon, Wai-Yin Poon

(Surveys of modern mathematics, 3)

International Press , Higher Education Press, c2012

  • : pbk

大学図書館所蔵 件 / 5

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注記

Includes bibliography and index

内容説明・目次

内容説明

With linear algebra and vector calculus as pre-requisites, the first part of this textbook presents an introduction to the geometry of graphs, encompassing the concepts of normal curvature, sectional curvature, Ricci curvature, and Gaussian curvature. The second part of the book provides background statistical concepts and basic models that form the fundamental knowledge necessary for better comprehension of the concept of local influence; while the third part focuses on the application of differential geometry to local influence analysis, and discusses when and how geometric concepts can be used in an effective manner to develop measures for assessing local influence. This textbook is intended for the use of senior undergraduate and graduate students in mathematics or statistics. For mathematics students, it illustrates how elementary differential geometry of graphs can be used effectively to tackle concrete problems outside mathematics. For statistics students, it facilitates an understanding of and direct access to differential geometric concepts currently used in statistics research. The inter-disciplinary nature of the concepts and terminologies presented herein help to bridge crucial knowledge gaps for mathematics and statistics students, and to facilitate further interaction, collaboration, and innovative research activities among mathematical scientists.|With linear algebra and vector calculus as pre-requisites, the first part of this textbook presents an introduction to the geometry of graphs, encompassing the concepts of normal curvature, sectional curvature, Ricci curvature, and Gaussian curvature. The second part of the book provides background statistical concepts and basic models that form the fundamental knowledge necessary for better comprehension of the concept of local influence; while the third part focuses on the application of differential geometry to local influence analysis, and discusses when and how geometric concepts can be used in an effective manner to develop measures for assessing local influence. This textbook is intended for the use of senior undergraduate and graduate students in mathematics or statistics. For mathematics students, it illustrates how elementary differential geometry of graphs can be used effectively to tackle concrete problems outside mathematics. For statistics students, it facilitates an understanding of and direct access to differential geometric concepts currently used in statistics research. The inter-disciplinary nature of the concepts and terminologies presented herein help to bridge crucial knowledge gaps for mathematics and statistics students, and to facilitate further interaction, collaboration, and innovative research activities among mathematical scientists.

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詳細情報

  • NII書誌ID(NCID)
    BB11045985
  • ISBN
    • 9781571462527
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Somerville, Mass.,Baijing
  • ページ数/冊数
    xiii, 174 p.
  • 大きさ
    26 cm
  • 親書誌ID
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