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    Functional Differential Geometry

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    Author(s)
    Sussman, Gerald Jay
    Wisdom, Jack
    Language
    English
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    Abstract
    An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.
    URI
    http://library.oapen.org/handle/20.500.12657/26057
    Keywords
    geometry; math
    ISBN
    9780262019347
    Publisher
    The MIT Press
    Publisher website
    https://mitpress.mit.edu/
    Publication date and place
    Cambridge, 2013
    Classification
    Differential and Riemannian geometry
    Relativity physics
    Pages
    248
    Public remark
    21-7-2020 - No DOI registered in CrossRef for ISBN 9780262315616
    Rights
    https://creativecommons.org/licenses/by-nc-sa/4.0/
    • Imported or submitted locally

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    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

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