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Elementary Topics in Differential Geometry

  • Textbook
  • © 1979


Part of the book series: Undergraduate Texts in Mathematics (UTM)

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About this book

In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under­ standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.

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Table of contents (24 chapters)

Authors and Affiliations

  • Queens College, City University of New York, Flushing, USA

    J. A. Thorpe

About the author

Bibliographic Information

  • Book Title: Elementary Topics in Differential Geometry

  • Authors: J. A. Thorpe

  • Series Title: Undergraduate Texts in Mathematics

  • DOI:

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1979

  • Hardcover ISBN: 978-0-387-90357-6Published: 16 April 1979

  • Softcover ISBN: 978-1-4612-6155-1Published: 12 October 2011

  • eBook ISBN: 978-1-4612-6153-7Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XIV, 256

  • Topics: Differential Geometry

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