Spivak's Differential Geometry I

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Discussion Overview

The discussion centers around the necessity of completing Spivak's "Calculus on Manifolds" before progressing to "Differential Geometry I." Participants explore whether the material on differential forms and integration on manifolds in the earlier book is adequately covered in the latter, and the implications of the different presentation styles.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that all necessary material is covered in "Differential Geometry I," but notes it is presented in a more abstract manner compared to "Calculus on Manifolds."
  • Another participant suggests that familiarity with "Calculus on Manifolds" could provide useful intuition for understanding the differential geometry concepts.
  • A different viewpoint recommends reading "Calculus on Manifolds" first, citing the likelihood of completing it and expressing a personal opinion that the first part of "Differential Geometry I" is lengthy and tedious, with the core differential geometry content found in volume 2.

Areas of Agreement / Disagreement

Participants express differing opinions on whether it is necessary to complete "Calculus on Manifolds" before "Differential Geometry I." There is no consensus on the best approach, as some advocate for completing the earlier book while others believe the latter suffices.

Contextual Notes

Participants highlight the differences in presentation style and depth between the two books, indicating that understanding may depend on individual preferences and learning styles.

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Is it necessary to finish Spivak's little book to move on to Spivak's Differential Geometry I, or is the material on differential forms and integration on manifolds in Chapter's 4 and 5 of Spivak's little book covered in Differential Geometry I?
 
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The material is all covered in his differential geometry book. However, the material is covered in a more abstract way than in his Calculus on Manifolds book. It might help to know Calculus on Manifolds in order to get intuition for what he's doing in his differential geometry book.
 
Ok, thanks very much.
 
i also recommend reading the little book first. for one thing you are more likely to finish it. i love mike's book's, but personally think that (especially the first part of) vol. 1 is a little on the long and tedious side. the actual differential geometry is in volume 2.
 

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