Spivak's Differential Geometry I

[sammycaps]

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?

 

[micromass]

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.

 

[sammycaps]

Ok, thanks very much.

 

[mathwonk]

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.

 

[blue_raver22]

It is not necessary to finish Spivak's little book in order to move on to Spivak's Differential Geometry I. The material on differential forms and integration on manifolds in Chapters 4 and 5 of Spivak's little book is covered in Differential Geometry I. However, completing the little book may provide a stronger foundation and deeper understanding of the concepts in Differential Geometry I. Ultimately, it is up to the individual to decide if they feel comfortable enough with the material in the little book to move on to the next level.