What comes first, spivaks manifolds or rudins pma?

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In summary, the conversation is about whether or not to read Spivak's "Calculus on Manifolds" before or after Rudin's "Principles of Mathematical Analysis" (PMA). Some sources recommend reading it as a second year text, others say to read it with or after Rudin, and some suggest skipping it altogether. The person asking the question wants to cultivate mathematical maturity and is considering starting with Rudin and supplementing with Spivak. It is suggested to have at least some understanding of analysis before diving into Manifolds. There is also a mention of "baby Rudin," which is a nickname for Rudin's "Principles of Mathematical Analysis" for its introductory level material.
  • #1
khemix
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im buying books to get better at proofs so that i can tackle rudins analysis text. my question is, do i read spivak manifolds before or after rudin?

a lot of sources list manifolds as a second year text, suggesting it is required reading. but some people also say it should be read after or with rudin. still other sources say to skip it entirely as it is a dumbed down treatment of more advanced analysis. i don't want any more dumbed down math books. so is manifolds really neccessary?

i am looking to "cultivate mathematical maturity to tackle rudins pma". and i think rudin has most of what manifolds does but more rigorously. thank you very much for the help.
 
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  • #2
What's your background in analysis?
 
  • #3
If you have a least some understanding of analysis (at least of the single variable like the treatment found in Kenneth Ross' Elementary Analysis) then I would go with Manifolds first.
 
  • #4
Never mind, I had not noticed It was baby rudin we were talking about. I would start with rudin until the multivariable sections and supplement with spivak.
 
  • #5
Whats baby Rudin and the difference it has with Rudin?
 

1. What is a Spivak's Manifold?

A Spivak's manifold is a type of mathematical structure that is used in the field of differential geometry. It is a generalization of the concept of a smooth manifold, which is a topological space that locally resembles Euclidean space.

2. What is Rudin's PMA?

Rudin's PMA (Principles of Mathematical Analysis) is a well-known textbook written by the mathematician Walter Rudin. It covers the fundamental concepts of real analysis, such as limits, continuity, and differentiation.

3. Which came first, Spivak's manifolds or Rudin's PMA?

Spivak's manifolds were developed before Rudin's PMA. Spivak's book "A Comprehensive Introduction to Differential Geometry" was published in 1979, while Rudin's PMA was first published in 1953.

4. Are Spivak's manifolds and Rudin's PMA related?

Yes, they are related in the sense that they both deal with advanced mathematical concepts and are used in the field of differential geometry. However, they are two separate entities and have different focuses.

5. Which one should I study first, Spivak's manifolds or Rudin's PMA?

It depends on your level of familiarity with mathematics and your specific interests. If you are interested in differential geometry, then studying Spivak's manifolds first may be more beneficial. However, if you are interested in real analysis, then studying Rudin's PMA first may be a better option.

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