What comes first, spivaks manifolds or rudins pma?

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Discussion Overview

The discussion revolves around the order in which to study Spivak's "Calculus on Manifolds" and Rudin's "Principles of Mathematical Analysis" (often referred to as "baby Rudin"). Participants are exploring the implications of reading one text before or after the other, considering their respective rigor and content.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant expresses a desire to improve proof skills to tackle Rudin's text and questions whether Spivak's book should be read before or after Rudin.
  • Some participants suggest that Spivak's "Manifolds" is often considered a second-year text and may be necessary for developing mathematical maturity.
  • Others argue that Rudin's text covers much of what is in Spivak's book but with greater rigor, leading to the question of whether Spivak is essential.
  • One participant recommends starting with Rudin until reaching the multivariable sections and then supplementing with Spivak.
  • A question is raised about the distinction between "baby Rudin" and the original Rudin text, indicating a need for clarification on the differences in content and rigor.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether to read Spivak before or after Rudin, and multiple competing views remain regarding the necessity of Spivak's text in relation to Rudin's.

Contextual Notes

There are varying assumptions about the level of prior knowledge in analysis required to approach these texts, as well as differing opinions on the rigor and depth of Spivak's treatment compared to Rudin's.

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 necessary?

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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What's your background in analysis?
 
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.
 
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.
 
Whats baby Rudin and the difference it has with Rudin?
 

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