What comes first, spivaks manifolds or rudins pma?

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SUMMARY

The discussion centers on the optimal sequence for studying mathematical texts, specifically whether to read Spivak's "Calculus on Manifolds" before or after Rudin's "Principles of Mathematical Analysis" (often referred to as "Baby Rudin"). Participants suggest starting with Rudin to build foundational analysis skills, particularly if the reader has some background in single-variable analysis, such as Kenneth Ross' "Elementary Analysis." It is recommended to supplement Rudin with Spivak during the multivariable sections for a more comprehensive understanding.

PREREQUISITES
  • Familiarity with single-variable analysis, preferably through Kenneth Ross' "Elementary Analysis."
  • Understanding of basic proof techniques in mathematics.
  • Knowledge of multivariable calculus concepts.
  • Exposure to rigorous mathematical texts and their structure.
NEXT STEPS
  • Read Rudin's "Principles of Mathematical Analysis" to establish a strong foundation in analysis.
  • Supplement Rudin with Spivak's "Calculus on Manifolds" during the multivariable sections.
  • Explore advanced proof techniques to enhance mathematical maturity.
  • Investigate other analysis texts that provide rigorous treatments of multivariable calculus.
USEFUL FOR

Students and self-learners in mathematics, particularly those preparing for advanced analysis courses and seeking to develop a deeper understanding of mathematical proofs and concepts.

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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