What comes first, spivaks manifolds or rudins pma?

[khemix]

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.

 

[dx]

What's your background in analysis?

 

[ytoruno]

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.

 

[ytoruno]

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.

 

[razored]

Whats baby Rudin and the difference it has with Rudin?