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 dont 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.