Missing from Spivak's Calc: Rudin & Pugh Books

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Reading Rudin's "Principles of Mathematical Analysis" (PMA) or Pugh's "Real Mathematical Analysis" provides a solid foundation in real analysis, potentially covering all essential concepts found in Spivak's "Calculus." Engaging deeply with Rudin's exercises can ensure a comprehensive understanding, making Spivak's content largely redundant. However, for those new to proofs or studying independently, these texts may not be the most effective choices. An alternative recommended for self-study is "Numbers and Functions: Steps to Analysis," which offers a structured approach with curated problems and solutions, although it is currently out of print.
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If I read and work through Rudin's PMA or Real Mathematical Analysis by Pugh, what in Spivak's Calculus am I missing? I have learned Calc 1-3 satisfactorily.

Thanks!
 
Hi Thinker301. I have gone through all of Rudin's PMA in a class and read through a good chunk of Spivak on my own time. I would say that if you read all of Rudin and do most of the problems, you won't be missing anything from Spivak. If you are studying real analysis by yourself and have no previous background in proofs, I don't think any of the books you listed are that good for self-study. Good luck :)!

On the other hand, the book "Numbers and Functions: Steps to Analysis" is pretty much designed for self-study. It is basically a curated sequence of problems with solutions provided. It's out of print, but used copies are available for ~$3 here
https://www.amazon.com/dp/0521457734/?tag=pfamazon01-20 .
 
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