Missing from Spivak's Calc: Rudin & Pugh Books

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SUMMARY

Reading Rudin's "Principles of Mathematical Analysis" (PMA) or Pugh's "Real Mathematical Analysis" provides a comprehensive understanding of real analysis that covers the essential concepts found in Spivak's "Calculus." Engaging with Rudin's problems ensures that students will not miss critical insights from Spivak. However, for those without a background in proofs, these texts may not be ideal for self-study. Instead, "Numbers and Functions: Steps to Analysis" is recommended for self-learners due to its structured problem-solving approach.

PREREQUISITES
  • Understanding of real analysis concepts
  • Familiarity with mathematical proofs
  • Experience with calculus (Calc 1-3)
  • Ability to solve mathematical problems independently
NEXT STEPS
  • Explore "Numbers and Functions: Steps to Analysis" for self-study techniques
  • Practice problem-solving with Rudin's "Principles of Mathematical Analysis"
  • Review proof techniques in real analysis
  • Investigate additional resources for foundational proof skills
USEFUL FOR

Students of mathematics, particularly those transitioning from calculus to real analysis, and self-learners seeking structured problem-solving resources will benefit from this discussion.

Thinker301
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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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