Missing from Spivak's Calc: Rudin & Pugh Books

  • Thread starter Thinker301
  • Start date
  • Tags
    Books
In summary, the conversation suggests that reading and working through Rudin's PMA or Real Mathematical Analysis by Pugh will cover everything in Spivak's Calculus. However, if the individual is studying real analysis on their own without prior experience in proofs, none of the mentioned books are recommended for self-study. Instead, it is suggested to use the book "Numbers and Functions: Steps to Analysis" which is designed for self-study and provides a curated sequence of problems with solutions.
  • #1
Thinker301
65
0
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!
 
  • #3
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 .
 
Last edited by a moderator:

Related to Missing from Spivak's Calc: Rudin & Pugh Books

What is the difference between Spivak's Calculus and Rudin & Pugh books?

Spivak's Calculus is a well-known and widely used textbook for introductory calculus. It covers topics such as limits, derivatives, and integrals. Rudin & Pugh books, on the other hand, are more advanced textbooks that cover real analysis, a more rigorous and theoretical approach to calculus.

Why are Rudin & Pugh books not included in Spivak's Calculus?

Spivak's Calculus is meant to be an introductory textbook for students who are just starting to learn calculus. As such, it does not cover the more advanced topics and theories found in Rudin & Pugh books. These books are typically used for upper-level undergraduate or graduate courses in mathematics.

Can Spivak's Calculus be used as a substitute for Rudin & Pugh books?

No, Spivak's Calculus is not meant to be a substitute for Rudin & Pugh books. While it may cover some similar topics, the level of rigor and depth in Rudin & Pugh books is significantly higher. It is important to use the appropriate textbook for the level of mathematics being studied.

Are Rudin & Pugh books necessary for understanding calculus?

No, Rudin & Pugh books are not necessary for understanding calculus. While they may provide a more rigorous and theoretical approach, Spivak's Calculus and other introductory textbooks are sufficient for understanding the fundamental concepts and applications of calculus.

Are there any advantages to using Rudin & Pugh books over other calculus textbooks?

One advantage of using Rudin & Pugh books is that they provide a deeper understanding of the theoretical foundations of calculus. This can be beneficial for students pursuing advanced studies in mathematics or related fields. Additionally, these books often have a more concise and rigorous presentation, making them a good choice for those who prefer a more challenging and in-depth approach.

Similar threads

  • Science and Math Textbooks
Replies
2
Views
2K
  • Science and Math Textbooks
Replies
1
Views
2K
  • Science and Math Textbooks
Replies
12
Views
6K
  • Science and Math Textbooks
Replies
12
Views
6K
  • Science and Math Textbooks
Replies
4
Views
3K
  • Science and Math Textbooks
Replies
1
Views
1K
  • Science and Math Textbooks
Replies
6
Views
2K
  • Science and Math Textbooks
Replies
5
Views
3K
  • Science and Math Textbooks
Replies
1
Views
2K
  • Science and Math Textbooks
Replies
2
Views
2K
Back
Top