Analysis Seeking a Rudin's PMA-level analysis book with abstract proofs

[bacte2013]

Dear Physics Forum personnel,

I recently got interested in the art of abstract proof, where the focus is writing the proof as general as possible rather than starting with a specific cases. Could anyone recommend an analysis book at the level of Rudin's PMA that treats the introductory analysis in an abstract level with abstract proof?

 

[micromass]

I recently got interested in the art of abstract proof, where the focus is writing the proof as general as possible rather than starting with a specific cases.

What does this mean? And why does Rudin not have good proofs?

 

[JonnyG]

Could anyone recommend an analysis book at the level of Rudin's PMA that treats the introductory analysis in an abstract level with abstract proof?

How about Rudin's PMA?...If you don't want his book, check out Pugh's "Real mathematical analysis". But if you haven't had any exposure to proofs before, I would suggest working through a book dedicated to single variable real analysis. Like Spivak, Apostol, or Courant.

 

[bacte2013]

What does this mean? And why does Rudin not have good proofs?

I found Bourbaki's series to be really concise! I love it!

How about Rudin's PMA?...If you don't want his book, check out Pugh's "Real mathematical analysis". But if you haven't had any exposure to proofs before, I would suggest working through a book dedicated to single variable real analysis. Like Spivak, Apostol, or Courant.

I already read Rudin's PMA several times. I was trying to find more concise book that presents general proof, rather than starting with specific cases like the concept of k-cell from Rudin. I actually found that Bourbaki's series to be really good!