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

  1. Feb 17, 2016 #1
    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?
     
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  3. Feb 17, 2016 #2

    micromass

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    What does this mean? And why does Rudin not have good proofs?
     
  4. Feb 18, 2016 #3
    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.
     
  5. Feb 23, 2016 #4
    I found Bourbaki's series to be really concise! I love it!

    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!
     
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