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Came across an Analysis post on this board while searching the net

  1. Jan 17, 2013 #1
    Hi All,

    I was searching for Analysis course that typically follows Spivak's Calculus.

    While searching the Net came across this post below and have couple questions if you dont mind:

    My questions:

    1. "Rigorous Advanced Calculus (Loomis and Sternberg)". Is that a single book or two different books by different authors? Couldnt find it on Amazon, but found Advanced Calculus by Loomis. What is the relation of the second book to the suggested one? Are they interchangeable? If not, what's the best alternative?

    2. "introductory real and complex analysis via metric spaces as in Mackey's complex analysis book". I couldnt find it anywhere. What would be the best alternative?

    3. "general analysis as in Royden". Found Real Analysis (4th Edition) by
    Halsey Royden, Patrick Fitzpatrick
    . Are these the same books? Or are they interchangeable? If not, what would be the modern alternative to the suggested text?

    4. "(big) Rudin, or Halmos and Ahlfors". I apologize for my ignorance, but could someone, please, elaborate on this one? Couldnt locate the book written by both Halmos and Ahlfors together.

    Thank You.
  2. jcsd
  3. Jan 22, 2013 #2


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    Yes, the book at your link is the right one. The title is Advanced Calculus, and it is a (very) rigorous book. It is out of print, and I see that the used copies on Amazon are obscenely priced. Fortunately, Sternberg has made it available for free in PDF form at his web site: http://www.math.harvard.edu/~shlomo/

    Yes, that's the right book. The earlier editions had Royden as the sole author, but he died in the 1990s. The 4th edition was updated by another author, Fitzpatrick. Be careful about the new edition: there are people complaining even in the past few days that the text contains Latex errors:

    This book is clearly damaged. The publisher is selling copies of the book that cannot be used. References to equations, theorems, references, are often numbered with two question marks (??) rather than giving the correct number. This is an elementary error. The book was typeset in Latex, and it wasn't compiled correctly. Most Latex users are familiar with this error, and know how to fix it. Apparently, this publisher is not.

    Big Rudin: https://www.amazon.com/Complex-Analysis-International-Applied-Mathematics/dp/0070542341
    Halmos: https://www.amazon.com/Measure-Theory-Graduate-Texts-Mathematics/dp/0387900888
    Ahlfors: https://www.amazon.com/Complex-Analysis-Lars-Ahlfors/dp/0070006571

    Big Rudin covers both real and complex analysis. Halmos is real analysis, Ahlfors is complex analysis. So mathwonk presumably meant, get either Big Rudin, or get both Halmos and Ahlfors.
    Last edited by a moderator: May 6, 2017
  4. Jan 23, 2013 #3
    Awesome! I appreciate you took your time to clarify all this. Thank You, Jbunniii.

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