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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 don't 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 couldn't 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.
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 don't mind:
mathwonk said:In the old days, the progression was roughly: rigorous one variable (Spivak) calculus, Abstract algebra (Birkhoff and Maclane), rigorous advanced calculus (Loomis and Sternberg), introductory real and complex analysis via metric spaces as in Mackey's complex analysis book, general analysis as in Royden, (big) Rudin, or Halmos and Ahlfors, algebra as in Lang, and algebraic topology as in Spanier. Then you specialize.
In particular Spivak was written for a first semester freshman book.
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 couldn't 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.