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REAL & COMPLEX ANALYSIS 3E (5P) (Int'l Ed) (McGraw-Hill International Editions: Mathematics Series) Paperback – 16 Mar 1987
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The book is divided in the two main parts, real and complex analysis. But in addition, it contains a good amount of functional and harmonic analysis; and a little operator theory.
I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.
What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.
Some of the exercises are notoriously hard, but I think that is good: It simply means that they serve as work-projects when the students use the book. And this approach probably is more pedagogical as well.
After surviving some of the hard exercises in Rudin's Real and Complex, I think we learn things that stay with us for life; you will be "marked for life!"
Review by Palle Jorgensen, December 2004.
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