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I am looking for mathematical analysis books whose explanation is polite. If they has many familiar example, I will be happier.

I am familiar with set theory, group theory, elementary theory, but am not familiar with analysis at all.

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marked as duplicate by amWhy, Danny Cheuk, Julian Kuelshammer, Myself, O.L. Jun 16 '13 at 16:11

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Have you covered single and multi-variable calculus? Also: "polite" means "courteous", which is something I hope all authors strive to be - perhaps you mean something like books whose explanations are "gentle" or "easy to follow"? –  amWhy Jun 16 '13 at 15:39
    
What do you mean by "elementary theory"? Also, do you have any relationship with the authors of these previous questions? 1, 2, 3, 4, 5, 6. –  Arthur Fischer Jun 16 '13 at 16:11

6 Answers 6

A first Course in Real Analysis by Sterling K Berberian

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You don't indicate anything about your interests and goals. A very accessible and concrete book, focusing almost entirely on $\mathbb R$, is Arthur Mattuck's Introduction to Analysis.

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Terence Tao - Analysis I Really great and easy understandable book !

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Understanding Analysis is a nice book for beginners. The book has many interesting examples and the material is nicely motivated.

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Tom A. Apostol Calculus part I and II both are good. Also authour has few more books about Analysis

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My favourite book for a first course in (real) analysis is Walter Rudin's Principles of Mathematical Analysis by far. The exposition is very clean and gentle.

For the complex side of things I quite like Ahlfors but this is not to everyone's taste.

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Quite, quite far from gentle. And not a single picture. I've taught students out of this book and most of them definitely need a dedicated teacher. –  Ted Shifrin Jun 16 '13 at 16:43

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