mathematical analysis books for self study

Question

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.

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. — user642796, Jun 16 '13 at 16:11

score 1 · Answer 1 · answered Jun 16 '13 at 15:45

1

A first Course in Real Analysis by Sterling K Berberian

answered Jun 16 '13 at 15:45

Myshkin

36,898
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168
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score 1 · Answer 2 · answered Jun 16 '13 at 15:54

1

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.

answered Jun 16 '13 at 15:54

Ted Shifrin

125,228

score 1 · Answer 3 · answered Jun 16 '13 at 15:55

1

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

answered Jun 16 '13 at 15:55

score 1 · Answer 4 · answered Jun 16 '13 at 15:59

1

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

answered Jun 16 '13 at 15:59

Mohan

15,494

score 0 · Answer 5 · answered Jun 16 '13 at 16:00

0

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

answered Jun 16 '13 at 16:00

Rusty

2,958

score 0 · Answer 6 · answered Jun 16 '13 at 16:08

0

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.

answered Jun 16 '13 at 16:08

goonfiend

2,884

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

mathematical analysis books for self study

6 Answers6