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I have studied Spivak's Calculus and Tao's Analysis 1(Not perfectly but glimpsed once) with my own(self-study). After comparing Tao's and other analysis books, I found that my understanding of analysis is very poor, so I decided to study analysis more rigorously with my own.

I liked the style of Spivak's Calculus. Because I can solve quite lot exercises using techniques which was used to prove some theorems on the text. And almost every pro lems gave me hints to solve. plus sometimes it dealt with some interesting topic such as Newton's derivation of the planetary motion and the irrationality of Pi. These made me motivated and keep going with my own. and solutions are availiable so I could check my proof giving myself feedback.

I think that the approachability and solution-availabilty, what extent the book covers are important factors when I choose the book to study, since I'm self-taught.

I searched a few recommendation and make a list of books.

Here's the list: 1. Strichartz's "The way of Analysis", I heard though it is very wordy, but good for self study analysis. But solutions are not completely available, it's only available to some parts.

  1. Zorich's "Mathematical Analysis vol1,2", I'm fascinated with the fact that this starts with very concrete concepts and generalize them wonderfully and deal with broad areas. But I've heard many problems on the exercises are quite difficult and solutions are not available.

  2. Rudin's "Principle of Mathematical Analysis" It's classic, concise. Everyone recommended it, but I doubt whether I could deal with it or not, since the problems looks hard for me and so concise that makes me frustrated. But there are many supplement notes and solutions.

  3. Etc. (Abbot's, Ross', Bartle's, Pugh's, Apostol's, Marsden's, Wade's, ……)

Which is the best book for me based on this condition? Could you recommend it? If you did, I'll be very thankful!

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  • $\begingroup$ Did you check the books Spivak mentions in his bibliography? Spivak acknowledges the importance of Hardy's classic A Course of Pure Mathematics honestly and you should get hold of this wonderful book. $\endgroup$ – Paramanand Singh Jun 4 '17 at 17:32
  • $\begingroup$ @Paramanand Singh I didn't l. But I heard Hardy's book is not easy for beginners, isn't it? $\endgroup$ – Seung Yong Yeo Jun 4 '17 at 22:15
  • $\begingroup$ Hardy's book is especially for those who are doing self study. It is very well written with very good explanations, examples and exercises. Most of my reputation points on this website are only because of that book. It does demand effort form the readers and you need to read the book completely without missing anything. $\endgroup$ – Paramanand Singh Jun 5 '17 at 2:44
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I don't know about the best book for you but Rudin's "Principles of Mathematical Analysis" is regarded as an excellent reference. I suggest that you try it out and if you find it too hard, then you could consider switching to Apostol's "Mathematical Analysis". Hope that helps.

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