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I have shortlisted two books irrespective of their price:

1)Real Mathematical Analysis by Charles Chapman Pugh and 2) Principles of Mathematical Analysis by Walter Rudin .I wish to self study analysis(I am in high school) and I was wondering which book is better.Any insight into this is appreciated.

UPDATE: I shall accept an answer soon.New opinions are welcome.

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marked as duplicate by Davide Giraudo, user127.0.0.1, Newb, Hagen von Eitzen, Your Ad Here Feb 19 at 18:58

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As stated on mathoverflow, I have learnt calculus from Apostol's Calculus volume 1. –  Squid Sep 10 '12 at 9:23

2 Answers 2

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Pugh: his exposition is fresh and aided with instructive pictures. But the reason I recommend it is for its broad selection of problems. There's the routine and easy kind to illustrate the concepts, but there's also plenty of the entertaining and challenging kind for the courageous. I'm fond of his topology chapter, I think it brings out the subject to life. Knot theory makes an appearance in both the chapter and the problems, and if you're at all interested in immersing yourself early in some advanced concepts, then Pugh would be the way to go.

Make sure you do lots of problems. That's really the only way around it.

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You are definitely ambitious! Both books are rather hard for a beginner. I learned mathematical analysis on Rudin's book, since I am older than Pugh's book.

I'd suggest to read Pugh's first, which is probably less pedantic. However, I still judge Baby Rudin a better book than Pugh's.

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Agreed. Rudin's book is a great book, but (because it is so terse) it is best studied with an instructor rather than on your own. –  GEdgar Sep 10 '12 at 13:47

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