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I am trying to decided which real analysis text book I should buy. I have the following in mind-

1)Walter Rudin's "Principles of Mathematical Analysis" 2)Charles Pugh's "Real Mathematical Analysis" 3)Richard Goldberg's "Methods of Real Analysis".

Please voice your opinion for and against each book.I have heard Rudin is terse but I don't know for sure.

Thanks for reading the question!

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4  
"terse" is an understatement. –  crf Dec 9 '12 at 8:56
    
@JasperLoy Every book seems to be brilliant,"elegant" and "beautiful" there. –  Richard Nash Dec 9 '12 at 9:06
    
See also here, here, here, and here‌​. My advice: get more than one book. –  Antonio Vargas Dec 9 '12 at 9:11

1 Answer 1

We can't really give a single recommendation. It depends so much 'where you are coming from' (as they say) -- i.e. what you know already, your current degree of 'mathematical maturity'. It also depends on the kind of text you find congenial (what someone finds helpfully discursive someone else will find too slow-moving, and so it goes). And even if we knew all that, so we knew the right ball-park to be looking in, many -- myself included -- would still warmly recommend not sticking to just one book. Seeing the same material presented in slightly different ways can be particularly helpful and illuminating.

Having said that, I do like Victor Bryant's Yet Another Introduction to Analysis, CUP. [I rather wanted to call my own intro logic book Yet Another Introduction to Formal Logic, but CUP didn't buy that title!]

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