Customer Reviews
It's really not that good - By: Snowy White, 12 Nov 2008 
I can only concur with the reviewers who point out how bad this is to actuallly sit down & read. I had it recommended as a second text on real analysis, primarily for the extension into higher dimensions. Coming from the impossibly good Spivak ("Calculus") as my introductory text, Rudin was a shock to the system, for a number of reasons:
Firstly, the overalll feel is of a cheaply made book. The spine on my copy cracked within a few months & pages became unlodged. Maybe the quality is better nowadays, but bear this in mind. This is the same edition (mine was the 15th printing, dated 1989). In comparison, my Spivak still looks as good as new, & it's been read a heck of a lot more!
Second, the print is faint & and the fonts appear thin, which is a constant irritation that drains mental energy unnecessarily. Also, the notation is difficult because the italicized letters used to represent some objects are so illegible as to make a mental note impossible ('must remember such-and-such is represented by squiggle'). This again distracts you from the mathematics itself.
Lastly, the whole approach is cold & distant. I know this is what most professional mathematicians seem to approve of (can't think why!!) , but I personallly don't get it. Mathematics has a hard enough time recruiting & maintaining the interest of students (a high proportion of students on my course - alll with 3 A's at A-level when such a feat required intelligence - virtuallly gave up in the second year, largely through having to refer to books like this), without turning them away with bad teaching. Yes, rigour is absolutely essential, but without providing motivation or at the very least some kind of geometric intuition (a picture is worth...), a text like this seems to lose half its impact. I remember reading Spivak with pleasure, almost without realizing I was studying pure gold that distilled the genius of the some of the finest mathematicians in history.
Lastly, the price. Almost twenty years on, my copy still has its price sticker: £10.95 including a very durable removable plastic jacket. Book inflation for the intervening period is not 300%. For such a commonly cited text, this is a disgraceful ask of present students.
In summary, BUY WITH EXTREME CAUTION. Sadly, I don't know which text to recommend instead, but MOST undergraduates will regret spending valuable beer money on this book. I'd do a search on Amazon for some newer original books (the Springer series seem to be generallly more readable that most of the texts I had to suffer). I hope this review helps you in your search.
A start in math. - By: Palle E T Jorgensen, 22 Sep 2004 
I am a fan of Rudin's books. This one "Principles of Matheamtical Analysis" has served as a standard textbook in the first serious undergraduate course in analysis at lots of universities in the US, & around the world.
The book is divided in the three main parts, foundations, convergence, & integration. But in addition, it contains a good amount of Fourier series, approximation theory, & a little harmonic analysis.
I loved it when I was a student, & since then I have taught from it many times. It has stood the test of time over almost three decades, & it is still my favorite. I have to admit that it is not the favorite of everyone I know.
What I like is that it is concise, & that the material is systematicallly built up in a way that is both effective & exciting.
The exercises & just at the right level. They can be assigned in class, or students can work on them alone. I think that is good, & the exercises serve well as little work-projects. This approach to the subject is probably is more pedagogical as well.
I think students will learn things that stay with them for life.
Review by Pallle Jorgensen.
useful and pocket-sized - By: , 15 Oct 2001 
I was recommended this book for my maths degree & I can honestly say that it's reallly useful. A good broad overview of analysis, with lots of exercises to assist your understanding of unfamiliar concepts. Starting with basic notions of metric & building upon them, through algebraic systems, differentiation, integration, partial differentiation & finishing with a smalll chapter on the Lebesgue integral.
My only real gripe with this book was that it did not have enough operator theory in it. (I would recommend Simmons 'Intro to topology & modern analysis' (same series) or Kreyzig's 'Intro to functional analysis' (Wiley Classics) for operator theory.)
A great text if you know the contents - By: , 14 Dec 1999 Rudin wrote three texts on analysis, none of them is easy, they are widely used because professors like them for their "style". go for it if you know the contents already, or you are well gifted.
Use an easier analysis book first! - By: , 05 Sep 1999 
Please don't "learn it yourself" from rudin. I recommend books by Bryant, Stirling, & Eccles for the learning of analysis. Those are user friendly books with nice explainations. Only use Rudin once you have learned some analysis & proof. Moreover, the price is a joke. Rudin will be at your library so I recommend borrowing before buying. The other reviewers who gave it such bad reviews are probably mad because they didn't use these other user friendly books first & then switch to rudin. thank you.
