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12 of 12 people found the following review helpful
5.0 out of 5 stars A start in math.
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, and around the world.
The book is divided in the three main parts, foundations, convergence, and integration. But in addition, it contains a good amount of Fourier...
Published on 21 Sep 2004 by Palle E T Jorgensen

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13 of 13 people found the following review helpful
3.0 out of 5 stars Poor introduction, Outstanding reference
I was terrified by this text my freshman year in college. Unfortunately, this book was the only required book for the class. The main difficulty is that the book resembles a magnificent outline of the material more than a text. The shortest, most elegant proof of anything is invariably choosen and there is little motivation given for the material. Thus, I found...
Published on 21 July 1999


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12 of 12 people found the following review helpful
5.0 out of 5 stars A start in math., 21 Sep 2004
By 
Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(REAL NAME)   
This review is from: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Hardcover)
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, and around the world.
The book is divided in the three main parts, foundations, convergence, and integration. But in addition, it contains a good amount of Fourier series, approximation theory, and a little harmonic analysis.
I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and 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, and that the material is systematically built up in a way that is both effective and exciting.
The exercises and just at the right level. They can be assigned in class, or students can work on them alone. I think that is good, and 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 Palle Jorgensen.
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13 of 13 people found the following review helpful
3.0 out of 5 stars Poor introduction, Outstanding reference, 21 July 1999
By A Customer
This review is from: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Hardcover)
I was terrified by this text my freshman year in college. Unfortunately, this book was the only required book for the class. The main difficulty is that the book resembles a magnificent outline of the material more than a text. The shortest, most elegant proof of anything is invariably choosen and there is little motivation given for the material. Thus, I found this book to be difficult to use to learn how to do mathematics. On the other side, if you know the basic ideas of analysis, then this book is a remarkable, clear, and elegant place to review and extend your knowledge. I therefore would HIGHLY recommend it as a companian text for an analysis course or as a reference. My rating therefore is an average: as an introduction to analysis by itself, it rates one star; as a supplement to another text, as a review text, or as a reference, it clearly rates five stars.
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5 of 5 people found the following review helpful
5.0 out of 5 stars A true classic, one that everyone should study., 4 Sep 1999
By A Customer
This review is from: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Hardcover)
For years, Dr. Rudin's book has been a standard introductory analysis text because of its wonderful, elegant exposition. It is not an easy book. It was never intended to be an easy book. But those who complain that the book lacks pictures are missing the point. The point of the book is to LEARN analysis. Rudin's book is excellent for this: you have to understand the theorems, definitions, and proofs, otherwise it's nonsense. If one takes the time to understand how all the statements follow from each other, then one will have truly learned analysis, and that is really the point.
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13 of 14 people found the following review helpful
3.0 out of 5 stars Use an easier analysis book first!, 5 Sep 1999
By A Customer
This review is from: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Hardcover)
Please don't "learn it yourself" from rudin. I recommend books by Bryant, Stirling, and Eccles for the learning of analysis. Those are user friendly books with nice explainations. Only use Rudin once you have learned some analysis and 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 and then switch to rudin. thank you.
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4 of 4 people found the following review helpful
5.0 out of 5 stars the Gita of elementary mathematical analysis, 1 Jan 1999
By A Customer
This review is from: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Hardcover)
this is the book which introduced me to "real" mathematics.i started reading it when i was in the second year of undergraduation and from that moment it became one my favourites (along with herstein's book on algebra and simmons' book on general topology). this book makes you think.(i still remember how that excercise "is there any nonempty perfect set with no rationals?" gave me sleepless nights!)
Dr.Rudin! thank you for giving me such a nice introduction of mathematical analysis.
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2 of 2 people found the following review helpful
3.0 out of 5 stars it is all there - but not easy to extract, 23 Dec 1998
By A Customer
This review is from: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Hardcover)
I used Rudin in my freshman analysis class as an undergraduate. I found it fairly difficult to read. It seems as though Rudin fine tuned his proofs mostly for brevity rather than clarity. For a young student of analysis I think it is better to see the ideas and structures rather than to be forced to decipher overly short proofs. On the other hand - I did learn the material pretty well. Still, I would not reccomend this as a first book and certainly not as a do-it-yourself.
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7 of 8 people found the following review helpful
4.0 out of 5 stars useful and pocket-sized, 15 Oct 2001
By A Customer
I was recommended this book for my maths degree and I can honestly say that it's really useful. A good broad overview of analysis, with lots of exercises to assist your understanding of unfamiliar concepts. Starting with basic notions of metric and building upon them, through algebraic systems, differentiation, integration, partial differentiation and finishing with a small 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 and modern analysis' (same series) or Kreyzig's 'Intro to functional analysis' (Wiley Classics) for operator theory.)
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1 of 1 people found the following review helpful
5.0 out of 5 stars Little in size, wide in scope, 5 July 2011
This book is popularly called the Little Rudin, compared to the Big Rudin which deals with more advanced topics in mathematical analysis. Thought as a textbook for an undergraduate course, it likely spans two years in a student's career, introducing to all the basic topics of univariate and multivariate calculus, together with complex analysis and formal power series, and even more specialized topics such as Euler's gamma function. The text is always clear and the proof are well constructed; some topics are put in the exercises sections, which forces the reader to actually go through them, a choice which I cannot object to. This book should have a place on the bookshelf of everyone who holds mathematics as a strong interest.
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5 of 6 people found the following review helpful
2.0 out of 5 stars It's really not that good, 12 Nov 2008
I can only concur with the reviewers who point out how bad this is to actually sit down and 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 overall feel is of a cheaply made book. The spine on my copy cracked within a few months and 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, and it's been read a heck of a lot more!

Second, the print is faint and 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 and distant. I know this is what most professional mathematicians seem to approve of (can't think why!!) , but I personally don't get it. Mathematics has a hard enough time recruiting and maintaining the interest of students (a high proportion of students on my course - all with 3 A's at A-level when such a feat required intelligence - virtually 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 generally more readable that most of the texts I had to suffer). I hope this review helps you in your search.
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3 of 4 people found the following review helpful
5.0 out of 5 stars It Will Teach You Mathematical Analysis!, 9 Mar 1999
By A Customer
This review is from: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Hardcover)
This book does not have a single picture or illustration in it. That is rare for a mathematical textbook (particularly analysis). You are forced, and rightly so, to form your own mental images of the mathematical objects defined and constructed within the text. This book is logical. Rudin lays it out in the definition, theorem, proof format, but does it in an amazing way. He leads you through a series of minor theorems and lemmas, you have no idea where he is going (unless you've already studied analysis) but then it all leads to a major result (for example the Heine-Borel Theorem in the Topology chapter) which is then used in the proof of many other theorems. Typical of how the book is written, he never tells you how important things like the Heine-Borel Theorem are, but the astute student soon figures it out. He does occassionally give a sentence or two of explanation or elucidation, but he mostly leaves that to the professor teaching the course. The exercises are excellent; tough and illuminating. Do as many as you can and you will learn a lot. If you can handle it, Rudin is the best way to learn Analysis (i.e., no BS). Good backround material before tackling Rudin would be Spivak's "Calculus" or Courant/John's "Introduction to Calculus and Analysis."
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