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Real Analysis (3rd Edition)

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Title: Real Analysis (3rd Edition)
by H.L. Royden
ISBN: 0-02-404151-3
Publisher: Prentice Hall
Pub. Date: 01 May, 1988
Format: Hardcover
Volumes: 1
List Price(USD): $102.67
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Average Customer Rating: 3.69 (16 reviews)

Customer Reviews

Rating: 3
Summary: Excellent Reference, Poor Introduction
Comment: This book is an excellent reference for analysis. The proofs are modern and generally excellent, and the treatment of measure and integration is very advanced. However, I would not recommend this book as an introduction; not very much motivation or intuition is provided for the material, and the double-coverage of abstract and real cases is awkward. Recommended substitute: Walter Rudin, Real and Complex Analysis, and Kolmogorov, Introductory Real Analysis.

Rating: 4
Summary: Excellent Moore Method Intro Text
Comment: I used this text as senior undergraduate in an introductory course to real variables. The course was structured as a sort of modified RL Moore method class: there were very few lectures, and we (the students) could only use theorems and propositions presented in the text if we had gone to the board and presented a valid proof for each. As such, most of the students learned the fundamentals very well. This in turn made my first graduate course in real variables much easier.

The biggest downside however is that most graduate students don't have the time needed to dedicate to the various problems in this text, which is why Royden is probably not the best choice for a first year graduate text. Instead I would recommend Bartle's Elements of Integration and Lebesgue Measure as a first year grad text on the subject. It was disappointing to use Bartle and discover that so many of the problems in Royden, which I had spent countless hours attempting to prove, had been completely worked out in Elements of Integration.

In short, Royden makes you work for many (most?) important results, and in the long run this makes for a much stronger understanding of the material- if you have the time to devote to it.

Rating: 5
Summary: this book is just plain good.
Comment: I began as a graduate student in applied maths less than a year ago; all of the students that I spoke with prior to that said that real analysis with rudin's book was their worse & hardest class..
So when I walked into MTH 5111 Real Variables I thought oh *&^% what am I in for?? but then I picked up the Royden book and I understood the way he was presenting the materail.. the book is very stright to the point + leaves channelgning problems to the HW sets but the autor clearly outlines. I have learned more from this book and course than any other...

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