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Rating: 
Summary: 6 star
Review: Great book, u will learn a lot, including basic topology, multivariable analysis beautiful and elegant proofs that are pricise and simple, easy to understand. Taiwan is independent
Rating:
Summary: Would be better if solutions are provided
Review: Great textbook, great afterchapter exercises! However, since the exercises are a bit challenging, it would have been better if solutions or hints for solutions are provided. By the way, I would be grateful if anyone could tell me where I can find solutions for the exercises.
Rating:
Summary: A thorough text for an advance undergraduate
Review: Having taken Pugh's honors analysis course, in which he used this book, I can strongly reccommend it to any student interested in the subject of analysis, especially students seeking to learn more than the average introductory real analysis book contains. Pugh's book contains advanced theorems and topics not often found in undergraduate level texts. Additionally, the problems are well thought out and tend to be of a high level of difficulty.
Rating:
Summary: Very good exposition, great problems
Review: Real analysis is a genre with an established classic (Rudin) and a plethora of available books and resources. Unfortunately, most analysis books cost a great deal of money so the average reader will only purchase one or two texts. In evaluating which book(s) to purchase two questions should be asked:1.) Why purchase this book rather than the classic of the genre? 2.) Is this book appropriate for me? So why buy this book rather than Rudin? It has great exposition (as does Rudin), very well chosen problems (as does Rudin), but Pugh manages to improve on the standard by supplementing his written explanations with diagrams and pictures that Rudin mostly lacks. Additonally, the price stands at something less than half the cost of Rudin's book. Who is this book appropriate for? This text delves into the topological underpinnings of analysis. It is not an "analysis-lite" textbook a la Ken Ross's Elementary Analysis. It is a rigorous treatment of the subject, and it has a comprehensive feel to it, covering topics like Lebesgue measure and integration, and multivariable analysis in addition to the normal topics one would expect. In short, it is appropriate for somebody who is seeking the challenges and rewards of a full treatment of what for many is a difficult subject. It is a very good book that does not shy away from difficult material that no amount of explanation or good writing will make easy to learn, but of all the analysis books I've seen, this comes the closest.
Rating:
Summary: excellent
Review: This is one of the best books on introductory real analysis that I have looked at. Before I found this book, I have been reading another work on real analysis which was also very good, but was far less comprehensive. Not only does this book present a precise exposition of concepts and theorems, it also gives illustrations to better explain the ideas and plenty of excercises at the end of each chapter. For example, the author does not only say what a "covering" means, but he gives an illustration of it. The style of exposition is fine and relaxed, but the rigor of presentation of theorems and proofs is not in the least compromised. I would think that this book will be of enormous help to anyone trying to make a transition from concrete to more abstract mathematical reasoning.
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