Pugh's exposition is a bit more relaxed, conversational, and informal (but without any dumbing down). He uses pictures to help readers develop a more intuitive understanding of analysis, which is incredibly helpful for beginners. This is great. Rudin for personal study is pretty intense, though I think that you only really know analysis when you can handle Rudin's books on the subject. As for it being "chatty"-well,ANY book compared to Rudin is going to be chatty!Apostol is FAR more chatty! Pugh's analysis book is incredible. Also, as an alternative to Rudin you might want to take a look at Pugh's "Real Mathematical Analysis" Jan 15, 2012 #7 Jorriss. But the multivariable chapters are weak. $\begingroup$ A great deal of point set theory is covered in Pugh and done more clearly then in Rudin. JG89 said: Also, as an alternative to Rudin you might want to take a look at Pugh's "Real Mathematical Analysis" This. In contrast, Pugh's book is delightfully lucid, neither too concise nor overly wordy. The writing is clear and quirky, and there are lots of interesting and hard problems. It's exactly the right level of abstraction. Economist a54f. It's of comparable quality to Rudin in my opinion but much better suited for self-study, with a greater emphasis on conveying geometric intuition and a larger selection of hard problems. "Materiality of the breach is a question of fact to be decided by the trier of fact on a case-by-case basis." Chapter 9 (differentiation in … I preferred Pugh's Real Mathematical Analysis for personal study and went to Rudin later to fill in gaps and get a different perspective. Charles Pugh's Real Mathematical Analysis covers a wide range, starting from real numbers, topology, and basic 1D calculus, and then moving into multivariable calculus, function spaces, and Lebesgue measure/integration, all in a compact 450 pages. If you have proof writing experience and are willing to put in the effort, I think Pugh's book would be a good choice at this point. Which is better written for introspection? Economist 755e. It is written for beginners. I think Pugh also contains more problems, and certainly more hard problems. In the Missouri Court of Appeals Western District STATE OF MISSOURI, v. CHARLES PUGH, ) Respondent, ) ) ) ) Appellant. ) 1,082 25. Pugh has a real gift for knowing exactly how many words it takes to explain something-not one word more, not one word less. Pugh vs. Baby Rudin. Having learned and taught from Baby Rudin, I can say the first eight chapters are the clearest exposition I've seen of the material they cover. 1 year ago # QUOTE 0 Good 0 No Good! I don't know where Anonymous was trained,but clearly came from a better system then most students come from. I have not read Abbott's book, but I can certainly recommend Ross's book. 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