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. JG89 said: Also, as an alternative to Rudin you might want to take a look at Pugh's "Real Mathematical Analysis" This. 87, 384 A.2d at 1240. Pugh's analysis book is incredible. I had attempted to study real analysis through baby Rudin, but found it too terse. It is written for beginners. 1,082 25. He spends a lot of time to teach you the 'rough work' that analysts do to get those epsilon-delta proofs. As for it being "chatty"-well,ANY book compared to Rudin is going to be chatty!Apostol is FAR more chatty! 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. $\endgroup$ – Mathemagician1234 Dec 2 '14 at 6:58 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. Pugh v. Holmes, 253 Pa.Super. WD73546 FILED: January 31, 2012 APPEAL FROM THE CIRCUIT COURT OF CALLAWAY COUNTY THE HONORABLE GARY M. OXENHANDLER, JUDGE BEFORE DIVISION FOUR: LISA WHITE HARDWICK, CHIEF JUDGE, PRESIDING, JAMES M. SMART AND ALOK AHUJA, JUDGES A jury convicted Charles Pugh … I think Pugh also contains more problems, and certainly more 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." I preferred Pugh's Real Mathematical Analysis for personal study and went to Rudin later to fill in gaps and get a different perspective. This is great. Economist a54f. Pugh has a real gift for knowing exactly how many words it takes to explain something-not one word more, not one word less. I don't know where Anonymous was trained,but clearly came from a better system then most students come from. $\begingroup$ A great deal of point set theory is covered in Pugh and done more clearly then in Rudin. It's exactly the right level of abstraction. 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. Pugh vs. Baby Rudin. In contrast, Pugh's book is delightfully lucid, neither too concise nor overly wordy. 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. In the Missouri Court of Appeals Western District STATE OF MISSOURI, v. CHARLES PUGH, ) Respondent, ) ) ) ) Appellant. ) I have not read Abbott's book, but I can certainly recommend Ross's book. 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