He spends a lot of time to teach you the 'rough work' that analysts do to get those epsilon-delta proofs. Also, as an alternative to Rudin you might want to take a look at Pugh's "Real Mathematical Analysis" Jan 15, 2012 #7 Jorriss. This is great. 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. 1,082 25. 87, 384 A.2d at 1240. I don't know where Anonymous was trained,but clearly came from a better system then most students come from. Pugh v. Holmes, 253 Pa.Super. He uses pictures to help readers develop a more intuitive understanding of analysis, which is incredibly helpful for beginners. 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. "Materiality of the breach is a question of fact to be decided by the trier of fact on a case-by-case basis." It's exactly the right level of abstraction. In contrast, Pugh's book is delightfully lucid, neither too concise nor overly wordy. Pugh's exposition is a bit more relaxed, conversational, and informal (but without any dumbing down). 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. I have not read Abbott's book, but I can certainly recommend Ross's book. 1 year ago # QUOTE 0 Good 0 No Good! 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 … $\endgroup$ – Mathemagician1234 Dec 2 '14 at 6:58 $\begingroup$ A great deal of point set theory is covered in Pugh and done more clearly then in Rudin. 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. As for it being "chatty"-well,ANY book compared to Rudin is going to be chatty!Apostol is FAR more chatty! I think Pugh also contains more problems, and certainly more hard problems. I preferred Pugh's Real Mathematical Analysis for personal study and went to Rudin later to fill in gaps and get a different perspective. Which is better written for introspection? The writing is clear and quirky, and there are lots of interesting and hard problems. I had attempted to study real analysis through baby Rudin, but found it too terse. But the multivariable chapters are weak. 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. 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