Better Analysis Book

[mruncleramos]

Which is the more thorough more rigorous book? Rudin's Principles of Mathematical Analysis, or Lang's Undergraduate Analysis?

[fourier jr]

I haven't really looked at Lang's book, but I think Rudin's is generally accepted as the most rigourous of the rigourous. I liked Pfaffenberger/Johnsonbaugh's better though. It's fairly rigourous and is better to learn from, imo. It also has a much better treatment of Fourier series & inner-product spaces than Rudin's. Rudin's only sort of tells you how to find the Fourier coefficients while Pfaffenberger's gives Fourier series 'with all the plumbing' (with all the linear algebra & inner product spaces stuff that goes with it).

[mathwonk]

I have read many of Langs book, but not this one, and taught from Rudin. It is true, Rudin is considered highly rigorous but often this is not intended as a compliment. Lang's books in general are both rigorous and insightful. I.e. Lang makes things look easy whereas Rudin makes them seem hard. I greatly prefer anything Lang writes to Rudin in general. But I suggest Apostol's Mathematical Analysis as a possibility. Certainly his Calculus is my favorite rigorous introduction to calc.