I want to know good books I can use to learn real analysis by myself. I only have the upcoming Christmas holidays were I get 2-3 weeks off. Any suggestions?
2026-03-30 12:00:38.1774872038
Good texts to learn real analysis by myself
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Although I have never read them, I've heard many good words about
From various user reviews, it seems that these two books are super user-friendly and full of motivations, albeit a bit pricey. Abbott's book covers the contents of a typical first course, while Bryant's book is more elementary.
However, I would like to recommend Robert Ash's Real Variables with Basic Metric Space Topology. Ash was a great expositor. Many of his textbooks are well-written and I believe this one on analysis is among his best. While this book may not be as friendly as two books mentioned in the above, it is still gentler to beginners than most in the wild are. The presentation is lucid and its format and pacing are suitable for private study. Its coverage of topics is broader than Bryant's but slightly narrower than Abbott's. As a Dover publication, the book is cheap (its list price is only USD 11.95 at the time of writing).
My only complaint about this book is that its discussion on interchange of certain operations is not deep enough. In particular, interchange of order of summation in double sequences/series, differentiation under the integral sign and Fubini's theorem are left out. However, as a first introduction to real analysis, it is a competent piece of work.