I'm sure his has been asked before but can someone recommend a real analysis text book with lots of worked examples practice questions and solutions? The sort of textbooks I've used and really benefited from before are Ken Stroud and Kuldeep Singh who use lots of questions which gradually increase in difficulty as the text progresses through the material. Any suggestions would be gratefully appreciated
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- $\begingroup$ Your request is probably more broad than you think. However, I'd like to recommend the lectures series in analysis by Elias Stein and Rami Shakarchi. It's a pretty large collection of future-practitioner friendly books, covering a pretty wide range of subjects and applications. $\endgroup$Callus - Reinstate Monica– Callus - Reinstate Monica2014-05-12 04:20:05 +00:00Commented May 12, 2014 at 4:20
- $\begingroup$ Does this answer your question? Good book for self study of a First Course in Real Analysis $\endgroup$user1124753– user11247532023-05-04 00:37:22 +00:00Commented May 4, 2023 at 0:37
- $\begingroup$ Does this answer your question? What books introduce the concepts of proof, using real analysis? $\endgroup$user1110341– user11103412023-10-09 02:12:09 +00:00Commented Oct 9, 2023 at 2:12
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2 Answers
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If you need a lot of worked problems in analysis, consider the three volumes of Problems in Mathematical Analysis by W. J. Kaczor and M. T. Nowak. About 100 pages of every volume are devoted to problems, and 300 pages to solutions.
What about regular textbooks: Charles C. Pugh's Real Mathematical Analysis is highly praised for its problems (contains about 600 problems). If you already have had one year of analysis, you might consider Folland's Real Analysis, it is quite challenging but readable.
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Try these monographs aimed at undergraduate first-timers (to real analysis).
| Title | Author | Publication Year |
|---|---|---|
| How to Think about Analysis | Lara Alcock | 2014 |
| Writing Proofs in Analysis | Jonathan M. Kane | 2016 |
| An Introduction to Proof through Real Analysis | Daniel J. Madden, Jason A. Aubrey | 2017 |
| The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs | Raffi Grinberg | 2017 |
| Real Analysis With Proof Strategies | Daniel W. Cunningham | 2021 |
| Analysis with an Introduction to Proof, 6th ed. | Steven R. Lay, Richard G. Ligo | 2023 |
