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I have studied calculus and a bit of linear algebra. And now, I'm finding a book about analysis, which I can self-study. Can anyone recommend me a good analysis book which has many examples, and is compact?

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  • Mathematical Analysis by Apostol is great. Depending on your background with proofs, you may want to jump right to Baby Rudin, Principles of Mathematical Analysis. Alternatively, you could read through Rudin and supplement with Apostle or other books where Rudin is a bit terse. – John P. Apr 19 '20 at 01:47
  • I recommend you " Introduction to Real Analysis" by Robert G. Bartle & Donald R. Sherbert. I used this book some year ago, it is my favorite. Another book is " Calculus, Volume I: One-Variable Calculus, with an Introduction to Linear Algebra" by Tom M. Apostol. Edit You can find those books here: http://gen.lib.rus.ec/search.php – tajiri_numero_1 Apr 19 '20 at 01:47
  • It depends on your experience and ability. Spivak's book is highly recommended. Baby Rudin is a piece of beauty, but I don't think it's ideal for self-study. I am very experienced in analysis, and I just recently started working through Baby Rudin to refresh. Some of the problems trip me up in ways most analysis books don't. I'm enjoying it though because I have background. – ProfOak Apr 19 '20 at 01:48
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    Does this answer your question? Good book for self study of a First Course in Real Analysis See also Good First Course in real analysis book for self study and (Self-study Real analysis Tao or Rudin?)[https://math.stackexchange.com/q/373401/70305] – Pedro Apr 19 '20 at 01:50
  • I don’t care for Apostol, but that’s largely a matter of taste. Baby Rudin is very efficiently organized, but it is not a good book for self-study. I consider Bartle’s The Elements of Real Analysis, 2nd ed., significantly better than Bartle & Sherbert. And depending on your current familiarity with proof-oriented math, all of these may be heavy going. – Brian M. Scott Apr 19 '20 at 02:02

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You should definitely try T.Tao's Real Analysis I then Analysis II. It consists of nice exercises and the terminologies are quite simple, and he also gives Remarks at the end of propositions or Theorems which might be a bit too rigorous for new readers to understand fully and thus clears ambiguities.

There's Baby Rudin too, but i would not recommedd it as the first book though, it can be read later after Tao's book