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I'm currently an undergrad student in pure maths and i'm at the third year of college. I was trying to study analysis (cause i'm really bad at it) and I noticed that i'm really into the "Enciclopedia" kind of books, like Zorich's ones.

Do you have any reccomendations on that matter? I don't like Zorich's books because of the way he treats limits with thos approximations that I really think make the text way more hard to follow.

EDIT: someone asked me about examples on the way that Zorich treats approximations, and it is not that difficult, it is just a notation convention that i really do not like. He defines $$\Delta(\hat{x}) = |x - \hat{x}|$$ $$\delta(\hat{x}) = \Delta(\hat{x})/|\hat{x}|$$ where $\hat{x}$ is an approximate value of $x$. The he procedes to prove some inequalities and tricks with this stuff to use in proofs about the continuity of some operations.

Lucas Giraldi
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    Terence Tao's "Analysis I" and "Analysis II" are both masterpieces, I highly recommend them. – lorenzo Aug 26 '21 at 20:42
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    I know, this is not what you want, but have a look at the recommendations here. Of course, Rudin is there, too. This can be compared with Zorich, see this post. – Dietrich Burde Aug 26 '21 at 20:53
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    If you like "encylopedic" books, then Dieudonne has a 8/10 volume series on analysis; though for the basics, volume 1 (which is a very nice book) alone should keep you busy for quite some time. Similarly, Amann and Escher have a 3-volume series of analysis books. Of course, I'm not saying you should study everything page to page of every single volume... just giving you ideas of what's out there. – peek-a-boo Aug 26 '21 at 20:54
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    Dieudonné wrote a book, Infinitesimal Calculus, mainly on complex analysis and differential equations, full of what could be called "hard" work, with inequalities and estimates. He wrote that this kind of training was indispensable before moving on to more abstract material such as that in Foundations of Modern Analysis, which is the first volume of his nine-volume treatise. – Anonymous Aug 26 '21 at 21:33
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    Could you give an example of what you mean when you mention the way Zorich treats limits using approximations? – Anonymous Aug 26 '21 at 22:16
  • @Anonymous edited – Lucas Giraldi Aug 27 '21 at 22:23
  • Thanks a lot for the suggestions guys, I alredy started in Amann and Escher books, i found them pretty interesting and loved the algebra background that they give (i do not needed it, but i think that is pretty cool causa I think algebra helps a lot in learning analysis) – Lucas Giraldi Aug 27 '21 at 22:25
  • @peek-a-boo I am looking at starting Amann-Escher and am trying to gather some intel. It is nice to see you here too! I am worried that, without a solution manual (I self-study as is probably clear from the various questions of mine which you answer), I could be left in trouble with this. If you have any opinion or suggestion here I would greatly appreciate it! To OP -- if you have any suggestions after having worked through AE, I would greatly appreciate it too. – EE18 Sep 07 '23 at 22:03

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