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I am currently ploughing through Zorich's Analysis Volume I, after which I plan on reading the Volume II. Truth be told, I am truly enjoying this read. A little background: I am a first year math undergraduate.

However, in my college, students and some professors consider Baby Rudin a "sacred" book and often look down upon other text books, in that they consider them to be, for some abstract and inexplicable reason, inferior. What bothers me is that they even have this opinion about text-books they have never read.

None of my peers and professors have ever heard of Zorich's two volumes on Analysis. Hence, my following question:

My question is, once I am able to complete both the volumes of Zorich, including all problems, will I need to read Baby Rudin? In other words can Zorich, Volumes I and II, be considered to be a good and complete (except for a few topics) substitute for Baby Rudin with regards to material, depth and problems?

Similar questions have been asked on StackExchange, but the answers do not really address my primary concern: Can Rudin be COMPLETELY ignored, with regards to Undergraduate Real Analysis curriculum, and Zorich be chosen in its stead? Will my understanding of the subject at the Undergraduate level be in anyway inferior if I choose to stick to Zorich and certain other text-books and not read Baby Rudin with regards to Real Analysis? What do I stand to lose or gain if I choose Zorich over Rudin if I desire to supplement my undergraduate studies with Zorich and not Rudin? Lastly, if at all there's any serious shortcoming(s) in Zorich, for instance if you think there is a paucity of good problems in them, what can be done in order to address it/them?

The above may seem like several questions, but they really are just the one question: "Is Zorich good enough?"

Thank you everyone. Any insights with regards to the above would be much appreciated!

SK2
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    A similar question is here. It might be useful to you. – Elias Costa May 21 '22 at 11:23
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    The joke about Baby Rudin is that a summary of the book is the book itself. Idolizing that book just shows how the mathematical community has plenty of groupies with the mentality of silly teenagers. Ignore them. – Rodrigo de Azevedo May 21 '22 at 11:25
  • @EliasCosta: Thank you! But I have long read that post. The post says that Zorich is a good book, but nowhere does it state that is a good enough substitute for Rudin. In that what do I actually truly lose/gain by studying Zorich over Rudin, or vice-cersa. – SK2 May 21 '22 at 11:27
  • @RodrigodeAzevedo: Good one! But what do you think of the book -- Zorich -- in question? Personally speaking? – SK2 May 21 '22 at 16:55
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    @SK2 I never touched it. I have experience with Fomin & Baby Rudin, but forgot almost everything. I preferred Fomin's book. – Rodrigo de Azevedo May 21 '22 at 17:00
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    Just try Zorich if you can borrow it from the library. There is no need to worry. – user1551 May 22 '22 at 03:12
  • @user1551: Hi thanks for the reply. However, I already have the book, what do you think of it vis-a-vis Zorich? Please. – SK2 May 22 '22 at 18:56
  • I have only browsed through Zorich once. When I was an undergraduate student, my assigned textbooks were Rudin and Apostol. My impression is that Zorich is broader and deeper in content, it is more conversational and it caters to students from more disciplines. Although I have never read Zorich carefully, I will bet that it is a better textbook than Rudin. – user1551 May 23 '22 at 18:47
  • A bit late but for future folks, yes read Zorich instead of rudin. It has much clearer and comprehensive exposition. In fact not only is it clearer, it is also at a level higher than rudin. It has much more advanced materials, and its exercises are also significantly harder than Rudin. Essentially zorich is easier to read than rudin, but its material and exercises are in fact (significantly) more advanced than rudin. – juekai Mar 29 '24 at 05:34

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