I am about to start my first year in college. I am not a class type student. I like going deep while studying myself and understanding the reasons, beauty behind these ideas. I have been looking for textbooks and realized there are many textbooks on the same subject. Of course some of them are highly recommended such as Spivak, Baby Rudin etc for analysis. I want to ask that if there are any significant differences between these top-level textbooks to understand the real theory and ideas? If I go with Baby Rudin and everything is clear for me, is reading one more top-level textbook a waste of time or could it really add my understanding more on this subject? Or should i continue studying another subjects? And also on the internet most people said that books like stewart and thomas' calculus are mostly for real life problems. Are books like them a requirement for me and are the problems on them rough? I want questions more like make me think and when I am able to solve I want to feel enlightened. Thank you for answers from now,I want to be a pure mathematician and I don't want to waste much time.

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    $\begingroup$ Having the mentality of not wanting to waste time in math can be a bit problematic - the goal is to learn well, not quickly. IMO, baby Rudin does a decent job at taking you through the material expected for a solid introductory analysis course, as well as providing decent problems. Of course, the terseness is a problem for some, but if it works for you, that's great. In my experience though, I think reading through a few textbooks helps solidify concepts in a way that a single text can't. But that might just be me. $\textbf{TL;DR}$: start with Rudin, see if you're handling the psets well. $\endgroup$ – Don Thousand Aug 9 at 0:05
  • $\begingroup$ For some more insight, at my uni, Spivak is used to teach the lowest level introductory calculus class, Rudin for the middle level, and Kolgomorov for the honors sequence. Note that all three sequences are aimed at STEM students, so don't take any of them lightly. $\endgroup$ – Don Thousand Aug 9 at 0:10
  • $\begingroup$ I disagree with the above comment about it being bad not to want to waste time. If you read through Rudin and understand it, then go on to other stuff. Reading other books like Spivak would be a waste of time. $\endgroup$ – mathworker21 Aug 9 at 0:21

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