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Combining Spivak and Apostol Calculus' textbook is enough (or too much) to prepare someone to take an undergraduate Real Analysis course? Would you have a better (and less time consuming) suggestion?

Daniel Fugisawa
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  • Rudin's PMA is the best (of course, IMO) real analysis book in existence. If that seems very thorough, then Bartle-Sherbert is a very good (again, IMO) replacement. – Aloizio Macedo Sep 24 '15 at 00:15
  • Thank you! Actually, I'm looking for some good Calculus (and other subjects if need be) to prepare to take a summer Real Analysis course. The Calculus I had (15 years ago!) was very rudimentary. Of course, an introductory Real Analysis is not discarded, but I'm afraid I'm not mature (mathematically speaking) even for Baby Rudin. – Daniel Fugisawa Sep 24 '15 at 00:23
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    It depends on your notion of time-consuming, but I found Francis Su's lecture videos very helpful in my undergrad course. – user170231 Sep 24 '15 at 00:26
  • Thanks, already bookmarked! – Daniel Fugisawa Sep 24 '15 at 00:30
  • @DanielFugisawa Although you may lack mathematical maturity, the maturity you have in order to say this is something to be cherished and will most certainly be something very positive for you.

    Back to the question, I read Calculus With Analytic Geometry in order to learn Calculus. I found it a really good book, but I don't really think it was very helpful in order to understand analysis. I think reading some introductory book on analysis will be far more helpful.

     – Aloizio Macedo Sep 24 '15 at 00:33
  • Maybe you're right. I'll give it a try. – Daniel Fugisawa Sep 24 '15 at 00:41
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    @DanielFugisawa I think Apostol is really good preparation for a first course in real analysis (don't skip the introduction!), if you can get through it. Also, if you are interested, I've been blogging all of the solutions to Apostol, Volume 1 (the link is in my profile). Maybe you'll find some of the solutions helpful. – Bamboo Oct 02 '15 at 01:00
  • Best news of the night!!!! Thank you! I never know if I got the right answer. Already bookmarked it! – Daniel Fugisawa Oct 02 '15 at 03:33
  • @DanielFugisawa No problem. Let me know if you find mistakes (which definitely exist). I'm only just now finishing blogging chapter 4, so nowhere near the whole book yet, but at least it's something. – Bamboo Oct 02 '15 at 03:53

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Have a look at the suggestions in this closely related MSE question - "Good book for self study of a First Course in Real Analysis".

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Jose Arnaldo Bebita Dris
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