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S.E. users,

Which one is better for the real analysis, "Mathematical Analysis" by Tom Apostol or "Undergraduate Analysis" by Serge Lang? It is my first time with real analysis, but I will be supplementing either of them with Ross, Abbott, etc. My ultimate plan is to study Rudin's PMA & Pugh's Real Mathematical Analysis after mastering some chapters in APostol or Lang, which will prepare me for my analysis course on this Fall.

Sincerely,

PK

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  • $\begingroup$ I just recently purchased Lang's UG analysis text. It looks to cover a lot of information. If you've already had an advance calculus course, I'd recommend N.L. Carothers' Real Analysis. It's a nice book for self-learning. $\endgroup$
    – MAM
    Commented Mar 12, 2015 at 22:53
  • $\begingroup$ I haven't tried either one, but I did like my analysis book -- Understanding Analysis by Stephen Abbott. $\endgroup$
    – user137731
    Commented Mar 12, 2015 at 23:06
  • $\begingroup$ Dear MAM, how is Lang's Undergraduate Analysis? Is it good for a first introduction to real analysis? Or do you rather recommend Apostol's Mathematical Analysis? Which one would make a good transition toward Rudin's PMA? $\endgroup$
    – user205011
    Commented Mar 13, 2015 at 6:24
  • $\begingroup$ I recommend you start with Blouch or Tao $\endgroup$
    – Saikat
    Commented Feb 28, 2016 at 7:11
  • $\begingroup$ I second the recommendation for carothers $\endgroup$
    – KyleW
    Commented Feb 28, 2016 at 7:20

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Haven't read Lang. Have only glanced at Apostol and it is not that different to Rudin from what I've seen in terms of sophistication. Abbott is definitely an easier book. My favourite is Elements of Real Analysis by Bartle. Might want to look through this too:Good book for self study of a First Course in Real Analysis

Just googled Ross. Both that and Abbott focus only on the real line. Whereas the books you mention go well beyond it to finite-dimensional Euclidean space and then to general Metric Spaces. So I don't know if Apostol, Pugh or Rudin would "prepare" you for this upcoming course. Having said that I've found it better to sometimes stay ahead of your college courses and know a bit more. So why not challenge yourself by taking a crack at Rudin and Pugh. Even if you only get through the first chapter in Pugh before your course it will be well worth your time.

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  • $\begingroup$ Thanks for the advice! I tried Bartle's two books on real analysis but I honestly did not like the writing style. I am still debating between Apostol and Lang; I have been reading them from the library and I understand their expositions but have difficulty tackling their problem sets. Should I go back to Ross/Abbott and come back with Apostol, Pugh, and Rudin on May? $\endgroup$
    – user205011
    Commented Mar 13, 2015 at 0:44
  • $\begingroup$ I will soon be conducting a research on the analytic number theory so I was wondering if Apostol, Lang, Pugh, and Rudin are good for the number theory too. $\endgroup$
    – user205011
    Commented Mar 13, 2015 at 0:44
  • $\begingroup$ Know very little beyond "elementary" number theory. IMHO you should persevere with the harder books. Again, this is just my opinion. I think you're supposed to spend a lot of time with the exercises. No one - except the truly extraordinary - should find them straightforward. $\endgroup$
    – Ishfaaq
    Commented Mar 14, 2015 at 11:52
  • $\begingroup$ Upvote for the advice to stay ahead of the course! $\endgroup$
    – Saikat
    Commented Feb 28, 2016 at 7:16

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