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I'm a undergraduate statistics student, I think that learn Real Analysis can be useful to me in some points, can anyone suggest a introductory book for self-study ?

I'm already multivariate calculus, algebra linear, and others math courses.

Someone said to me to start with Analysis: With an Introduction to Proof and then move to By Walter Rudin The Principles of Mathematical Analysis. Is that a good idea, or I shoud start directly with Rudin?

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    $\begingroup$ I used the book "Understanding Analysis" by Stephen Abbott for my undergraduate analysis class. It's a nice introduction for a first-time student studying analysis $\endgroup$ – Brenton Jun 25 '16 at 3:31
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    $\begingroup$ I would recommend "Introduction to Analysis" by Rosenlicht. It's cheap, easy to follow, and compact (no pun intended). $\endgroup$ – Math1000 Jun 25 '16 at 8:32
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The standard undergraduate text for real analysis is Rudin's Principles of Mathematical Analysis (affectionately referred to as "Baby Rudin" since he wrote it when he was quite young).

Another text I enjoyed was Serge Lang's Undergraduate Analysis.

I think they're both have their pros and cons but are ultimately both fine books for first learning some rudimentary real analysis.

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    $\begingroup$ I thought the term "baby Rudin" os to distinguish it from another more advanced Rudin textbook in analysis. Baby Rudin is great as a textbook for a course with an instructor. But it is sometimes quite terse, so may not be good for self-study. $\endgroup$ – GEdgar Jun 25 '16 at 16:23
  • $\begingroup$ @GEdgar I didn't personally have trouble reading through Baby Rudin as a first analysis textbook (I did take it in a class but didn't go to any of the lectures). It was definitely a little hard at times, but I think that only helped me learn. Some people may not be as persistent, etc. $\endgroup$ – MCT Jun 25 '16 at 22:49

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