S.E friends,

I am currently trying to prepare myself for upcoming reading course that focuses on Walter Rudin's " Real and Complex Analysis" to learn the basics of complex analysis and measure theory that are needed for my research in the theoretical data science. Unfortunately, I have little background in the real analysis as I have not taken any course in the introductory analysis (but planning to do so in Fall).

What could I do to prepare myself for RCA? Is the prior experience with introductory analysis really needed? Is there way to study them simultaneously? What topics from introductory analysis are most essentials for RCA? On the side note, I heard Rudin's PMA is terrible compared to RCA, and I could not check out a copy of PMA.

I took courses like general topology (Engelking), abstract algebra (Lang, Aluffi), linear algebra (Hoffman/Kunze), etc.

  • $\begingroup$ A background in elementary analysis is absolutely necessary. You should probably read Rudin's principles of mathematical analysis. Neither of these texts may be particularly good to learn directly from. You could consider other sources which present material in a less terse way. $\endgroup$ – Chickenmancer May 1 '17 at 15:28
  • $\begingroup$ I find Stephen Abbott's "Understanding Analysis" to be excellent. The title speaks for itself. $\endgroup$ – Simon May 1 '17 at 19:38
  • $\begingroup$ For Complex Analysis I recommend Brown and Circumstances Churchill's "Complex Variables and Applications". $\endgroup$ – Simon May 1 '17 at 19:39
  • $\begingroup$ If you don't like Rudin's Principles (which I don't think is bad), you can use Apostol's book Mathematical Analysis instead. $\endgroup$ – user49640 May 3 '17 at 3:13

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