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What are the prerequisites for the complex analysis part of Rudin Real and Complex analysis book? Is it possible to start studying the complex analysis part with the knowledge acquired from the first 2 chapters of the book? My background in analysis: first 7 chapters of PMA Rudin.

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  • $\begingroup$ first 7 chapters of PMA rudin; yes $\endgroup$ – mathworker21 Aug 10 at 7:34
  • $\begingroup$ @mathworker21 so the complex part of RCA does not depend a lot on the first 9 chapters? $\endgroup$ – HAT Aug 10 at 7:37
  • $\begingroup$ i never said that. what i said was that the first 2 chapters are sufficient. i dont know if the first 2 chapters are needed for the complex part of RCA, since dominated convergence theorem might be important. my guess is that one would be fine reading the complex part of RCA knowing just the first 7 chapters of PMA rudin $\endgroup$ – mathworker21 Aug 10 at 7:48
  • $\begingroup$ Most of the second half of RCA is more or less independent of the first half. There may be things like applications of dominated convergence, but those argumments can easily be modified. Of course if you skip the R and start with the C you'll miss a lot of the good stuff, meaning non-trivial applications of R to C and vice versa, but most of those things are in the later chapters; if you want just a basic course in complex the start of the second half of the book is enough. $\endgroup$ – David C. Ullrich Aug 10 at 14:50
  • $\begingroup$ Of course it would be a shame to read the C without the R. A lot of stuff towards the end (Hardy spaces, Banach algebras) is fundamental, fascinating, and does depend on R and C. $\endgroup$ – David C. Ullrich Aug 10 at 14:52

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