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I'm debating whether I should take a course, in complex analysis (using Bak as a text). I've already taken Munkres level topology and "very light" real analysis (proving the basic theorems about calculus) using the text Wade.

The complex analysis course is supposedly difficult and will even cover the Prime Number Theorem in the end. Do you think it's better to take Rudin level real analysis first?

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    It will depend on (among other things) how the course is taught in the beginning, i.e. what you are assumed comfortable with, which we don't have enough info to judge. If you are not already pretty comfortable with $\varepsilon$-$\delta$ proofs, sequences, series, and functional limits, then more primer on the basics of analysis would serve you well. Beyond mathematical maturity and these basics there isn't much needed specifically from real analysis to take on complex analysis. (In particular, the pathological cases you have to be wary of in real analysis do not appear in complex analysis.)2012-01-16
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    Why don't you ask the instructor of the course? He or she should be able to tell you how much of a background in real analysis the students will be expected to have.2012-01-16
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    Can you take both at once?2012-01-16
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    As Jonas said, "It will depend on how the course is taught." There *could be* a lot needed from real analysis and even functional analysis - e.g. you could get the Prime Number Theorem by a route passing through Wiener's and Ingham's Tauberian theorems.2012-01-16
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    Agreed with the above; just glancing through Bak's book, it doesn't seem like he requires a great deal of analysis. The Prime Number Theorem part is at the very end as a "special application", but the rest seems par for the course.2012-01-16
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    (I looked at "Complex Analysis - Bak and Newman" for this) Since you've read Munkres, I'm assuming you are pretty mathematically mature and since you read Wade, I assume you "get" analysis. It definitely wouldn't hurt to take a Rudin-based course before this but I wouldn't say it's necessary at all, this type of complex analysis is pretty self-contained (and when it does borrow from real analysis, it's usually stuff like "definition of derivative" and done "in the obvious way").2012-01-16
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    Echoing the comments above, I'd say that the technical difficulty of a 1st complex analysis course is arguably less than that of a Rudin level real analysis course, but that one may need some maturity (which it sounds like you have) to get to grips with the conceptual gear change. But if you are OK with open and compact subsets of the plane and can integrate continuous functions rigorously, you're pretty much good to go I think2012-01-16

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