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Complex analysis prerequisites may be outdated, as it was written in 2013 (I don't know anything about complex analysis!). If Complex analysis prerequisites is not outdated, please close this question as a duplicate.

Which courses should I have read before I can take the course 'Complex Analysis'? Please write the courses/ areas of study in a somewhat cronological order. I would very much like if you could add the book/-s that is/are needed on every topic, if you have the possibility to do so.

I want to study on my own, that is why I'm asking this question here.

My current level of knowledge are on preuniversity level, knowledge of derivatives, integrals, summation, and so on. (My current knowledge should not be any hindrance in climbing the ladder to Complex Analysis on my own).

Thank you for any answer, Andreas

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    Understand power series, green's theorem, and depending on the level, have had a proof's course. Back in the day Churchill's book was good, if you want to get serious Ahlfor's book fits the bill. – 2017-01-16
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    I'd say that it helps to go through multivariate calculus first in order to understand how path/line integrals work. Green's theorem/Stokes' theorem are good too, but not strictly necessary. – 2017-01-16
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    How is it outdated? Basic complex analysis has not changed significantly since 2013. – 2017-01-16
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    Just a comment regarding the above suggestion: the author is called Ahlfors, where the s is a part of the name. :) – 2017-01-16
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    @NateEldredge Please take a look at my text now, I have edited it. – 2017-01-16

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I'm doing an independent study on Complex Analysis right now and have come across several things I wish I would have known before. Geometry is a must. The book I'm using (Visual Complex Analysis - Needham) does an excellent job of explaining all of the Euclidean Geometry in the first chapter and has a separate chapter for non-Euclidean, but it would have made my life easier had I taken a full Geometry course before. A two-semester sequence of single variable calculus including series is an absolute must and is really the bare minimum calculus you will need to know. Other than that, vectorial operation and topology(again, Needham's book explains what you need to know about this) are both important and Astract Algebra (Group theory and Automorphisms) is also good. As I've already implied, Needham's book is really excellent as every idea is a given a visual argument rather than a non-intuitive computational one. Traditionally, these topics are explored in the following order:

Single-Variable Calculus (Most Calc textbooks are perfectly sufficient for this) Linear Algebra (Linear Algebra Done Right - Axler, If you would like a more rigorous approach Linear Algebra Done Wrong - Triel, An open-source textbook) Geometry (The Four Pillars of Geometry - Stillwell, A classic text and referenced by Needham regularly) Abstract Algebra ( Abstract Algebra - Judd, open source) Topology (Topology Now - Straffin et al, meant to be used by undergraduates without a ton of prereqs) Complex Analysis (Visual Complex Analysis - Needham)

I have not completed a Geometry or Topology course and I am doing alright. Not great, but alright. You can learn some of the stuff as you go. Don't try to rush through the prerequisite topics as they have value on their own and are gateways to other topics.

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    A knowledge of the Fourier series convergence theorems is important too. – 2017-07-21