My last course M208 Pure Mathematics, lightly touched upon complex analysis, only as far as arithmetic and basic manipulation of complex numbers, is concerned. My current plans include completing the Open University course M337, Complex Analysis, in 2014. As such, I am planning a very slow study of the course, prior to starting it, next year.
When I say slow, I mean glacial.
I am in no rush whatever. So, alongside my Groups, and number theory preparation over the next few months; I am planning on studying a page or two from the first couple of units in M337, every few days.
I am hoping that the basic concepts will then slowly simmer in my unconscious mind, over the next year, prior to starting the course, proper, next October.
I don't have any number theory books to pre-study, prior to October this year, other than my trusty copy of 'How to Prove it' by Velleman. It contains some nice set theory along with some logic and practise at working out basic proofs. I would recommend that book to anyone who wants extra practice at creating proofs from first principles, in a systematic, logical way.
In the early stages it's definitely worth spending time learining about complex logarithms and their periodicity. Also probably the most trickiest concept I found was the continuity of the Arg Function. I would like to revisit M337 in slow time as well before I'm ready for the Applied Complex Variable course in the MSc
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