After passing my two most recent exams with much better marks than I ever hoped for, I have decided to hit the big red button and go for the nuclear option for my next course - Complex Analysis M337 with the Open University.
I think that this (apart from the old Topology course) is probably the most challenging of the OU maths courses of recent years.
Looking at the preparation available for this course being Pure Maths and Mathematical methods, both level 2 courses with the OU - these don't seem to be very comprehensive prerequisite courses for tackling Complex Analysis.
Of course, there are other courses which are not analysis based which use calculus, or alternatively, provide practice at reading and producing complex proofs, such as the fluids dynamics course etc...
But I haven't taken those other courses and my own background comes from pure mathematical courses alone.
So, I have started planning some pre-course study, to get me back up to speed with analysis. The books that I am using are:
Calculus. Spivak
Complex Analysis. Gamelin
A First Course in Mathematical Analysis. Brannan
A Course of Pure Mathematics. Hardy
I won't study them in depth and also not in the order listed above. I will also be referring back to my trusty annotated M208 Pure Maths handbook from my course in 2012, which has all those handy little notes which now make no sense at all, two years on.
My preparation will consist of two strands.
1. An overview and recap of main concepts, starting with limits, bounds and series / sequences; leading on to continuity, epsilon-delta, properties of integrals, power series etc...
2. A sharp facility in the rapid calculation of most basic differentiation and integration problems with some memorization of basic derivatives and integrals.
Spivak has a nice section for practicing facility with derivatives and integrals - and I particularly like his humor as he describes this passage of work:
'Although rapid calculation is not the goal of mathematics, if you hope to treat theoretical applications of the chain rule with aplomb, these concrete applications should be child's play - mathematicians like to pretend that they can't even add, but most of them can when they have to'! Spivak.
On the bright side, I have now only signed up for 30 points this year; half of last years study time. I will be pushing for a distinction on this course, which should line me up nicely for a half decent grade on final graduation next Summer.
Because my OU studies will come to an end at that time- I have now started to look at all the available MSc courses which provide distance learning or part time options, which require a high mathematical content.
I will need to start applying for my MSc course, after this Christmas.
I'll try and give an in-depth critique of the options available for a distance learner, in a future post.
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