Using AWS and being able to program on top of it are galaxies apart. If you are not a programmer, I wouldn't bother with it just yet. I could explain it, but I don't want spend the time unless you can consume the answer [because I don't have time] However, you might be seeing some cool public trading apps built ontop of them both "soon". You might or might not know that AWS and/or GCE are the technology driving behind them.
I can program...all my trades are automated. It seems like a way to scale up code to more machines, but I am not sure if I need that.
39 Lectures on FPGA programming in Verilog. The modern way is probably to use OpenCL, but I believe it is correct to learn the "C" analog of FPGA programming first.
It is very possible that the market does not have the necessity for mathematical unitarity. At least for short periods of time.
Kullback–Leibler divergence "...Although it is often intuited as a way of measuring the distance between probability distributions, the Kullback–Leibler divergence is not a true metric. It does not obey the triangle inequality, and in general DKL(P‖Q) does not equal DKL(Q‖P). However, its infinitesimal form, specifically its Hessian, gives a metric tensor known as the Fisher information metric...." https://en.wikipedia.org/wiki/Kullback–Leibler_divergence
Hard to tell how much of the run up was in anticipation of this going through, but I would not be surprised to see a 5% or more down move in oil in the night session: Oil-Freeze Talks End in Failure Amid Saudi Demands Over Iran http://www.bloomberg.com/news/artic...s-end-in-failure-amid-saudi-demands-over-iran
Interesting post on Math.Net. Accord.Net, python, Matlab, R etc. A bit old, but still worth understanding http://richardminerich.com/2013/08/all-machine-learning-platforms-are-terrible-but-some-less-so/