I've seen a strategy called Stochastic Calculus appear in quantitative analysis for the stock market, but it may be worth investigating advanced mathematics for FOREX as well. The way the trends in the market appear, using differentiation and integration to figure out the general "acceleration" of the market and in which direction it's occurring could work.

It would require something like Microsoft Excel, for you to plot a best fit curve. Using that, you could take the derivative of the given function to find the general direction of the market at specific points on the function. Following that, you could take the second derivative to find how volatile the market is at the time.

This doesn't take into account oddities in the news and such, however if compensated for, advanced math could easily be applied to FOREX.

For those who don't know:

Derivative (differentiation): Basically tells you the slope of a curve, and when applied to a function will tell you the slope of said function at each individual point on the curve.

Integral (integration): Basically the area under the curve, and if you have the slope function, it allows you to find the normal function for which that is the slope of

Different strategy than the Fibonacci sequence style trading, but still a good idea. The two could be used in conjunction with eachother to figure out when the next phase in the sequence would be coming around.

Successful option of trading requires that you understand

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Advanced mathematics didn't help LTCM at its trading...
Forget about heavy mathematics. The chart is what you should be looking at. Learn to identify and trade basic chart patterns, and you are good to go.

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You are talking about mathmatics in such a complicated manner. All the newbies reading this post will find Forex trading complicated. I want to say that anyone may become a successful trader no matter of your math education.
The thing required is hard work.
Find a strategy that suits you and follow it.
Wish you, guys, good results in trading.

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Think, Feel, Trade

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One of example is Murrey Math trading system?