Just to add one more note, if you REALLY want to get specific, HFTs will require a greater degree of computer science than mathematics. In HFTs, you are essentially finding ways to improve the speed in execution of trades. This most likely comes in finding new ways to have your program place the order with the counter parties.

Examples in which this could be done are:
1. Knowing when to break out of sorting algorithms when you have sorted enough data, i.e., filtering out prices from three banks from that of twenty others.
2. The shifting of calculations on hardware before it gets to the software, i.e., the use of FPGA to sort prices before reading them into a data structure.
3. Testing the robustness of your algorithm in finding a offer less than a bid. Your algorithm must be able to confirm two counter parties which are willing to deal at a certain price BEFORE dealing with either of them. In HFT, you rarely have an open position, thus, it's dangerous to open a position without knowing in advance on whether you can close it out with a certain counter party.

As you can tell, 1 to 3 is almost all about computer science skills and not about math. When you start moving into the realm of price forecasting in speculative trading, then it's time to brush up on those stochastic calculus chomps.

Cheers,
Donny