How to access RAM for use with an FPGA for high performance computing
For a variety of reasons, the Digilent Basys2 and the Xilinx Spartan-3E are not going to work for you.

For that amount of RAM, you will need something like DDR2 or DDR3 SDRAM running at a fairly high clock rate.  This is not something that you can just solder down onto a prototype PCB.  The PCB needs to be designed for interfacing to memory, ideally with the RAM already soldered down onto the PCB.  If you have never designed such a circuit, I suggest you get an FPGA board that already has the RAM on it.  This is going to be difficult, however, since all of the FPGA boards I saw (in 5 minutes of looking) had much less than 4 GB of RAM.

Next, you need something newer than the Spartan-3/3A/3E.  While the S3 is an otherwise good FPGA, the Spartan-6 series has much more to offer you.  It has much more internal RAM (but you still need external RAM), a lot more DSP48 blocks, and more logic.  But most important, it has a much better SDRAM interface on it than what the Spartan-3 has.  And by "much better", I mean "much easier for a beginner to successfully use".  The memory controller in the S6 is a hard-IP, which for you means that it is much easier to achieve the strict timing requirements of interfacing to SDRAM.

But controlling DDR2/DDR3 SDRAM is not easy.  Xilinx has a tool called the "Memory Interface Generator", which can be found in Core Generator.  This will generate the memory interface logic for you, and gives you lots of cool features that will make your life easier.  

An alternative to the Spartan-6 would be a Virtex-5 or any of the 7-series parts.  All of these have memory interfaces as good or better than the Spartan-6.

This Virtex-7 based board has a socket for two SO-DIMM modules, which could get you past 4 GB of RAM-- but it is super expensive at US$5,000.

I should also mention that if you are doing this because you want to learn about FPGAs and electronics then I support your efforts.  But if you think that this is somehow going to be faster than standard PC's then I have bad news for you. For the money, it is hard to beat an Intel i7 based quad-core machine with a reasonable GPU card.  Just warning you, in case all you really care about is math speed.