Here's what I came up with without including graphics:
($230) Intel i5-2500K
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115072
In your price range this processor is the absolute minimum. I have a feeling that of your listed usages gaming is going to be the most demanding. If you really tax matlab then you could justify the i7-2600K but most people won't notice the difference in matlab.
($55) Thermaltake Frio
http://www.newegg.com/Product/Product.aspx?Item=N82E16835106150
The stock cooler is garbage.
($205) ASUS P8Z68-V PRO/GEN3
http://www.newegg.com/Product/Product.aspx?Item=N82E16813131790
This board will get you x8/x8 SLI mode for two graphics cards, a nice port cluster, good overclocking potential, and a really reliable brand. However if you ever want to run an x4 peripheral (like a RAID card) in that third x16 slot then you'll likely want a different board but most people don't care about that.
($47) G.Skill Ripjaw 8GB (2x4GB) RAM at 1600mhz, CL9, and 1.5V
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231314
Some people use more than 8GB of RAM. I have programs that I have written myself that use over 12GB of RAM. However most everyone will have plenty at 8GB - especially for gaming. If you find yourself needing more RAM you can add another 8GB (2x4GB) kit later.
($190) Crucial M4 128GB SSD
http://www.newegg.com/Product/Product.aspx?Item=N82E16820148442
SSD's don't help your FPS in gaming, but they are a gigantic overall system upgrade. If you've never used one before then sometimes it's hard to justify the price per gigabyte, but once you've used an SSD you'll never go back. Also, if you have programming applications (like matlab) that use a lot of i/o then you will notice a huge difference with an SSD.
($130) Hitachi 2TB HDD
http://www.newegg.com/Product/Product.aspx?Item=N82E16822145475
The SSD isn't enough space - you need a standard HDD for mass storage.
($20) ASUS Optical Drive
http://www.newegg.com/Product/Product.aspx?Item=N82E16827135204
($200) OCZ 1000W Z-series PSU
http://www.newegg.com/Product/Product.aspx?Item=N82E16817341045
Normally I don't recommend OCZ PSU's but this one is a really great unit with lots of power. You can power two 580's and a healthy overclock with this one.
($100) Your favorite case. There are a lot of cases in the world and there is a lot of personal preference. Here are two good choices:
Antec Nine Hundred:
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129021
CoolerMaster HAF 922:
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119197
($150) Monitor: 22" ASUS Monitor wth 1920x1080
http://www.newegg.com/Product/Product.aspx?Item=N82E16824236051
This is a no-frills monitor with decent gaming performance. You can definitely spend more here, but I wouldn't if it were me.
($14) Logitech Wired Keyboard
http://www.newegg.com/Product/Product.aspx?Item=N82E16823126096
An expensive gaming keyboard is not as important as an expensive gaming mouse. The one thing you want, though, is to make sure your keyboard is wired. You don't want to lose keyboard connectivity when you're trying to return the flag.
($68) Logitech G9x 5700dpi Gaming Mouse
http://www.newegg.com/Product/Product.aspx?Item=N82E16826104261
You're going to want high DPI for gaming. Anyone who says a mouse is just a mouse and the $15 ones are fine has never used a good mouse. It makes a difference.
So far that's $1409 with plenty of room for graphics.
Now for graphics, which are the most important part of the system. My choice would be a single GTX 580. You'll be able to run almost everything that's out right now at the highest available settings. However, this is only the option that you want if you plan on adding a second card later when you can afford it. If you're not going to add that second card later then you want to go with two cards right now. Two GTX 560ti's will be about the same price as a single GTX 580 and will be better than a single GTX 580. Note that if you go with two 560ti's then you can use a weaker power supply.
($500) MSI Twin Frozr II/OC GTX 580 1.5GB
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127567
There are cheaper cards and there are cards with a higher factor overclock, but I picked this one because it cools well. Two 580's put out a LOT of heat. Cooling is important.
($500) 2x EVGA Superclocked GTX 560ti
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130610
There are a lot of 560ti's and I'm not an expert at picking the right one. Make sure to get 1GB cards and stay away from the 448 core cards.
($530) 2x MSI N560GTX-Ti Hawk GeForce GTX 560 Ti
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127578
If you want one of the best factory overclocks you can find in a GTX 560ti and you're willing to pay for it then I think the Hawk is the one. However it's not that hard to get an overclock yourself.
If you go with a $500 graphics option then you're at $1909. That leaves room for Windows 7 if you need it. You also may need to buy a couple of little extras like thermal grease, SATA cables, or extra case fans.