I have a 75 gallon fish tank, and I want to use a water heater heating element to provide the temp control (http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=370512031785). This listing says it's 120 volts, 1750 watts. I'm deducing that the amps will be at about 15. The problem is that I want to control the temperature using an arduino relay that's rated at 10 amps only.

My question is what resistor should I use to drop the amperage to 10? Also, if you can help me with the math you used to figure it out would be great, so I don't need to keep bothering people next time I come across the same problem.

Two of those elements in series would probably work - note any resistor to drop the current will itself be a mains heater... Finding the right relay (or a lower power heater) would perhaps be a more elegant solution?

Also, if you can help me with the math you used to figure it out would be great, so I don't need to keep bothering people next time I come across the same problem.

The relationship between Voltage, Resistance, and Current is defined by [u]Ohm's Law[/u]:
I = V/RR = V/IV = I x R

(I is current in amps)

Power is calculated as P = V x I.

And with some algebra you can come up with:
P = Voltage squared/ResistanceP = Current squared x Resistance