Heatsticks. It's an electric water heating element that plugs into your wall outlet. Dip them in your water/wort to heat/boil it.
You can make them yourself for pretty cheap. The heating element costs about $10 plus some other drain pipes and fittings.
They use a ton of power and will require their own circuit, so don't use your microwave at the same time.
If you're handy and willing to build this, check out the circuit breakers in your apt. If they are 20 amp then you could use a 2000 watt stick. If they are 15 amp then you will have to settle for a 1500 watt element.