What is the sole purpose of finite mathematics?

Finite mathematics is the science of manipulating finite sets of objects -- discrete objects -- to model an analog world. Given that computers operate with binary numbers, the marriage of the two was inevitable. So finite mathematics is essentially a way of understanding how to apply computers and computational analysis to real-world problems. Some of the most fascinating algorithms I've seen have been ways of getting what I would have considered continuous-looking functions from using these building blocks. So FM shows us how to build computer programs and calculation functionality from our digital machines. If you want a good introduction or overview of FM, look over the internet for some short tutorials. They will give you a painless preview of what you're getting into and how much fun it can be.