35: Please Be Discrete (Discrete Math)

Centuries ago, there began something of a curiosity between mathematicians that didn't really amount to much but some interesting thoughts and cool mathematical theorems. This form of math had to do with strictly integer quantities; theorems about whole numbers. Things started to change in the 19th century with some breakthroughs in decrypting intelligence through examining the frequency of letters. In the fervor that followed to increase the security of existing avenues of communication, and to speed up the newfound media of telegraphy, came a field of mathematics called discrete math. It is now an essential part of our world today, with technologies such as online banking being essentially impossible without it. So what have we learned from discrete math? What are some essential methods used within it? And how is it applied today?