ELI5: The role of Discrete Mathematics in programmatic problem solving

Discrete mathematics gives you the language you need to formally talk about and compare algorithms. An example is Big O notation for describing computational complexity.
This is a discrete math concept and notation that formalizes this very useful concept.

When you write a program, you're writing a specific implementation of an algorithm in a specific syntax, specific to a platform. It's a very concrete thing. An algorithm, though, is a more abstract, general concept. You can implement the same algorithm in many different programming languages. Discrete math is the branch of mathematics that describes this space, so studying it will directly, immediately go in your problem-solving toolset for coding.

The only reason I know this is because I took a discrete math class. I had no clue what it meant either when the class started but clicked by the end of week one. Math has always been a weak subject for me but my programming experience made up for it here - first A in any math class since probably 6th grade.

Discrete math is the part of math that can be broken into discrete parts like all of the logic statements that make a computer.