Universities are not in the business of cramming useless info. If what they were teaching wasn't useful, they wouldn't bother. I recommend taking a more accepting attitude to life. If you go to college expecting to learn nothing, this is a self-fulfilling prophecy: you will learn nothing, so college will be wasted and you might as well start flipping burgers now.
Integers are a very simple form of data structures. Many of the algebraic structures that come up when studying functions that operate on integers also arise in the study of data structures.
Taking the size of a data structure maps the algebraic constructions on data structures to the corresponding algebraic constructions on integers. For example, the length of the concatenation of two lists is the sum of the length. This applies more generally to taking the site of a slice of a data structure, for example counting the substructures of a certain shape. For this reason, discrete mathematics often come up when studying the complexity of algorithms on data structures.
For examples of discrete mathematics at work, see
I recommend the book Concrete Mathematics by Ronald Graham, Donald Knuth, and Oren Patashnik.
Mathematics of almost any kind is also a way to gently introduce important concepts of rigorous proofs and abstraction. When reasoning about computer programs, you often need to keep track both of what is mathematically true, and of what the computer knows to be true, so to speak — the data that is available at each point of the program. It helps to first train your brain to cope with the mathematical truths, and gently graduate to following both the math and the program.