In addition to Set Theory and Formal Logic, Computer Science relies heavily on Boolean Algebra, Graph Theory, and other areas of Discrete Mathematics. Computer Science is inherently cross-disciplinary, but at its core it is closer to Mathematics than it is to Engineering or Science.
You miss the parts that are very close to Linguistics and Information science: Ontologies, Information retrieval, Semiotics, and the all-important Human-Computer Interaction - how to build a computation environment that's efficient for humans to interact with. Maybe this is not a well-defined problem in a mathematical sense, but it's at the core of all programming activity beyond the level of micro-instructions.
This is not merely cross-disciplinary work; those are also essential parts of the science of computation, little related to mathematics yet highly relevant to all projects in the computing field, either in research or business - although many are unaware of their relevance.