That's why the course is cross listed in both the Mathematics and Computer Science departments.
Another answer: some logic, some set theory, some combinatorics, some probability theory, some number theory, a few discrete mathematical structures (partially ordered sets, trees, ...), and the tools for investigating those ideas - examples, experiments, algorithms, proofs.
(For an answer to a more general question I recommend the famous What is Mathematics? by Richard Courant and Herbert Robbins. Too bad it's not an appropriate text for this course.)
Here is the course description from the web page maintained by the Computer Science Department:
An introduction to the mathematical structures and concepts used in computing: sets, mathematical induction, ordered sets, boolean algebras, predicate calculus, trees, relations and lattice theory, formal theory of languages and automata theory. Formal and informal theories and corresponding mathematical proofs are taught.