Computer science and computer engineering are two different fields. Think software/hardware. It gets confusing because some companies call a software developer a software engineer. Semantics, sigh.
Very important to find out the courses one can take in math and computer science at each school. btw- different schools offer different amounts of material for a given CS class. Friend covered more material as a TA in a quarter class than she was expected to teach in a semester class at a podunk U. It is a lot easier to have a good background without needing to catch up, although CS lends itself to self teaching (son does that, and reminded me he is in development, not research)