I recommend The Incompleteness Phenomenon over GEB[1]. It thoroughly presents Gödel's Completeness and Incompleteness theories at a level appropriate to the collegiate Math or Computer Science student.
The discussion of Gödel's theorems is not the only thing that makes GEB an interesting read.
What's more, GEB presents Aristotelianism vs. Platonism in the context of _computation_.
_That_ is a question CS majors should at least be aware of.
The question of whether computations can _ever_ be brought to have consciousness.
Then again, given my limited knowledge, I am far from being an authority on the topic and look forward to gaining more insight by hearing other opinions.
Undoubtedly. However, from a standpoint of teaching a class to Math and Computer Science students you can and should present the backing theories in full detail. Student benefit greatly from having a common write up on the proofs. The philosophical discussion can be saved for the classroom (with supporting supplementary readings).
[1] http://www.amazon.com/Incompleteness-Phenomenon-Martin-Golds...