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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.

[1] http://www.amazon.com/Incompleteness-Phenomenon-Martin-Golds...

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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).

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