Charles already posted Takhtajan's book, which is my first choice --- it's geared towards early graduate students. A more elementary book, geared towards math undergrads, is by Fadeev (who is, incidentally, Takhtajan's adviser, and Takhtajan's book can be understood as some sort of sequel).
The book Mirror Symmetry by Hori et al. includes a whirlwind overview of quantum mechanics and quantum field theory. It's not mathematical in the sense that it contains no proofs and even fewer definitions, but it doesn't require any particular background.