I've been reading about Hilbert spaces and I noticed something that bugs me. All the math books state that the scalar product is linear in its first argument and antilinear in the second, while all the physics books say it's linear in the second argument and antilinear in the first.
I'm confused. Am I right to assume that the conversion between mathematical and bra-ket notation is:
$$\langle a,b\rangle=\langle b|a\rangle$$
or is there something else going on here?