Why does Griffiths define the complex inner product differently? I have just now noticed that Griffiths (in his book Introduction to Quantum Mechanics) defines the complex inner product as 
$$\big<z,w\big>~=~\sum_{i=1}^n\overline{z}_iw_i.$$ 
In all mathematics books (I study math and physics) I have ever come across, it is defined as 
$$\big<z,w\big>~=~\sum_{i=1}^nz_i\overline{w}_i.$$ 
Maybe there is an answer to this question, maybe there isn't, but why on earth is this defined differently in physics than in math?
If this question just doesn't belong here, let me know and I will delete it and eat my frustrations for dinner :).
 A: As a rule of thumb, in mathematics a complex inner product or sesquilinear form is conjugate-linear/antilinear in the second entry (in the tradition of listing the least complicated arguments first), while in physics it is the other way around: It is conjugate-linear in the first entry (in order to make contact to the Dirac bra-ket notation).
A: Its only the more elementary math textbooks that use the opposite convention.
Every physics book puts the conjugate first. And when you get to more advanced operator theory math books eventually everyone switches to the other convention because it does make things easier.
And the only reason math books do it the wrong way is so they can use the word sesquilinear. If saying that word isn't super important, then why not do it the way that eventually makes it easier.
It also is nice that then you conjugate on the left put the operator in the middle and then have the operator act on the right when you do an expectation value. Whereas saying 1+1/2 linear (sesquilinear) is still vague: it's a half linear half conjugate-linear operator.
A: To be honest it doesn't matter unless and until one of them is complex conjugated and the same is maintained throughout the course. Most books I have come across conjugate the first term.
