I am in the second year of my PhD in mathematics and I have recently decided I want to go into industry after I'm finished. I feel like a lot of what I'm learning in the program does not have direct, real-world applications, and I'd like to remedy this problem by getting some work experience while I'm still in graduate school.
I have some programming background (but not as much as a CS grad) and a couple years experience doing simple data analysis programming. I also have a BS in physics. It seems like there should be a place in industry for me somewhere, but I don't know how to go about finding it.
I would like to work part-time, or as a consultant, so that the job won't greatly hinder my progress towards my degree. (Of course, some time will be lost that could have gone to my dissertation, but this is made up for by gaining marketable skills.) I'd like to work in science or in software. I am aware of internships, but it seems like most are either for undergraduate students or engineers.
Can a math grad student work part-time in industry during his PhD? If so, how would one go about finding jobs?