Internships are a very good way to test out different career opportunities before committing to a full-time position post-grad, so you're definitely ahead of the game. I'd definitely say reach out to your professors. Often times they have worked in the field before teaching and/or have a large network they can reach out to in order to help guide you. I know many schools also hold career fairs where companies come to recruit new students for both internships and full time positions. If you can reach out to your career center and get a list of the companies that will be in attendance, you can do research on what different companies have to offer before going. Math can be used in a number of different fields so be open!
Good luck with the process!