At the time of this writing, standard funding packages for Ph.D. students do not include summer funding. Don’t fret though, there are several ways to make sure you can eat and have a place to live over the summer!
Many students find summer teaching positions through the math department. Unless you’ve advanced to candidacy (and maybe even if you haven’t), these are TA jobs in one of the two summer sessions. These positions can fill up quickly, so if you’re interested, keep an eye open for the announcement.
Some students’ advisors have money to support students over the summer. This can be very helpful for accomplishing research over the summer. Having nothing to do but your own math can make for a very productive couple of months.
Be advised that your total funding for the summer cannot exceed 100% FTE (during the academic year, most graduate students have a 50% TA position). This is not really an issue for most people, but some students are in the lucky position of receiving a 100% RA position from their advisor over the summer. If you happy to be one of these people, it’s probably a good idea not to take a teaching job in the department, unless you don’t mind working for free. That is, if you accept a 50% TA position, then you can have at most a 50% RA position at the same time. Keep these restrictions in mind if you’re lucky enough to have this problem.
For those who have advanced, a limited number of associate instructorships are available. Allocation of these positions is handled by the graduate vice chair and your departmental teaching evaluations are taken under advisement.
In the Fall, students may apply to become a Summer Teaching Fellow for the following summer. This is different from an associate instructorship, in that it is a university wide program to teach a course in the summer.
It is an open competition, and you need to fill out an application form, have a faculty person agree to be your teaching mentor, and have strong teaching evaluations. The Math Department often gets two of these slots, partly because we are an impacted department where we have over 6,000 undergraduates per quarter taking our math classes. The Summer Teaching Fellow gets paid slightly more than an Associate Instructor during the year. Also, the Faculty Mentor gets a small honorarium.