I am applying to U.S. PhD programs in mathematics. I have noticed that the school websites (and the official offers I have received) all separate the summer funding from the overall stipend; the summer funding being an additional $3-5k over the $20-40k funding given already for the academic year itself. Why is this the case? Isn't the expectation that students will work full time? If students get all the money, wouldn't it be more convenient (and look more impressive) to just state the full amount as the "stipend"?