Prospective graduate students should know the answers to the following questions before deciding to enter a program.
What is the mission of the program; that is, in what areas (subdisciplines, applied/interdisciplinary work, industrial problems, preparation for university teaching, and so on) does it specialize and what are its goals in those areas? Are the areas of specialization consistent with the areas in which you would like to specialize?
At what level does the program begin?
What is the completion rate? (Students should be wary of enrolling in a program with a low completion rate.) What is the average length of time to a doctorate? What is the placement record for new PhD graduates?
Does the program have a positive (supportive) learning environment? Are advisors available? Will course work provide a sufficiently broad background in the mathematical sciences? Is support in studying for qualifying examinations available from the department or from groups of students? Is clear information on the qualifying examinations and on the research period available from the department?
What type of financial support is available? What teaching work or other work is required to obtain that support? Will that work realistically take 20 hours per week or less?
Care in the selection of a graduate school will lead to a more successful doctoral experience.