What Do Graduate Students Do?
A Masters degree typically takes about two academic years to complete, while a Ph.D. can take between 4 and 8 years, depending on many factors. Masters students take courses for one or two years. The usual course load is nine units: while less time is spent in class, much more is required of the students out of class. Masters students either work on a research project with an advisor and write a thesis, or pass a series of exams to complete their degree.
Ph.D. students also begin by taking classes. As they progress, the time in class decreases, and the time they spend working on independent research increases. Most schools require Ph.D. students to pass a series of written exams, an oral exam, and written exams on one or two foreign languages.
During the last few years of the Ph.D. program, students work on the research and the writing of a Ph.D. dissertation. The final step is presenting and defending the dissertation to a committee of faculty. Most graduate students in Mathematics do not pay tuition in graduate school: expenses are met through a combination of scholarships, research assistantships, and teaching assistantships.
Assistantships employ the student within the department : they may work with a faculty member on research or assist a faculty member in teaching classes. The usual workload is 20 hours per week. Students working as assistants are provided office space and are usually more actively involved in the life of the department.
Sometimes an employer will support an employee who is returning to school, maybe requiring the employee to return to the company for a minimum time after finishing the degree. You won’t get rich in graduate school, but you should be able to support yourself.