在该计划的第一年，学生通常会参加课程作业和研讨会，从而为参加资格考试做准备。这两门考试测试学生的代数和实数分析知识的广度。在该课程的第二年春季学期末，学生必须拥有论文顾问并申请候选人资格;在第三年学期中，学生将参加区域考试，该考试必须在春季学期末完成。该考试评估学生在其特定研究领域中的知识广度。区域考试还为学生提供了向其委员会介绍迄今为止进行的研究摘要以及其余研究的详细计划的机会。
The Ph.D. is conferred upon candidates who have demonstrated substantial scholarship and the ability to conduct independent research and analysis in Mathematics. Through completion of advanced course work and rigorous skills training, the doctoral program prepares students to make original contributions to the knowledge of Mathematics and to interpret and present the results of such research. Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest. During their first year in the program, students typically engage in coursework and seminars which prepare them for the Qualifying Examinations. Currently, these two exams test the student's breadth of knowledge in algebra and real analysis. Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics: (i) algebra, (ii) real analysis, (iii) geometry and topology, (iv) applied mathematics.