The plan of work for the Ph.D. degree includes the comprehensive exam and qualifying examinations. Ph.D. in Mathematics students will all take the qualifying examination in the same two areas, Algebra and Real Analysis, within two years. Students in the Ph.D. in the Applied Program will follow a parallel policy and tested on two different areas, Statistics and Applied Probability for students in the Statistics track and Analysis and Differential Equations for students in the Applied Mathematics track.

In addition, each student will be required to prepare a written plan for additional advanced course work and substantial reading of research articles. An advanced topic examination will also be required in the third year. A general exam, in which the candidate describes the thesis program, and the doctoral dissertation and its defense complete the work for the Ph.D. degree. A student entering Lehigh without a masters degree must take 72 credits including at least 48 regular course credits (i.e. not dissertation credits). These students typically earn as Masters degree during the process of their work. A student entering Lehigh with a masters degree must take 48 credits including at least 18 regular course credits (i.e. not dissertation credits).