PhD in Mathematics
The PhD in Mathematics at Drexel features research opportunities in many areas of both core and applied mathematics. Departmental research interests include mathematical biology, applied dynamical systems, combinatorics, matrix and operator theory, geometry, optics, inverse problems, probability, numerical analysis and partial differential equations.
The department runs a biweekly colloquium series and as well as a number of research seminars whose speakers come from either the department or other institutions. Current seminars, which usually meet weekly, are the Analysis Seminar, the Combinatorics and Algebraic Geometry Seminar, and the PDE/Applied Math Seminar. The SIAM (Society for Industrial and Applied Mathematics) student chapter runs their own seminar series as well.
The coursework for first year students include core courses in Linear Algebra and Matrix Analysis; Principles of Analysis I,II; Real Analysis I; Abstract Algebra I; and Complex Analysis I. These courses provide a foundation for the PhD Qualifying Exam (more details below) taken at the end of the first year.
Recent courses offered in addition to the core are Ordinary Differential Equations I,II,III; Partial Differential Equations I,II,III; Real Analysis II; Complex Analysis II; Functional Analysis; Harmonic Analysis; Operator Theory; Calculus of Variations; Optimization; Mathematical Neuroscience; Numerical Analysis I,II,III; Numerical Computing; Lie Groups and Lie Algebras I; Algebraic Combinatorics; Topics in Abstract Algebra.
In the second year, students take advanced courses in preparation for choosing a thesis research area and a PhD thesis adviser. The second year culminates in the PhD Candidacy examination, which has written and oral components.
The bulk of the PhD program is spent in thesis research that may include research seminar or conference presentations and publishing research articles. The structure of the program allows for completion in five years.
Learn more about the degree in the Course Catalog
PhD Qualifying Exam
Each PhD student will be required to pass a qualifying examination. The purpose of this written examination is to ensure that the student has the potential to complete the PhD program. The list of topics is strictly defined (available through the Graduate Program Committee) and parallels roughly the content of MATH 504-506 sequence: Linear Algebra (one term) and Principles of Analysis, I, II (two terms). The syllabi for these courses are standardized. The examinations will be given twice a year, in June and in September.
A student is allowed no more than two attempts for this exam. Unless there are serious extenuating circumstances, the first attempt is to take place no later than June of the first year of study and the second attempt (if it is needed) should take place the next available date.
Qualifier Exam Topics [PDF]
Previous Written Qualifier Problems [PDF]
PhD Candidacy Exam
The PhD candidacy examination must be attempted for the first time by the end of the second year of study. The examination will take the form of an oral presentation followed by a question period during which only the PhD Candidacy Committee will be present. The PhD Candidate will prepare a written report corresponding to the presentation and distribute hard copies to the members of the committee no later than 10 days prior to the exam.
The purpose of the oral section of the exam is to present the objectives and merits of the student's proposed research project and to demonstrate his/her knowledge of the methods and techniques used in the general area of the proposed research. The purpose of the written component is to familiarize students with the methods of scientific writing.
This examination will be scheduled individually and is supervised by the PhD Candidacy Committee. The University regulations specify composition of this committee as well as procedures for this examination and re-examination. They currently mandate that the PhD Candidacy Examination must take place after successful completion of at least one year of graduate work at Drexel, and prior to the end of the second year of doctoral study.
The doctoral program prepares students for a wide range of careers both in academia and a variety of other industries. Recent PhD graduates have gone on to positions including tenure-track assistant professor appointments, visiting assistant professor appointments, postdoctoral research positions, positions in financial institutions and in software development.
Organizations that hire mathematicians include government labs, research offices and agencies; engineering research organizations; computer information and software firms; energy systems firms; aerospace and transportation; financial service and investment management firms; communication services; chemical or pharmaceutical manufacturers; medical device companies; producers of petroleum and petroleum products (source: SIAM website on careers).
Teaching Fellow Policy
The College of Arts and Sciences regards training in pedagogy and instruction to be core to the mission of doctoral education. Therefore, all PhD students in the College are required to perform significant teaching duties (defined over multiple terms) during their pursuit of their degree. These activities may include, but are not limited to:
- Supervising teaching labs
- Running course recitations
- Teaching as the primary instructor
- Running student seminars
- Training junior researchers in core research methods
- Running or actively participating in pedagogical seminars or conferences
Alternate fulfillment of this requirement is at the discretion of the program director and the head of the student's home department.
How to Apply
Interested applicants should use the online application found on the Office of Graduate Admissions website. The application deadline for the Fall Quarter is January 15th. The FAQs webpage includes common questions and answers about the program. The faculty research areas webpage has a list of the various research topics within the department.
Inquiries about admissions should be directed to the chair of graduate admissions:
R. Andrew Hicks, PhD
Korman Center - Room 206
General inquiries about the program should be directed to the graduate program adviser:
Robert P. Boyer, PhD
Korman Center - Room 206