The doctoral program provides exciting opportunities for students interested in studying advanced mathematics and conducting independent research.
This program begins with graduate coursework and advanced seminars and culminates in a dissertation consisting of original research in mathematics. The PhD is designed to train students as research mathematicians for careers in academia, government, and private industry.
Fellowships and Assistantships
The Department of Mathematical Sciences offers a limited number of merit-based teaching assistantships. Other sources of support, such as research fellowships and assistantships, are available as funding permits. Graduate students also have the opportunity to work in the Math Tutoring Center.
Admissions
University-wide admissions policies can be found in the Graduate Admissions Policies section of this catalog. International students and students having earned international degrees should also refer to Admission of International Students for additional requirements.
Eligibility
It is expected that all applicants have a recent bachelor's degree in mathematics or an equivalent amount of undergraduate mathematics preparation with a GPA of at least 3.00 in their last 60 credits of study from an institution of higher education accredited by a Mason-recognized U.S. institutional accrediting agency or international equivalent. Students without this background who have had an upper-division course in linear algebra (equivalent to MATH 322 Advanced Linear Algebra), an upper-division course in advanced calculus (equivalent to MATH 315 Advanced Calculus I), and an upper-division course in group theory (equivalent to MATH 321 Abstract Algebra) are encouraged to apply to the Mathematics, MS. Such students may subsequently apply to the PhD when all background issues have been addressed.
It is recommended that all applicants have some familiarity with mathematical software.
Application Requirements
To apply for this program, prospective students should submit the George Mason University Admissions Application and its required supplemental documentation, a goals statement, and three letters of recommendation.
The GRE is not required for admission into this program.
Policies
For policies governing all graduate programs, see AP.6 Graduate Policies.
Transferring Previous Graduate Credit into this Program
Previously earned and relevant graduate credits may be eligible for transfer into this program; details can be found in the Credit by Exam or Transfer section of this catalog.
Degree Requirements
Total credits: 72
Students should refer to the Admissions & Policies tab for specific policies related to this program.
Core Courses
Students must earn a grade of 'B' or better in each core course.
| Code | Title | Credits |
|---|---|---|
| MATH 675 | Linear Analysis | 3 |
| Select nine credits from the following: | 9 | |
| Algebra I | ||
| Topology I: Topology of Metric Spaces | ||
| Ordinary Differential Equations | ||
| Numerical Analysis | ||
| Seminar | ||
| Students must register for a 1 credit seminar each semester until they advance to candidacy, or have acquired at least 4 seminar credits 1 | ||
| MATH 795 | Graduate Seminar | 4 |
| Total Credits | 16 | |
- 1
Students must take at least 4 credits of seminar MATH 795 Graduate Seminar and may take an additional 2 credits as electives.
Preliminary Written Exam
Students are required to pass three preliminary written exams and complete four core courses by the end of their second year. Preliminary exams are offered twice a year and students may take each exam up to three times.
Dissertation Advisor and Examination Committee
After passing the preliminary written exams, the student chooses a dissertation advisor and a three person examination committee. In consultation with the advisor and committee, the student chooses a major and a minor area of study (the major and minor areas are presumed to be in two different branches of mathematics).
Electives
| Code | Title | Credits |
|---|---|---|
| Students complete 32-44 credits of approved MATH electives 1 | 32-44 | |
| Total Credits | 32-44 | |
- 1
Courses not designated as MATH courses must be approved by the graduate committee.
Classes at the 500 level, MATH 600 Special Topics in Mathematics - MATH 614 Rational Numbers and Proportional Reasoning for K-8 Teachers, and actuarial classes MATH 653 Construction and Evaluation of Actuarial Models I, MATH 654 Construction and Evaluation of Actuarial Models II and MATH 655 Pension Valuation cannot be used for credit.
Qualifying Examinations
Students are required to take a qualifying exam after passing the preliminary written exams. The qualifying exam may have oral and written components. In consultation with the advisor and committee, the student chooses a major and a minor area of study (the major and minor areas are presumed to be in two different branches of mathematics). The qualifying exam typically covers the equivalent of approximately four courses of material from the major area and three courses from the minor area.
Dissertation Proposal and Advancement to Candidacy
After passing the qualifying exam, each doctoral student prepares a written dissertation proposal while taking MATH 998 Doctoral Dissertation Proposal. The proposal must be approved by the dissertation committee, which consists of the three qualifying exam committee members, plus a fourth member from outside the Department of Mathematical Sciences. After successfully completing this requirement, the student advances to doctoral candidacy.
Dissertation Research
| Code | Title | Credits |
|---|---|---|
| Select 12-24 credits from the following: | 12-24 | |
| Doctoral Dissertation Proposal | ||
| Doctoral Dissertation | ||
| Total Credits | 12-24 | |
Doctoral Dissertation
After advancing to candidacy, the student will work on a doctoral dissertation while enrolled in MATH 999 Doctoral Dissertation. The dissertation is a written piece of original mathematics that demonstrates a doctoral candidate's mastery of the subject matter. A student is expected to produce new and original research worthy of publication in a peer-reviewed journal. After the dissertation is completed, the committee will review the dissertation and examine the student in a public oral thesis defense.