2014-2015 University Catalog 
  
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2014-2015 University Catalog

Mathematics, PhD

Banner Code:  SC-PHD-MATH

The Department of Mathematical Sciences offers a PhD in mathematics. The program begins with graduate course work and advanced seminars and culminates in a thesis consisting of original research in mathematics. The PhD program in mathematics is designed to train students as research mathematicians for careers in academia, government, and private industry.

This program of study is offered by the Department of Mathematical Sciences in the College of Science.

Admission Requirements

Applicants to all graduate programs at George Mason University must meet the admission standards and application requirements for graduate study as specified in the Admission  section of this catalog. 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. Students without this background who have had an upper-division course in linear algebra (equivalent to MATH 322 ), an upper-division course in advanced calculus (equivalent to MATH 315 ), and an upper-division course in group theory (equivalent to MATH 321 ) are encouraged to apply to the MS program in mathematics. Such students may subsequently apply to the PhD program when all background issues have been addressed. It is recommended that all applicants have some familiarity with mathematical software.

To apply, prospective students should forward a completed Mason graduate application, two copies of official transcripts from each college and graduate institution attended, three letters of recommendation, and a goals statement to the COS Fairfax Campus Graduate Admissions Processing Center. TOEFL scores are required for all international applicants. GRE scores are recommended but not required.

Reduction of Credit

For students entering the doctoral program with a master’s degree in a related field from a regionally accredited institution, the number of required credits may be reduced up to 30 credits, subject to approval of the program faculty and the associate dean for student and academic affairs. See the College of Science graduate policies section for more information.

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 and the Math Learning Center.

Degree Requirements

Students must satisfy all requirements for doctoral degrees expressed in the Academic Policies  section of this catalog.

The program requires 72 credits beyond the baccalaureate degree, with a minimum of 48 credits in course work and 12–24 credits of dissertation research. For those holding master’s degrees, the 72 required credits may be reduced by up to 30 credits, depending on graduate courses completed.

Graduate mathematics courses taken elsewhere may be counted toward the degree either as transfer credit or through reduction of credit. Classes at the 500 level, MATH 600  - MATH 614 , and actuarial classes MATH 653 , MATH 654  and MATH 655  cannot be used for credit toward a PhD in mathematics.

Students must complete the following curriculum requirements:

Doctoral Course Work (48-60 credits)

Core Courses (12 credits)

Preliminary Written Exam

Students are required to pass preliminary written exams after completing the core courses, usually by the end of their second year. These exams are based on material presented in three of the five core courses (the student may choose which topics to exclude). These exams are offered twice a year and students may take each exam up to three times. A grade of “pass” on three preliminary written exams is sufficient to satisfy the creative component of the master’s degree in mathematics. 

Dissertation Advisor and Examination Committee

After passing the preliminary written exam, 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).

Seminar (6–9 credits)

All PhD students are required to take a 1-credit seminar each semester until they advance to candidacy or have acquired at least 6 credits of MATH 795 . A student entering without a master’s degree in mathematics should expect to take a total of 6 to 9 credits of MATH 795 .

Electives (27-42 credits)

Students complete 27-42 credits of approved MATH electives. Courses not designated as MATH courses must be approved by the graduate committee.

Qualifying Examinations

Students are required to take a qualifying exam after passing the preliminary written exam. The qualifying exam will 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 cover 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

Approximately one semester 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 thesis committee, which consists of the three qualifying exam committee members, plus a fourth member from outside the department. After successfully completing this requirement, the student advances to doctoral candidacy.

Dissertation Research (12–24 credits)

Doctoral Dissertation

After advancing to candidacy, the student will work on a doctoral dissertation while enrolled in MATH 999  . 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 thesis is completed, the committee will review the thesis and examine the student in a public oral thesis defense.

Total: 72 credits