2011-2012 University Catalog 
  
2011-2012 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

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 familiarity with basic group theory (such as presented in 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.

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.

Preliminary Written and Qualifying Exams

Students are required to take a preliminary written exam after completing the core courses, usually by the end of their second year. The exam is based on material presented in three of their four core courses (the student may choose which topic to exclude). These exams are offered two times a year. Students may take the exam as often as they like. A grade of “pass” on the preliminary written exam is sufficient to satisfy the creative component of the master’s degree in mathematics.

Students are required to take a qualifying exam after passing the preliminary written exam. This exam will have oral and written components. 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). The qualifying exam will cover the equivalent of approximately four courses of material from the major area and three courses from the minor area.

Dissertation and Committee

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.

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.

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 and actuarial classes MATH 653, 654, and 655 cannot be used for credit toward a PhD in mathematics.

Students must complete the following curriculum requirements:

Core Courses (12 credits):


Electives (27-42 credits):


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

Preliminary Written Exam


Students are required to take a preliminary written exam based on material in three core courses of their choice.

Portions of the preliminary written exam may be waived with approval of the graduate coordinator if the student enters the PhD program with a master’s degree in mathematics

Qualifying Exam


Students take a qualifying exam after passing the preliminary exam. The qualifying exam will have oral and written components.

Seminar (6–9 credits):


All PhD students are required to take a 1-credit seminar (MATH 795) each semester. A student entering without a master’s degree in mathematics should expect to take a total of 8 to 9 credits of MATH 795.

Research (12–24 credits):


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.

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