University Catalog > College of Science > Mathematical Sciences

Mathematical Sciences

• Faculty
• Course Work
• Undergraduate Programs
  • Mathematics, BA
  • Mathematics, BS
    • Departmental Nonmathematical Requirements:
    • Mathematical Requirements:
    • General Comments
  • Writing-Intensive Requirement
  • Minor in Mathematics
  • Minor in Mathematics for Undergraduates in the School of Management
  • Math Tutoring Center
  • Math Learning Center
  • Teacher Licensure
  • Mathematics, Bachelor's/Accelerated Master's Degree
• Graduate Programs
  • Mathematics, MS
    • Assistantships
    • Admission Requirements
    • Degree Requirements
    • Emphasis in Computational and Applied Mathematics
  • Research/Creative Component
  • Graduate Certificate in Actuarial Sciences
    • Admission Requirements
    • Requirements
    • Counting Actuarial Courses for Other Mathematics Degrees
    • Counting Actuarial Courses toward the Statistical Sciences MS Degree
  • Certificate in College Teaching
  • Mathematics, PhD
    • Fellowships and Assistantships
    • Admission Requirements
    • Degree Requirements
    • Preliminary Written and Qualifying Exams
    • Dissertation and Committee

Phone: 703-993-1460

Web: math.gmu.edu

Faculty

Professors: Alligood, Colonna, Fischer (chair), Kulesza, B. Lawrence, J. Lawrence, Levy, Morris, Polyak, Sachs, Saperstone, Sauer (COS Distinguished Scholar), Shapiro (undergraduate coordinator), Singman, Soltan, Walnut (graduate coordinator)

Associate professors: Anderson, Gabel, Goldin, Kiley, Lamba, Lim, Lin, Sander, Wanner, Zoltek

Assistant professors: Agnarsson, Griva

Adjuncts: Chouikha, Crain, Ellis, Hiles, Lightbourne, Perencevich, Roberts, Shaw, Wallace, Romanovskaya, Zampedro

Admin Professional: O'Brien

Term instructors: Crossin, Goldman, Granfield, Matveev, Nuttall, O'Beirne, Orlova-Shokry

Affiliates: Loustaunau, Peterson

The department offers undergraduate and graduate degree programs in mathematics for students with various interests and career goals. Students may pursue the standard program or pursue a program focused on either actuarial mathematics or applied mathematics. Students may complement other interests by taking a double major in mathematics and a related field, such as chemistry, economics, physics, computer science, or engineering.

Graduating seniors are required to have an exit interview.

Course Work

The Mathematical Sciences Department offers all course work designated MATH in the Course Descriptions chapter of this catalog.

Undergraduate Programs

Mathematics, BA

In addition to satisfying university-wide general education requirements and requirements for the BA degree in COS, students must present the following:

• 26 credits of required MATH courses: MATH 113, 114, 125, 203, 213 or 215, 214 or 216, 290, and 322
• 12 credits of electives in MATH numbered above 300
• CS 112 is recommended.

The above courses satisfy the university-wide requirement in quantitative reasoning. A maximum of 6 credits of grades below 2.00 in course work designated MATH may be applied toward the major.

Mathematics, BS

Students must pursue one of the following concentrations: traditional mathematics, actuarial mathematics, or applied mathematics. In addition to satisfying the university-wide general education requirements for the BS degree, students majoring in mathematics must present the following. (These courses satisfy the university-wide requirement in quantitative reasoning and natural sciences. A maximum of 6 credits of grades below 2.00 in course work designated MATH may be applied toward the major.)

• Mathematics core requirements: MATH 113, 114, 203, 213 or 215, 214 or 216, 290, and 322
• Science, accounting, and economics requirements:
  • For all students, a one-year sequence of a laboratory science selected from one of the following:
    • BIOL 213, and 303 or 304
    • CHEM 211 and 212
    • GEOL 101 and 102
    • PHYS 160, 260, 261
• Computational requirement: 4 credits of CS 112 for all students; for students in the actuarial concentration, 3 credits of STAT 362
• Program and concentration-specific requirements:

Departmental Nonmathematical Requirements:

• Students with a traditional or applied concentration must select a second year of science from one of the following three options: A second sequence from the list above; 6 credits from more advanced courses in biology, chemistry, geology, or physics (but only courses acceptable for credit toward a natural science major); or the 4-credit option PHYS 262, 263.
• Students with an actuarial concentration must have 3 credits of ACCT 203 and 6 credits of economics, including ECON 103 (3 credits) and either ECON 306 or 310, or FNAN 321. (The Economics Department has agreed to waive ECON 104 as a prerequisite for ECON 306 for mathematics majors.)

Mathematical Requirements:

• Students in traditional mathematics must have 24 credits of MATH (MATH 125, 315, 316, and 321 or 431) and 12 credits of course work above MATH 300.
• Students with an applied mathematics concentration must have 24 credits of MATH (MATH 125, 315, 351, 413, 414, and 446) and 6 credits of course work above MATH 300.
• Students with an actuarial concentration must also have 24 credits of MATH (MATH 351, 352, 551, 554, 555, 556) and 6 credits from MATH 441, 442, or 446.
• The department recommends proficiency in French, German, or Russian.

General Comments

For math majors:

• MATH 105, 106, 108, 110, 111, 112, 271, and 272 cannot be used as substitutes for any requirements of the major in mathematics.

For nonmath majors:

• MATH 108, 110, and 111 are designed for students in the social and behavioral sciences.
• Liberal arts majors are advised to take MATH 106, 110, or 111.
• Students in the natural sciences who plan to do graduate work are advised to add courses from MATH 313, 314, 351, 352, 382, 441, 442, 446, and 447.
• For both majors and nonmath majors:
• MATH 105, 106, 108, 110, 111, 112, 113 have a qualifying score on the Math Placement Test as a prerequisite. The Math Placement Test is given frequently; for the schedule, inquire at the department office or check the Mason web site.
• Students who do not achieve the necessary test score needed to take a math course may go to the Math Learning Center (see below), or they may study and retake the test on their own. If they do not complete the relevant program in the Learning Center or do not achieve the necessary score after retaking the test, they are dropped from the course. Depending on their test scores, students who do not place into MATH 113 will be advised to take MATH 105 or visit the Math Learning Center to prepare for MATH 105.
• MATH 105 does not fulfill the university quantitative reasoning requirement.
• Students may not receive credit for both MATH 214 and 216; both MATH 213 and 215; both MATH 351 and STAT 344; and both MATH 352 and STAT 354.
• After receiving a grade of C or better in one of the courses listed below on the left, students may not receive credit for the corresponding course on the right:
  • MATH 113 MATH 105 or 108
  • MATH 351 or STAT 344 MATH 110
  • MATH 441 MATH 111
  • MATH 125 MATH 112

Writing-Intensive Requirement

Mason policy requires all students to complete at least one course designated as "writing intensive" in their majors at the 300 level or above. Students majoring in mathematics fulfill this requirement by successfully completing MATH 290.

Minor in Mathematics

To receive a minor in mathematics, students must complete 21 credits that include a total of 8 hours of math that are not applied toward the major. These courses must have a minimum GPA of 2.00, distributed as follows:

• five required courses (15 credits): MATH 125, 203, 213 or 215, 214 or 216, and 290
• 3 credits from any math course that requires MATH 290 as a prerequisite
• One elective course in math at the 300 or 400 level, or STAT 344.

Students must earn a 2.00 or better in MATH 290 and the courses chosen to fulfill the second requirement.

Minor in Mathematics for Undergraduates in the School of Management

To receive this minor, students must complete 20 credits with a minimum GPA of 2.00, including MATH 113, 114, 203, 213, and 351; and one course chosen from MATH 352, 441, and 554.

For policies governing all minors, see the Academic Policies chapter of this catalog.

Math Tutoring Center

The department manages the Math Tutoring Center, which offers free tutoring for first- and second-year math courses (math.gmu.edu/tutorcenter.htm). Tutoring is given by advanced mathematics students and available on a drop-in basis with daytime and evening hours throughout the term.

Math Learning Center

The Math Learning Center (math.gmu.edu/mathlearningcenter.htm) for a small fee offers self-paced and classroom noncredit tutorial programs for students who do not place into the math course they need. Special tutors and tutorial software are available to those enrolled in the program. Successful completion of the relevant program enables students to enroll in Math 105, 106, 108, 110, 111, 112, or 125.

Teacher Licensure

Students who wish to become teachers should consult the College of Education and Human Development chapter and attend an information session early in their undergraduate career. For more information, call 703-993-2892, e-mail gseadmit@gmu.edu, or go to gse.gmu.edu.

Mathematics, Bachelor's/Accelerated Master's Degree

This five-year degree program allows academically strong students to obtain a BS and MS by successfully completing 144 credits within five academic years and one summer. Well-prepared students are admitted to this program on completion of 90 credits, take selected graduate courses during their senior year, and are able to use up to 6 graduate credits to partially satisfy requirements for the undergraduate degree. On completion of that degree and with satisfactory graduate-level performance (3.00) in graduate courses, students are given advanced standing in the master's program and complete an additional 24 credits to receive the master's degree. All other master's degree requirements must be met.

Graduate Programs

Mathematics, MS

The Department of Mathematical Sciences offers courses in pure and applied mathematics leading to the master of science degree in mathematics. The program offers a standard mathematics program and an emphasis in computational and applied mathematics.

Assistantships

A limited number of merit-based teaching assistantships are available for students taking at least 6 graduate credits each semester. Other sources of support, such as research assistantships, are available as funding permits. Graduate students also have the opportunity to work in the Math Tutoring Center and Math Learning Center.

Admission Requirements

In addition to fulfilling admission requirements for graduate study, applicants must submit three letters of recommendation. GRE scores are not required.

Students intending to pursue the MS degree must have taken an upper-division course in advanced calculus (equivalent to MATH 315) and an upper-division course in linear algebra (equivalent to MATH 322). Students intending to go into the computational and applied mathematics emphasis must have some computer knowledge.

Degree Requirements

Standard Program

In addition to fulfilling degree requirements for graduate study, students must complete 30 credits distributed as follows:

• 6 credits of MATH 621 and 675
• Six approved graduate courses (18 credits), at least four of which are MATH. All six courses must be approved by the student's advisor. Courses not listed as MATH courses must be approved by the Graduate Committee. Different rules apply if the student wishes to count graduate actuarial courses toward his or her degree (see below).
• Research/creative component (see below).

Emphasis in Computational and Applied Mathematics

The emphasis in computational and applied mathematics provides students with the analytical skills and background in computational techniques most relevant to the needs of business, industry, and government. The large number of high-technology firms, telecommunications firms, and government laboratories in the Washington, D.C., metropolitan area gives students an opportunity to gain practical experience and secure employment after graduation.

In addition to fulfilling degree requirements for graduate study, students must complete 30 credits distributed as follows:

• 12 credits of MATH 621, 675, 677 or 678, and MATH 685
• Four approved graduate courses (12 credits), at least two of which are MATH courses. All four courses must be approved by the student's advisor. Courses not listed as MATH courses must be approved by the Graduate Committee.
• Research/creative component (see below)

Research/Creative Component

A student may fulfill the research/creative component of the MS degree in any one of the following three ways:

• Thesis Option. In preparation for this option, the student must form a committee comprising a chair and two other faculty members. The chair and at least one other member must be from the department; one member may be from a related field.
  
  The student completes a thesis under the direction of the committee chair. The thesis work is typically completed while students are registered for 6 credits of MATH 799. A thesis proposal and thesis are submitted in accordance with university rules. The student must give an oral defense of the thesis to the committee and the Mason community at large. Students are expected to respond to questions on the thesis and related material. The committee determines whether the defense is satisfactory.
• Paper presentation option. In preparation for this option, the student must form a committee comprising a chair and two other faculty members. The chair and at least one other member must be from the department; one member may be from a related field. The student gives an oral presentation of a paper (or series of papers or book chapter) chosen in consultation with the chair of the committee and approved by the full committee. The chosen material must be distinct from work done in fulfillment of course requirements. Students choosing this option take 6 additional credits of electives. The oral presentation is given to the committee and the Mason community at large. Students are expected to respond to questions on the paper and related material. The committee determines whether the defense is satisfactory.
• Preliminary exam for the PhD. The research/creative component of the MS degree can be fulfilled by passing the preliminary written examination for the PhD degree (see below).

Graduate Certificate in Actuarial Sciences

The certificate in the actuarial sciences is designed to serve students and professionals in the Washington, D.C., area who are interested in pursuing careers as actuaries. The course content provides students with specific training related to the Society of Actuaries (SOA) Exam FM (formerly Course 2), SOA Exam M (formerly Course 3), SOA Exam C (formerly Course 4), VEE for applied statistics (formerly part of Course 4), and Exam EA-1 and EA-1A (for those pursuing EA designation from the U.S. Treasury). The courses also provide a solid foundation for the corresponding Casualty Actuary Society (CAS) exams. Preparation for the first exam is achieved in meeting the prerequisites for the certificate courses in the area of probability and statistics.

Admission Requirements

In addition to fulfilling admission requirements for graduate study, applicants must submit three letters of recommendation. GRE scores are not required.

Students intending to pursue a certificate in the actuarial sciences must have three semesters of calculus, a course in linear algebra (equivalent to MATH 203), a calculus-based course in probability (equivalent to MATH 351), and statistics (equivalent to MATH 352). Completion of the SOA Exam P is also sufficient preparation for the certificate program.

Requirements

Students must complete six courses (18 credits): MATH 551, 554, 555, 556, and two courses chosen from MATH 653, 654, or 655 (MATH 655 is recommended only for students who wish to pursue a career as a pension actuary). Substitutions for the elective courses may be made with approval of the Graduate Committee. The graduate certificate course work provides preparation for SOA and CAS exams as follows. MATH 551 is the SOA VEE for Applied Statistics and is preparation for part of the CAS Exam 3. MATH 554 covers all of the SOA Exam FM material (as well as CAS Exam 2). MATH 555, 556, and 653 cover all of the Exam M material and much of the CAS Exam 3 as well as the EA1 exam. MATH 654 covers most of the SOA Exam C material (as well as CAS Exam 4). MATH 655 covers all of the EA2-A Exam material and some of the SOA Exam 8.

Counting Actuarial Courses for Other Mathematics Degrees

A student enrolled in the certificate program in actuarial sciences and another graduate degree program in mathematics can count actuarial mathematics courses toward that degree according to the following rules:

• None of the actuarial mathematics courses MATH 551, 554, 555, 556, 653, 654, and 655 can count toward the PhD degree in mathematics.
• None of the actuarial mathematics courses MATH 551, 554, and 655 can count toward the MS degree in mathematics.
• Up to four of the actuarial mathematics courses MATH 555, 556, 653, and 654 can count toward the MS degree in mathematics provided that all other courses counted toward that degree are MATH courses. An exception can be made if the student wishes to count only one actuarial mathematics course from the list toward the MS degree. In this case, at most one other non-MATH course can be counted toward the degree with approval of the graduate coordinator.

Counting Actuarial Courses toward the Statistical Sciences MS Degree

A student enrolled in the certificate program in actuarial sciences and in the MS program in statistical science can count MATH 555 and 556 as approved non-STAT elective courses and can count MATH 653 and 654 as STAT electives when designing a curriculum for this degree. The full curriculum should be designed in consultation with the student's Statistics Department advisor.

Certificate in College Teaching

A student enrolled in the MS or PhD program in mathematics primarily interested in pursuing a career in undergraduate education at the community college or four-year college level is encouraged to consider enrolling in the higher education program's college teaching certificate.

Students must complete 18 credit hours as follows: CTCH 601, 602, 603, 604, 885, and 3 credits of CTCH electives. Credit can be earned for CTCH 885 (Internship) by working one semester as a graduate teaching assistant in the Mathematics Department.

Mathematics, PhD

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.

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.

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.

Degree Requirements

The program requires 72 credits beyond the baccalaureate degree, with a minimum of 48 credits in course work and 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. Students must complete the following curriculum requirements:

• Core courses: 12 credits in MATH 621, 631, 675, and 677
• Seminar (MATH 795): 6-9 credits
• Preliminary written exam based on material in three core courses
• Qualifying exam
• Dissertation proposal and research: 12-24 credits of MATH 998 and 999

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. 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. 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.

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 the four required 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.