George Mason University 1998-99 Catalog

Catalog Index
Course Descriptions

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Mathematical Sciences

Faculty

Professors: Fischer, Levy, Polyak, Sachs (Chair), Saperstone, Sauer, Shapiro, Struppa

Associate Professors: Alligood, Colonna, Gabel, Kan, Kiley, Kulesza, B. Lawrence, J. Lawrence, Lim, Lin, Morris, Singman, Walnut, Zoltek

Assistant Professor: Peterson

Lecturers: Ailes, Goel, Keller, Kim, Krasnov, Lieberman, Lightbourne, Mannina, Nanry, O'Brien, Orlova-Shokry, Senus, Sklar


Visiting Lecturers: Dick, O'Beirne

Affiliate Associate Professor: Loustaunau


The degree programs in mathematics serve the needs of students with various interests and career goals from business/industry/research to graduate and professional school. Concentrations are available for students in traditional mathematics, actuarial mathematics, or applied mathematics. Students may complement other interests by taking a double major in mathematics and a related field such as finance, economics, physics, computer science, or engineering.

Graduating seniors are required to have an exit interview and to take an assessment exam.

Course Work

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

Undergraduate Programs

B.A. Degree with a Major in Mathematics

In addition to general requirements for a B.A. degree, the following courses are required: MATH 113, 114, 125, 203, 213 or 215, 216, 290, and 322, plus 12 additional credits numbered above 300 for a total of 38 credits in mathematics. CS 112 is recommended.

Students who are pursuing licensure for secondary school mathematics teaching must complete at least 34 credits in mathematics and computer science as prescribed on the mathematics endorsement form available in either this department or the Office of Teacher Education, Graduate School of Education.

B.S. Degree with a Major in Mathematics

In addition to the general requirements for a B.S. degree, the student must select a concentration, either in traditional mathematics, actuarial mathematics, or applied mathematics. Students must complete all course work for their concentration in each of the four groups A, B, C, and D below:

  1. Mathematics Core Curriculum--all concentrations (23 credits): MATH 113, 114, 203, 213 or 215, 216, 290, and 322
  2. Science, Accounting, and Economics Requirement-- (At least one year of laboratory science is required of all concentrations. A second year of science is required for the traditional and applied concentrations, and one year of economics and one semester of accounting are required for the actuarial concentration.)

    Science Requirement

    1. All concentrations--a year of natural science from one of the following four sequences (8-9 credits):

      • BIOL 213 and 303 or 304
      • CHEM 211, 212
      • GEOL 101, 102
      • PHYS 250, 350, 351

    2. Traditional and applied concentrations--a second year from one of the following three options (5-8 credits):
      1. The list above, or

      2. Six credits chosen from more advanced courses in one of the natural science fields represented in the list above (only courses that are acceptable for credit toward the natural science major are permitted), or

      3. PHYS 352, 353.

    Accounting Requirement
    for actuarial concentration (3 credits)

    ACCT 202 (special arrangements may be made to waive ACCT 201 prerequisite)

    Economics Requirement
    for actuarial concentration (6 credits)

    ECON 103, and one of ECON 306, ECON 310, or FNAN 321. (The Economics Department has agreed to waive 104 as a prerequisite for 306.)

  3. Computational Requirements
    1. All concentrations: CS 112 (4 credits)
    2. Actuarial concentration: STAT 362 (3 credits)
  4. Concentrations
    1. Traditional mathematics (24 credits)

      MATH 125, 315, 316; MATH 321 or 431; and 12 credits numbered above MATH 300

    2. Actuarial mathematics (24 credits)

      MATH 351, 352, 551, 554, 555, 556, and six credits from MATH 441, 442, 446, 557, 558, 559

    3. Applied mathematics (24 credits)

      MATH 125, 315, 325, 351, 413, and 414, and six credits numbered above MATH 300

The department recommends that a two-year proficiency in either French, German, or Russian be demonstrated.

MATH 214 is not recommended for mathematics majors. In special circumstances a student may substitute both MATH 203 and 214 for MATH 216. MATH 105, 106, 108, 110, 111, 271, and 272 do not count toward satisfying the requirements for a major in mathematics.

For all students:

  1. Students may not receive credit for
  2. After receiving a grade of C or better in one of the courses listed below in the left column, students may not receive credit for the corresponding course in the right column.
  3. General elective credit awarded by the Office of Admissions for mathematics courses does not fulfill the College of Arts and Sciences analytic reasoning requirement unless explicitly approved by the Department of Mathematical Sciences.

For Nonmajors:

MATH 108, 110, and 111 are designed for students in the social and behavioral sciences. Liberal arts majors are advised to take either MATH 106 or MATH 110 and 111 (MATH 105 does not fulfill the College of Arts and Sciences analytical reasoning requirement). Students in the natural sciences who plan to do graduate work are advised to add to their basic calculus sequence courses from MATH 313, 314, 351, 352, 382, 441, 442, 446, and 447.

Writing-Intensive Requirement

The university requires all students to complete at least one course designated Ñwriting intensiveÉ in their majors at the 300 level or above. However, students majoring in mathematics fulfill this requirement by successfully completing MATH 290.

Minor in Mathematics for Undergraduates in the School of Management

A minor requires 20 credits based on the following courses: MATH 113, 114, 213, 203, and 351 and one course chosen from MATH 352, 441, and 554.

The Math Tutoring Center

The department manages the Math Tutoring Center, which offers free tutoring for first- and second-year math courses. The tutoring is done by faculty and mathematics majors and is available on a drop-in basis throughout the term with daytime and evening hours.

The Math Literacy Center

For a small fee, the Math Literacy Center offers a self-paced, noncredit tutorial program in high school algebra for those students who need to review such material. Special tutors and tutorial software are available to those enrolled in the program. Successful completion of this program makes the student eligible to enroll in either MATH 105 or MATH 108.

Graduate Program

Mathematics, M.S.

The Department of Mathematical Sciences offers courses in pure and applied mathematics leading to the M.S. in Mathematics. The program offers two concentrations: computational and applied mathematics, and actuarial mathematics. The student whose interests fall outside these concentrations may choose the standard option.

The concentration in computational and applied mathematics provides the student with the analytic skills and background in computational techniques most relevant to the needs of business, industry, and government. The large number of high-tech firms, telecommunications firms, and government laboratories in the Washington metropolitan area gives the student an opportunity to gain practical experience and to secure employment after graduation. The concentration in computational and applied mathematics also provides the necessary background for advanced graduate work, in particular for the Ph.D. in Computational Sciences and Informatics.

The actuarial mathematics concentration prepares the student for a career as an actuary. Actuaries are highly paid certified professionals who manage, evaluate, and price risks for insurance companies, pension funds, accounting houses, financial institutions, governmental agencies, and consulting firms. The courses offered in this program cover the material included in some of the exams required for certification as an associated in the Society of Actuaries.

The standard option allows the student some flexibility in designing his or her own program of study. This must be done with the approval of the student's faculty advisor.

Assistantships/Internships

The Department of Mathematical Sciences offers a limited number of merit-based teaching assistantships to students taking at least six graduate credits each semester. Research assistantships are also available as funding permits. Graduate students also have the opportunity to work in the Math Tutoring Center and the Math Literacy Center.

Co-op and internship opportunities are available to all students.

Co-ops provide qualified students with professional, paid work positions related to their interests. Co-ops are available with both private and public sector employers.

Internships are employment situations (paid or unpaid) that help students learn more about and gain experience in their areas of interest. Frequently, internships are project oriented and part time, and last for one semester and/or summer.

Admission Requirements

In addition to fulfilling the admission requirements for graduate study, applicants must have three letters of recommendation. Students intending to go into the actuarial mathematics concentration must have three semesters of calculus, a course in linear algebra, equivalent to MATH 322, and a calculus-based course in probability, equivalent to MATH 351.

All other students must have a course in linear algebra, equivalent to MATH 322, and a course in advanced calculus, equivalent to MATH 315. Students intending to go into the computational and applied mathematics concentration must have some computer knowledge. GRE exams are recommended but not required.

Degree Requirements

Computational and Applied Mathematics Concentration
In addition to fulfilling the degree requirements for graduate study, the candidate must complete the following:

  1. The core requirement for this concentration, which consists of the following four courses: MATH 621 (Algebra I), MATH 675 (Linear Analysis I), MATH 677 (Ordinary Differential Equations) or MATH 678 (Partial Differential Equations), and MATH 685/CSI 717 (Numerical Analysis).
  2. Four approved graduate courses, at least two of which are listed as 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.
  3. The research/creative component of the degree (see description below).
  4. No more than 12 credits earned by transfer credit.
  5. Students are required to become familiar with different computing environments and languages. This computer requirement will be integrated into many courses. Students are encouraged to use the varied computing hardware and software available.

Actuarial Mathematics Concentration
In addition to fulfilling the degree requirements for graduate study, the candidate must complete the following:

  1. The core requirement for this concentration, which consists of the following four courses: MATH 551 (Regression and Time Series), MATH 554 (Mathematics of Compound Interest), MATH 555 (Actuarial Mathematics I), and MATH 556 (Actuarial Mathematics II).
  2. Four approved graduate courses, at least two of which are actuarial 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.
  3. The research/creative component of the degree (see below for description).
  4. No more than 12 credits earned by transfer credit.
  5. Credit for an actuarial course may be granted if the corresponding Society of Actuaries, Casualty Actuary Society, or Enrolled Actuary exam has been passed in the preceding five years.

Standard Program (No Concentration)
In addition to fulfilling the degree requirements for graduate study, the candidate must complete the following:

  1. The core requirement for this program, which consists of the following two courses: MATH 621 (Algebra I) and MATH 675 (Linear Analysis I).
  2. Six approved graduate courses, at least four of which are listed as MATH courses. All six courses must be approved by the student's advisor. Courses not listed as MATH courses must be approved by the Graduate Committee.
  3. The research/creative component of the degree (see description below).
  4. No more than 12 credits earned by transfer credit.

Research/Creative Component

Thesis Option

The thesis option is particularly recommended for those students who wish to develop and document their research skills (e.g., for employment purposes), and/or who contemplate subsequent enrollment in a Ph.D. program. The thesis should reflect a significant independent research effort and demonstrate the student's ability to apply his or her mathematical knowledge to research problems. The student is required to make an oral defense of the thesis.

The thesis work is expected to be completed while the student is taking six credits of MATH 799. The student may register for more than six credits of MATH 799, but only six credits will be applied toward the degree.

The thesis work is to be conducted under the guidance of a faculty thesis advisor, and the final written thesis and oral defense are approved by a three-member faculty advising committee, which includes the student's thesis advisor. The student is responsible for forming this advising committee.

All students must present a thesis proposal, which consists of a short written document (approximately five pages) and an oral presentation. The proposal consists of a statement of the problem, a description of the techniques to be used in the investigation, and a statement of anticipated results. The oral presentation is to the advising committee, at least two members of the Graduate Committee, and all other interested parties. Committee members must be provided with the written document at least one week before the oral presentation. Members of the advising committee and of the graduate committee can, at the time of the presentation, ask questions on the core material relevant to the thesis proposal. The thesis proposal must be approved by the advising committee no fewer than three months before the thesis defense.

Nonthesis Option

This option consists of two parts:

  1. At least six additional credits of graduate math courses, including MATH 795 (Seminar in Mathematics).
  2. A comprehensive written exam that covers the material contained in the core courses. The examination will be given twice a year (January and August). This examination is waived for students in the actuarial mathematics concentration.


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