Graduate Programs
M.A. Coordinator: Phillip E. Johnson
MASTER OF ARTS DEGREE IN MATHEMATICS
The Master of Arts degree in Mathematics is designed both to provide
advanced skills and knowledge for persons seeking either positions
in industry or in government, or teaching positions at the community
college level, and to provide professional development to persons
currently in such positions. Graduates of the program also are
prepared to enter directly into at least the second year of a
Ph.D. program in mathematics, applied mathematics or statistics,
depending on the particular course of study.
Additional Requirements for Admission into the M.A. Program
in Mathematics. In addition to the general requirements for
admission to the Graduate School, the following are required for
graduate study in Mathematics:
Group I Applied Mathematics:
Comprehensive Examination. Each candidate must perform
satisfactorily on an oral comprehensive examination over the candidate's
program of study.
Additional Requirements for Admission into the M.A. Program
in Mathematics Education. In addition to the general requirements
for admission to the Graduate School, the following are required
for graduate study in Mathematics Education:
Comprehensive Examinations. Each student must pass a comprehensive
examination, including an oral examination, on the overall work
presented for the degree.
Additional Requirements for Admission into the M.S. Program
in Applied Statistics. In addition to the general requirements
for admission to the Graduate School, the following are required
for graduate study in Applied Statistics:
Core Requirements (24 semester hours)
Research Seminar and Thesis Option (3 semester hours)
Students who, because of their undergraduate work or other experience,
can demonstrate sufficient knowledge of the material in one or
more of the core courses may be exempted from taking the course
or courses. Exemption from a course carries no credit towards
the degree.
All candidates for the Master of Science degree in Applied Statistics
are required to complete 3 hours of MATH 7691 (Research Seminar)
in which they carry out an independent project under the supervision
of a member of the graduate faculty. The project could involve
a specific application of techniques identified in the literature
or studied in other courses. All projects are subject to the prior
approval of the department Graduate Committee and must be successfully
defended before a committee of three graduate faculty members
appointed by the department Graduate Committee.
A student may choose to expand the work begun in MATH 7691 (Research
Seminar) into a Master's Thesis by registering for 3 hours of
MATH 7893 (Thesis) to fulfill the elective requirement under (2)
above. This thesis option affords the student the opportunity
to do professional and scholarly work demonstrating proficiency
in the area of applied statistics.
Comprehensive Examination. Each candidate for the Master
of Science degree in Applied Statistics must perform satisfactorily
on an oral comprehensive examination over the candidate's program
of study.
Additional Requirements for Admission into the Ph.D. program
in Applied Mathematics. In addition to the requirements of
the Graduate School for admission to doctoral study, applicants
must have completed at least 27 hours of courses in the mathematical
sciences at the undergraduate level, as approved by the department
Graduate Committee, with grades of C or better. Admission
requires that the candidate be able to take Real Analysis 7143
(or its equivalent). Applicants who have not completed the equivalent
of MATH 5143-5144 but whose record is otherwise satisfactory may
be admitted to one of the master's programs in the department.
For prospective students who have done work in mathematics beyond
the bachelor's degree, performance on that work will be considered
in admissions decisions. Candidates for admission must make satisfactory
scores on both the aptitude portion of the Graduate Record Examination
(GRE) and the subject test in mathematics.
Students are admitted to the program by the Graduate School, based
on the recommendation of the department Graduate Committee or
its designate, the Graduate Program Coordinator. Recommendations
are based on the Committee's judgement of the candidate's ability
to complete the program, as supported by the application materials.
The department may waive certain requirements if it judges the
candidate to be capable of completing the program. If there are
more candidates than can be accommodated, candidates are admitted
in order of perceived mathematical ability, promise of success,
and suitability to the program.
Degree Requirements
Program of Study.The student must complete an approved
program of study, including a minor, typically including approximately
54 credit hours. The minor is interdisciplinary and may be satisfied
by 9 hours of course work outside the mathematics department,
by 6 credit hours for a project in an area of application, or
by a combination of external coursework and directed project in
an area of application totaling 9 credit hours.
Each student will have an advisory committee appointed by the
department Graduate Committee in consultation with the student
and approved by the Department Chair. It includes the prospective
dissertation adviser as chair, or co-chair, if the dissertation
adviser is not a member of the Department of Mathematics. The
advisory committee should be appointed as soon as is feasible,
usually within a year after passing the Preliminary Examination.
It will have the responsibility of constructing and approving
the program of study which includes the minor. Prior to the appointment
of the advisory committee the student will be advised by a graduate
faculty member appointed by the department Graduate Committee.
Grades. A student is expected to achieve A's or B's in
all courses included in the program of study and must have at
least a 3.0 GPA to graduate. The dissertation is graded on a pass/unsatisfactory
basis and, therefore, will not be included in the cumulative average.
An accumulation of more than two marginal (C) grades will
result in termination of the student's enrollment in the program.
If a student makes a grade of U on any course, enrollment
will be terminated and the student cannot take further graduate
work without being readmitted to the program. Readmission to the
program requires approval of the Dean of the Graduate School upon
the recommendation of the department Graduate Committee.
Transfer Credit. Only courses with grades of A or B may
be accepted for transfer credit. Transfer credit must be approved
by the department Graduate Committee, and cannot exceed the limit
set by the Graduate School.
Preliminary Examination. The student is expected to take
the preliminary examination within three semesters of being admitted
to the Ph.D. program. The examination consists of two parts: a
written examination based on Real Analysis I and II (7143-7144)
and a written examination based on two other related courses chosen
by the student and approved by the department Graduate Committee.
The student must pass both examinations in a single attempt in
order to pass the preliminary examination. At the discretion of
the department Graduate Committee, the student passing only one
part of the examination on the first attempt may be allowed to
retake the preliminary examination a second time. A student who
fails the preliminary examination twice is disenrolled from the
Ph.D. program.
Qualifying Examination and Admission to Candidacy.
Each student must pass a comprehensive oral examination covering
her/his chosen field of research and related advanced course work.
The exam is conducted by the student's Advisory Committee and
may include an additional written examination. The exam is open
to the graduate faculty of the department. The student is expected
to take the qualifying examination within two years of the appointment
of the student's Advisory Committee. A student who fails the qualifying
examination twice is disenrolled from the Ph.D. program. The dissertation
topic may be proposed after the student has passed the qualifying
examination. A doctoral student advances to candidacy after the
dissertation topic has been approved by the student's advisory
committee and the dean of the Graduate School.
Dissertation. The student must complete and defend a dissertation
based on a research program approved by the student's dissertation
adviser which results in a high quality, original and substantial
piece of research. The student must orally present and successfully
defend the dissertation to the Dissertation Defense Committee
in a defense that is open to the public. A copy of the dissertation
must be made available to the graduate faculty of the department
at least two weeks prior to the public defense. The dissertation
will be graded on a pass/no credit basis by the Dissertation Defense
Committee and must be approved by the Department Chair and the
Dean of the Graduate School.
Residency Requirement. The student must enroll
for one continuous full-time year (i.e. two consecutive semesters
of at least nine graduate credit hours in each semester) following
admission to the program.
Language and Research Tool Requirements. Each student must
demonstrate a reading knowledge of French, German or Russian by
passing a written translation exam in one of these languages conducted
by the Mathematics Department. In addition, the student must demonstrate
significant computer expertise applicable to research or teaching
in his or her major field as approved by the student's Advisory
Committee. The computer expertise requirement may include course
work or work on a project and may overlap with the minor requirement.
Time Limit for Degree Completion. The student must achieve
admission to candidacy within six years after admission to the
program and complete all requirements within six years after admission
to candidacy for the Ph.D. degree. All requirements for
the degree must be completed within eight years after first registration
as a doctoral student.
Mathematics Education
Degree Requirements. The Master of Arts degree in Mathematics
requires successful completion of at least 30 semester hours of
graduate work approved by the department Graduate Committee including:
MATH 5143 and 5144 or their equivalents, at least one course each
from two of the groups I, II, III, and V, and at least 15 hours
in 7000-level courses. With the approval of the department Graduate
Committee, one 3-hour, non-thesis 6000-level course in computer
science of a theoretical nature may be applied toward the 15 hours.
Candidates for the degree must demonstrate, to the satisfaction
of the department Graduate Committee, competence on the general
knowledge in at least three of five groupings of courses listed
below. This may be accomplished by (a) successful performance
on a written comprehensive examination or (b) successful completion
of courses in these areas.
OPRS 4113 Game Theory (3G)
OPRS 4114 Dynamic Programming (3G)
OPRS 5111 Linear Programming (3G)
OPRS 5112 Non-Linear Programming (3G)
MATH 5165 Numerical Linear Algebra (3G)
MATH 5172 The Finite Element Method (3G)
MATH 5173 Ordinary Differential Equations (3G)
MATH 5174 Partial Differential Equations (3G)
MATH 5176 Numerical Methods for Partial Differential Equations
(3G)
MATH 7172 Partial Differential Equations (3G)
MATH 7176 Advanced Numerical Analysis (3G)
MATH 7177 Applied Optimal Control (3G)
MATH 7178 Comp. Methods for Fluid Dynamics (3G)
MATH 7273 Advanced Finite Element Analysis (3G)
Group II Probability-Statistics:
STAT 5123 Applied Statistics I (3G)
STAT 5124 Applied Statistics II (3G)
STAT 5126 Theory of Statistics I (3G)
STAT 5127 Theory of Statistics II (3G)
STAT 7027 Topics in Statistics (3G)
STAT 7123 Advanced Statistics II (3G)
STAT 7127 Linear Statistical Models (3G)
MATH 5128 Applied Probability I (3G)
MATH 5129 Applied Probability II (3G)
MATH 7120 Probability Theory (3G)
MATH 7121 Statistics (3G)
MATH 7125 Stochastic Processes (3G)
Group III Algebra-Topology:
MATH 4163 Modern Algebra (3G)
MATH 4164 Abstract Linear Algebra (3G)
MATH 4181 Introduction to Topology (3G)
MATH 7163 Modern Algebra I (3G)
Group IV Analysis:
MATH 5143 Analysis I (3G)
MATH 5144 Analysis II (3G)
MATH 7141 Complex Analysis I (3G)
MATH 7143 Real Analysis I (3G)
MATH 7144 Real Analysis II (3G)
Group V Computer Science:
All 5000- and 6000-level Computer Science courses.
Thesis. Completion of a thesis is optional. With the approval
of the department Graduate Committee, a candidate may receive
up to six of the 15 hours required at the 7000 level for the writing
of a master's thesis on an approved topic. This thesis may be
original work, work of an expository nature, or the mathematical
formulation and solution of a particular industrial or business
problem suggested by the career interests of the student. A candidate
may receive no more than six of the hours required at the 7000
level for course and thesis work in computer science. If the thesis
option is elected, the candidate will be required to defend his/her
thesis in an oral examination.
MASTER OF ARTS DEGREE IN MATHEMATICS EDUCATION
The Master of Arts degree in Mathematics Education is designed
primarily for secondary school teachers interested in professional
growth and graduate certification in mathematics. Emphasis in
this program is given to developing depth and breadth in mathematics
appropriate to the role of the teacher.
Degree Requirements. Each candidate for the degree and
for graduate certification in mathematics must complete at least
30 hours of graduate credit including at least 15 hours in courses
at the 6000-level or above. Programs of study beyond these 30
hours may be required to remove deficiencies in undergraduate
programs or to develop areas of need, interest, or desired experience.
Specific requirements are:
Approval of the program of each student and provision of advice
regarding progress toward the degree are the responsibility of
an adviser appointed by the Department of Mathematics at the time
of admission.
MASTER OF SCIENCE DEGREE IN APPLIED STATISTICS
The Master of Science degree in Applied Statistics is designed
to provide advanced skills and knowledge in the planning, design,
testing, and implementation of statistical methods. These skills
will include those necessary for dealing with the problems encountered
in statistical applications in business, industry and government;
holding administrative positions requiring planning and implementation
of statistical analysis; teaching statistics at the undergraduate
or community college level; and further study in statistics leading
to the Ph.D. degree.
Degree Requirements. A candidate for the Master of Science
degree in Applied Statistics must complete a minimum of 33 semester
hours of graduate work approved by the department Graduate Committee
including:
STAT 5123 Applied Statistics I (3G)
STAT 5124 Applied Statistics II (3G)
STAT 5126 Theory of Statistics I (3G)
STAT 5127 Theory of Statistics II (3G)
STAT 7027 Topics in Statistics (3G)
STAT 7127 Linear Statistical Models (3G)
STAT 7133 Multivariate Analysis (3G)
MATH 7691 Research Seminar (1-3G)
Electives (9 semester hours)
(1) Two course selected from among:
CSCI 5131 Computer Simulation (3G)
STAT 7027 Topics in Statistics (3G)
STAT 7133 Multivariate Analysis (3G)
MATH 5128 Applied Probability I (3G)
MATH 5129 Applied Probability II (3G)
MATH 5143 Analysis I (3G)
MATH 5165 Numerical Linear Algebra (3G)
MATH 7120 Probability Theory I (3G)
MATH 7121 Probability Theory II (3G)
MATH 7143 Real Analysis I (3G)
MATH 7692 Research Seminar (3G)
OPRS 4113 Game Theory (3G)
OPRS 4114 Dynamic Programming (3G)
OPRS 5111 Linear Programming (3G)
OPRS 5112 Non-linear Programming (3G)
(2) Any MATH/STAT/OPRS course at the 7000 level.
DOCTOR OF PHILOSOPHY DEGREE IN APPLIED MATHEMATICS
The Ph.D. degree program in Applied Mathematics is designed to
enable its students to master a significant body of mathematics;
including a specialty in applied mathematics, to relate this knowledge
to a coherent area of science or engineering and to carry on fundamental
research in applied mathematics at a nationally competitive level.
The recipient of this degree will, according to his or her abilities
and choice of sub-specialty, be able to work effectively in a
research and development environment involving mathematical or
statistical analysis and modeling in business, government or industry;
to teach mathematics at the college or university level; or to
carry on fundamental research in his or her area of specialty.