Nov 28, 2024

2013-2014 Graduate Catalog

2013-2014 Graduate Catalog [ARCHIVED CATALOG]

Doctor of Philosophy in Applied Mathematical Sciences

Print Degree Planner (opens a new window) |

Department of Mathematics and Statistics
368 Science and Engineering Building (map)
(248) 370-3430 • Fax (248) 370-4184
http://www.oakland.edu/math/

► Apply Online

► Class Schedule Search

Graduate Coordinator:
Meir Shillor
554 Science and Engineering Building
(248) 370-3439
shillor@oakland.edu

Program description

The Doctor of Philosophy in applied mathematical sciences degree program is designed with three specialization areas in applied mathematical sciences: applied continuous mathematics, applied discrete mathematics, and applied statistics. The program prepares students for employment in business, industry, or government, as well as traditional academic positions.

Admission terms and application deadlines

Before an applicant’s file can be reviewed for full program admission, all application documents must be received in Graduate Study and Lifelong Learning by the semester deadlines listed below. Incomplete applications will not be sent to departments for admission review.

July 15 for fall semester
November 15 for winter semester
March 15 for summer semester

Readmission and program transfer

Requests for readmission and program transfers must be completed and approved prior to the beginning of a semester.

International application deadlines

International applications are reviewed for fall and winter admission only. To ensure adequate time for review, international applications must be completed at least six months before the desired date of intended enrollment in the University. All international application materials must be submitted by May 1 for fall admission and by September 1 for winter admission. International applicants are not eligible for Special Graduate classification.

Application requirements

To be considered for graduate admission, applicants must submit all of the following University and Program application documents by the published application deadlines:

University graduate application requirements

Online Application for Admission to Graduate Study
Official transcripts providing evidence of an earned baccalaureate degree from an accredited U.S. institution, OR a degree equivalent to a four-year U.S. baccalaureate degree from a college or university of government-recognized standing.
Official transcripts for all post-secondary educational institutions from which the applicant earned a degree (beginning with the first baccalaureate) and for all enrollment in graduate-level coursework beyond the bachelor’s degree. International university transcripts must be evaluated by a professional credential evaluation service.
- As part of the admission requirements, graduate programs may require official transcripts from post-secondary educational institutions from which the applicant earned an associate’s degree and all enrollment in coursework both pre- and post-bachelor’s degree.
Two official and original Recommendation for Graduate Admission forms.
(Note: Some programs require more than two recommendation forms. Refer to the program application requirements listed below for additional requirements.)
Proof of English language proficiency
International supplemental application and supporting documentation must be submitted before international applicants can be issued the Certification of Eligibility (I-20). This certificate is required to apply for a student visa from the U.S. embassy or consulate.

Program application requirements

Additional Recommendation for Graduate Admission form
In addition to the two recommendations listed above, a third recommendation is required by the program.
Recommendation requirements
All three forms must be from individuals who are capable of evaluating scholarly achievements and potential for independent research.
Official results of the Graduate Record Examination (GRE) may be required.
The Test of English as a Foreign Language (TOEFL) must be submitted by applicants who are graduates of programs taught in a language other than English
A brief personal statement (not more than 500 words) describing their goals in pursuing the Ph.D. Applicants who wish to be considered for a teaching assistantship should also describe any prior teaching experience or other potentially relevant background. All application materials must be received no later than the beginning of March in order to be considered for a teaching assistantship appointment for the following academic year.
A bachelor’s degree from a regionally-accredited institution with at least a 3.0 grade-point average, with a major in one of the mathematical sciences, engineering, computer science, the physical sciences, the biological sciences, or the health sciences
Knowledge of a scientific programming language is strongly recommended

Admission review and assessment

Admission to graduate study at Oakland University is selective. In making admission recommendations to Graduate Study and Lifelong Learning, each department assesses the potential of applicants for success in the program by examining their undergraduate records, goal statement, letters of recommendation, prerequisite courses and any other admission requirements established by the academic department.

Specific course prerequisites for regular admission into the program (with relevant Oakland University course numbers) include:

Multivariable Calculus (MTH 254)
Linear Algebra (MTH 275)
Advanced Calculus (MTH 452)

In addition, there are specialization prerequisites (with relevant Oakland University course numbers):

a. Applied Continuous Mathematics

Differential Equations (required prerequisite) (APM 255)
Complex Variables (recommended prerequisite) (MTH 352)

b. Applied Discrete Mathematics

Abstract Algebra (MTH 475)
Discrete Mathematics (APM 263)

c. Applied Statistics

Twelve credits in statistics are required. Example:

STA 226, Applied Probability and Statistics (4 credits)
STA 402, Applied Linear Models I (4 credits)
STA 403, Applied Linear Models II (4 credits)

Students who lack the necessary background may need to complete a few prerequisite undergraduate courses prior to regular admission into the program.

Degree requirements

A minimum of 90 credits beyond the bachelor’s degree is required for the Doctor of Philosophy in applied mathematical sciences degree consisting of 60 credits (15 courses) of coursework, 3 credits of APM 695 or STA 695 (Problem Solving Seminar) and 27 credits of APM 790 or STA 790 (Dissertation Research).

Students who have earned a master’s degree may petition to have prior coursework applied toward the 60 credits. The Committee on Graduate Programs will evaluate the student’s prior master’s degree work and allow Ph.D. credits for courses judged to be relevant to the proposed Ph.D. course of study. A maximum of 32 credits may be applied; all candidates must complete at least 28 credits of additional coursework exclusively at Oakland University.

In the Ph.D. program, courses awarded a grade of less than 3.0 will not count toward the degree: however, all numerical grades earned are used in computing a student’s GPA, and an overall 3.0 GPA must be maintained.

Course requirements

The course requirements and options for each specialization are as follows:

1. Applied Statistics Specialization

a. Specialization requirements

Nine courses are required in the applied statistics specialization consisting of:
STA 613 - Mathematical Statistics I (4 credits)
STA 614 - Mathematical Statistics II (4 credits)
STA 527 - Linear Statistical Models (4 credits)
and six courses selected from the following list; these six courses must include one of the following sets of courses: (STA 515 , STA 615 ), (STA 521 , STA 621 ), (STA 528 , STA 628 ), (STA 530 , STA 630 )
STA 503 - Applied Linear Models II (4 credits)
STA 504 - Discrete Data Analysis (4 credits)
STA 506 - Statistical Computing (4 credits)
STA 515 - Stochastic Processes I (4 credits)
STA 521 - Multivariate Statistical Methods I (4 credits)
STA 522 - Statistical Process Control (4 credits)
STA 526 - Nonparametric Methods (4 credits)
STA 528 - Reliability and Life Data Analysis I (4 credits)
STA 529 - Statistical Methods in Sample Surveys (4 credits)
STA 530 - Time Series I (4 credits)
STA 531 - Bayesian Data Analysis (4 credits)
STA 603 - Advanced Design of Experiments (4 credits)
STA 610 - Probability Theory (4 credits)
STA 615 - Stochastic Processes II (4 credits)
STA 621 - Multivariate Statistical Methods II (4 credits)
STA 628 - Reliability and Life Data Analysis II (4 credits)
STA 630 - Time Series II (4 credits)
In addition, the requirements include completion of at least 3 credits (included in dissertation research credit requirements) of the following 1-credit seminar:
APM 695 - Problem Solving Seminar (1 credit)

b. Distribution requirements

Two courses are required in the applied continuous mathematics area consisting of:
MTH 551 - Real Analysis (4 credits)
and one other course selected from the applied discrete mathematics specialization list (4 credits).

Two courses are required in the applied discrete mathematics area consisting of:
APM 563 - Applied Mathematics: Discrete Methods I (4 credits)
and one other course selected from the applied discrete mathematics specialization list (4 credits).

In addition, there are two free elective courses for a total of fifteen courses to satisfy the 60-credit course requirement, exclusive of dissertation research credit.

c. Exit

APM 790 - Doctoral Dissertation Research (27 credits)
or
STA 790 - Doctoral Dissertation Research (27 credits)

2. Applied Discrete Mathematics Specialization

a. Specialization requirements

Nine courses are required in the applied discrete mathematics specialization consisting of:
APM 568 - Mathematical Modeling in Industry: Discrete Models (4 credits)
APM 569 - Graph Theory and Applications (4 credits)
APM 664 - Combinatorial Optimization (4 credits)
MTH 571 - Algebra I (4 credits)
MTH 572 - Algebra II (4 credits)
and four courses selected from the following list:
APM 564 - Applied Mathematics: Discrete Methods II (4 credits)
APM 567 - Algorithms and Complexity (4 credits)
APM 577 - Computer Algebra (4 credits)
APM 581 - The Theory of Computation (4 credits)
APM 665 - Approximation and Randomized Discrete Algorithms (4 credits)
APM 673 - Coding Theory (4 credits)
MOR 554 - Linear and Integer Optimization (4 credits)
MOR 555 - Nonlinear Optimization (4 credits)
MTH 670 - Algebraic Number Theory (4 credits)
In addition, the requirements include completion of at least 3 credits (included in dissertation research credit requirements) of the following 1-credit seminar:
APM 695 - Problem Solving Seminar (1 credit)

b. Distribution requirements

Two courses are required in the applied statistics area consisting of:
STA 613 - Mathematical Statistics I (4 credits)
and one other course selected from the Applied Statistics specialization list (4 credits)
Two courses are required in the applied continuous mathematics area consisting of:
MTH 551 - Real Analysis (4 credits)
and one other course selected from the applied continuous specialization list (4 credits)

In addition, there are two free elective courses for a total of fifteen courses to satisfy the 60-credit course requirement, exclusive of dissertation research credit.

c. Exit

APM 790 - Doctoral Dissertation Research (27 credits)
or
STA 790 - Doctoral Dissertation Research (27 credits)

3. Applied Continuous Mathematics Specialization

a. Specialization requirements

Nine courses are required in the applied continuous mathematics specialization consisting of:
APM 533 - Numerical Methods (4 credits)
APM 557 - Advanced Partial Differential Equations (4 credits)
APM 658 - Mathematical Modeling in Industry: Continuous Models (4 credits)
MTH 551 - Real Analysis (4 credits)
MTH 651 - Functional Analysis (4 credits)
and four courses selected from:
APM 534 - Applied Numerical Methods: Matrix Methods (4 credits)
APM 553 - Advanced Ordinary Differential Equations (4 credits)
APM 566 - Computational Geometry (4 credits)
APM 634 - Numerical Methods for Partial Differential Equations (4 credits)
APM 605 - Applied Continuous Mathematics: Selected Topics (4 credits)
MOR 558 - Mathematical Modeling in Industry: Operations Research Models (4 credits)
MTH 555 - Complex Analysis (4 credits)
In addition, the requirements include completion of at least 3 credits (included in dissertation research credit requirements) of the following 1-credit seminar:
APM 695 - Problem Solving Seminar (1 credit)

b. Distribution requirements

Two courses are required in the applied statistics area consisting of:
STA 613 - Mathematical Statistics I (4 credits)
and one other course selected from the applied statistics specialization list (4 credits)

Two courses are required in the applied discrete mathematics area consisting of:

APM 563 - Applied Mathematics: Discrete Methods I (4 credits)
and one other course selected from the applied discrete mathematics specialization list (4 credits)

In addition, there are two free elective courses for a total of fifteen courses to satisfy the 60-credit course requirement, exclusive of dissertation research credit.

c. Exit

APM 790 - Doctoral Dissertation Research (27 credits)
or
STA 790 - Doctoral Dissertation Research (27 credits)

Satisfactory academic progress

Satisfactory Academic Progress (SAP) is the term used to denote a student’s successful completion of coursework toward a certificate or degree. Federal regulations require the Office of Financial Aid to monitor Satisfactory Academic Progress for all financial aid recipients each semester.

Students who fall behind in their coursework, or fail to achieve minimum standards for grade point average and completion of classes, may lose their eligibility for all types of federal, state and university aid. Contact the Office of Financial Aid for additional details.

Good academic standing

All graduate students are expected to remain in good academic standing throughout the entire course of their graduate program. To be in good academic standing, a graduate student must make satisfactory progress toward fulfilling degree requirements, including the completion of critical degree milestones as set forth by the academic program. The student must also maintain a minimum semester and overall GPA of 3.0.

Good academic standing is a requirement for:

Holding a Graduate Assistantship
Receiving a fellowship or scholarship
Advancing to candidacy for a graduate degree
Going on a leave of absence
Obtaining a graduate certificate or degree from Oakland University.

Additionally, graduate students must meet all department academic standards which may be more stringent than the minimum set forth by the University.

Department requirements: In the Ph.D. program, courses awarded a grade of less than 3.0 will not count toward the degree: however, all numerical grades earned are used in computing a student’s GPA, and an overall 3.0 GPA must be maintained.

Graduate students who are not in good academic standing for any reason are subject to probation and/or dismissal from further graduate study.

Related program information

Plan of study

All accepted applicants, in consultation with their assigned faculty program adviser, must develop a plan of study that details specific courses the students will use to satisfy their degree requirements. The plan of study must be approved by the faculty program adviser and submitted to Graduate Study and Lifelong Learning.

Master’s and graduate certificate students must submit a department-approved plan of study by the end of their first semester of graduate coursework. Doctoral students must submit an approved plan of study prior to completion of the first year of coursework.

General examination and dissertation

The General Examination is intended to assess the student’s overall knowledge of mathematical sciences at the graduate level and the student’s ability to pursue the doctoral degree in his or her selected specialization. The General Examination is administered by the Committee on Graduate Programs and consists of two parts:

Part I consists of three written section exams and is offered once near the beginning of the fall term (normally in August) and once near the beginning of the winter term (normally in January). Each section exam covers material in one of the areas of continuous mathematics, discrete mathematics and statistics.
Part II of the General Examination may only be attempted after passage of Part I. Part II consists of a single written exam and is offered within a month after the results of Part I are announced. The material covered in this single exam involves only the area of the student’s prospective specialization.

Both parts of the General Examination must be passed within 13 months of the initial attempt at Part I, and a student may attempt each part of the General Examination no more than twice.

Detailed guidelines about the material to be covered on both parts of the General Examination are available from the Graduate Coordinator. Exception to the above must be approved by the Committee on Graduate Programs.

A student must have completed at least 12 credits of graduate coursework at Oakland with a GPA of 3.0 or better before taking the General Examination. No student with a GPA below 3.0 will be permitted to take the General Examination. Students in the Ph.D. program will not be allowed to accumulate more than 32 credits toward the Ph.D. degree without taking the General Examination. A student must have passed the General Examination to be eligible to register for Doctoral Dissertation Research.

Dissertation committee

Each student who has passed the General Examination will have a dissertation committee prior to registration for doctoral research credit.

The dissertation committee will be appointed by the Committee on Graduate Programs, with the approval of Graduate Study and Lifelong Learning. The dissertation committee will consist of five faculty members, at least three of whom will be in the specialization area of the student. Prior to the formation of the committee, the student will nominate one faculty member from the student’s area of specialization with the concurrence of the faculty member. At least one member of the committee will be selected by the Committee on Graduate Programs from faculty in the department but outside the student’s area of specialization. The chair of the dissertation committee will be the intended supervisor of the doctoral dissertation for the student and is normally the faculty member nominated by the student. The membership of the committee may be changed by action of the Committee on Graduate Programs, with the approval of Graduate Study and Lifelong Learning.

Final oral examination and dissertation defense

The chair of the dissertation committee is responsible for keeping the committee members informed about the progress of the dissertation research and making preliminary drafts of the dissertation available to all members of the dissertation committee in a manner which permits timely suggestions for improvements. When the chair of the committee determines that the dissertation is ready for oral presentation, the chair will request that a colloquium talk be scheduled where the student presents the dissertation. Immediately following the colloquium, the committee will continue an oral examination of the candidate. Others are welcome to attend this portion of the final examination, with the consent of the candidate and the committee. When this oral examination is concluded, the committee will meet privately and decide whether the candidate, with possible modifications in the dissertation, will be recommended by the committee to receive the Ph.D. Every member of the committee must be present at the oral examination and be willing to sign the dissertation (after suitable and specified modifications, if any) for the student to pass this final oral examination.

Residency requirements

A minimum residency requirement is full-time residency (a minimum of 8 credits per semester) for at least three consecutive full semesters (fall-winter-fall, fall-winter-summer, winter-summer-fall, etc.) with at least two of these devoted to dissertation research. The demands of this research activity imply that the student may not be employed in work which is not directly related to dissertation research, for more than 20 hours a week while satisfying this residency requirement. Petitions for exceptions to this policy may be submitted to the Committee on Graduate Programs.

Continuous enrollment

The continuous enrollment policy for doctoral students requires continuous registration of graduate students for at least 1 credit each semester in the academic year to maintain an active graduate student status. This includes semesters in which the comprehensive, preliminary or qualifying examination is taken, defense, and each subsequent term (fall and winter) until the degree requirements are met and the dissertation is submitted to Graduate Study and Lifelong Learning.

Some agency and graduate assistantship eligibility may have course-load requirements that exceed the minimum registration requirements of the Continuous Enrollment Policy (e.g., Veterans Affairs, Immigration and Naturalization for international students, and federal financial aid programs). Therefore, it is the student’s responsibility to register for the appropriate number of credits that are required for funding eligibility and/or compliance as outlined by specific agency regulations under which they are governed.

Time to degree

The maximum time limit for completing a Ph.D. degree program is no more than ten years from the term of the first course enrollment in the doctoral program.

The time limit for completing a Ph.D. degree requires a student to achieve candidacy within six years from the first course enrollment in the doctoral program. After being advanced to candidacy, a student is expected to complete the remaining degree requirements within four years (including the dissertation defense).