Department of Mathematics
and Statistics
Mathematics and Science Center, Room 368
146 Library Drive
Rochester, MI 48309-4479
(map)
phone: (248) 370-3430
fax: (248) 370-4184

Hours:
Monday–Friday: 8:00–11:59 a.m. and 1:00–5:00 p.m.

Ph.D. Program

The Ph.D. Program is designed with three specialization areas in applied mathematical sciences: Applied Continuous Mathematics, Applied Discrete Mathematics and Applied Statistics.

Specific course prerequisites for regular admission into the program (with relevant Oakland University course numbers) include courses in Multivariable Calculus (MTH 254), Linear Algebra (MTH 256), and Advanced Calculus (MTH 351). In addition, there are specialization prerequisites of: Differential Equations (APM 257) for Applied Continuous; Abstract Algebra (MTH 475) and Data Structures (CSE 231) for Applied Discrete; and 12 credits in Statistics (e.g., STA 226, STA 322, STA 323) for Applied Statistics. In addition, Complex Variables (MTH 352) is recommended for Applied Continuous. Students who lack the necessary background may need to complete a few prerequisite undergraduate courses prior to regular admission into the program. For detailed admission information, click here.

A minimum of 80 credits beyond the bachelor's degree is required for the Ph.D. degree in Applied Mathematical Sciences. Transfer credits must receive approval by the Committee on Graduate Programs and the Dean of Graduate Study. The total course requirement is 15 courses (60 credits), exclusive of dissertation research credit, with a minimum of 8 courses in the specialization and 2 courses in each of the other areas. There is a minimum of 2 free electives. For each specialization, the course requirements and options are listed below.

Applied Continuous Mathematics Specialization
Specialization requirements:

Nine courses are required in the Applied Continuous specialization consisting of

  1. APM 533, Numerical Methods,
  2. APM 557, Advanced Partial Differential Equations,
  3. APM 566, Computational Geometry,
  4. APM 634, Numerical Methods for Partial Differential Equations,
  5. APM 658, Mathematical Modeling in Industry: Continuous Models,
  6. MOR 554, Mathematical Programming,
  7. MTH 551, Real Analysis,
  8. MTH 651, Functional Analysis,
  9. and one course selected from
    APM 605, Applied Continuous Mathematics: Selected Topics,
    MOR 558, Mathematical Modeling in Industry: Oper. Research Models,
    MTH 555, Complex Analysis.

Distribution requirements:

Two courses are required in the Applied Statistics area consisting of

  1. STA 613, Mathematical Statistics I
  2. and one other course selected from the Applied Statistics specialization list.

Two courses are required in the Applied Discrete area consisting of

  1. APM 563, Applied Mathematics: Discrete Methods I
  2. and one other course selected from the Applied Discrete specialization list.

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.


Applied Discrete Mathematics Specialization

Specialization requirements:

Nine courses are required in the Applied Discrete specialization consisting of

  1. APM 568, Mathematical Modeling in Industry: Discrete Models,
  2. APM 569, Graph Theory and Applications,
  3. APM 664, Combinatorial Optimization 
  4. MTH 571, Algebra I
  5. MTH 572, Algebra II
and four courses selected from the following list
  1. APM 564, Applied Mathematics: Discrete Methods II,
  2. APM 567, Algorithms and Complexity,
  3. APM 577, Computer Algebra,
  4. APM 581 The Theory of Computation
  5. APM 665 Approximation and Randomized Discrete Algorithms
  6. APM 673, Coding Theory,
  7. MOR 554 Linear and Integer Optimization
  8. MOR 555 Nonlinear Optimization
  9. MTH 670, Algebraic Number Theory
  10. MTH 671 Communtative Algebra
  11. MTH 672 Algebraic Geometry

Distribution requirements:

Two courses are required in the Applied Statistics area consisting of

  1. STA 613, Mathematical Statistics I
  2. and one other course selected from the Applied Statistics specialization list.

Two courses are required in the Applied Continuous area consisting of

  1. MTH 551, Real Analysis
  2. and one other course selected from the Applied Continuous specialization list.
In addition, there are three free elective courses for a total of fifteen courses to satisfy the 60 credit course requirement, exclusive of dissertation research credit.

Applied Statistics Specialization

Specialization requirements:

Nine courses are required in the Applied Statistics specialization consisting of

  1. STA 613, Mathematical Statistics I,
  2. STA 614, Mathematical Statistics II,
  3. STA 527, Linear Statistical Models,
  4. and six courses selected from
    STA 504, Discrete Data Analysis
    STA 506, Statistical Computing
    STA 515, Stochastic Processes I,
    STA 521, Multivariate Statistical Methods I
    STA 522, Statistical Process Control,
    STA 526, Nonparametric Methods,
    STA 528, Statistical Methods in Reliability and Life Data I,
    STA 529, Statistical Methods in Sample Surveys,
    STA 530, Time Series I,
    STA 531, Bayesian Data Analysis,
    STA 603, Advanced Design of Experiments,
    STA 615, Stochastic Processes II,
    STA 621, Multivariate Statistical Methods II,
    STA 628, Statistical Methods in Reliability and Life Data II,
    STA 630, Time Series II.

These six courses must include one of the following sets of courses {STA 515, STA 615}, {STA 528, STA 628}, {STA 530, STA 630}.

Distribution requirements:

Two courses are required in the Applied Continuous area consisting of

  1. MTH 551, Real Analysis
  2. and one other course selected from the Applied Continuous specialization list.

Two courses are required in the Applied Discrete area consisting of

  1. APM 563, Applied Mathematics: Discrete Methods I
  2. and one other course selected from the the Applied Discrete specialization list.

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.

General Examination and
the 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. 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.

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 the Dean of Graduate Studies. 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 the Dean of Graduate Studies.

For the first five Ph.D candidates who take a final oral examination, two of the five members of each dissertation committee shall be faculty members from other research universities with long standing Ph.D. programs in the mathematical sciences. These outside members of the dissertation committee will normally be in the broad area of specialization of the student.

Final Oral Examination
and
Defense of Dissertation

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 dissertation 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 examination form for the student to pass this final oral examination.

Time Limits

If more than five years have elapsed since passing the General Examination, the student may be required to retake the General Examination before the dissertation committee considers the dissertation for possible acceptance. The decision to require the student to retake the General Examination is made by the Committee on Graduate Programs in consultation with the present members of the dissertation committee.

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, winter-fall-winter, fall-winter-spring-summer, winter-spring-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 twenty hours a week while satisfying this residency requirement. Petitions for exceptions to this policy may be submitted to the Committee on Graduate Programs.