Mathematical Sciences, Ph.D.
Minimum Totals for Graduation: 75 hours
The Ph.D. degree is a content-based degree program that has two concentrations: Concentration in Mathematics and Concentration in Collegiate Mathematics Education. Coursework is broadly distributed across the various areas of mathematics and mathematics education.
The Ph.D. degree is designed (a) to develop well-prepared teachers to teach college level mathematics and conduct independent research effectively in their areas of expertise or (b) to prepare students with advanced knowledge and applications in mathematics to work effectively in non-academic environments.
- For students who are interested in teaching at universities, the program has a unique component of two courses on teaching pedagogy in addition to two semesters of teaching internships.
- For students who are interested in the Concentration in Mathematics, this concentration features choices for broad or in-depth coursework in different branches of pure and applied mathematics.
- For students who are interested in the Concentration in Collegiate Mathematics Education, in addition to the unique feature of teaching pedagogy and teaching internships, this concentration also includes coursework in the theory of learning and research methodology.
Admission Requirements, Retention & Termination Standards
Admission Requirement Snapshot
GPA: 2.7 (see Item 2 below)
Entrance Exam: GRE
Application Deadline: February 15 for full consideration
See Admission Requirement Details Below
Admission
- Applicants must meet all CMU Graduate Studies admission requirements. This includes official transcripts and a resume. International students should take note of any special admission considerations required by the College of Graduate Studies, including TOEFL requirements.
- Applicants with a Bachelor's degree must have successfully completed 20 semester hours of mathematics including Multivariate Calculus (equivalent to MTH 233), Abstract Algebra (equivalent to MTH 523), and Advanced Calculus (equivalent to MTH 532). A minimum GPA of 2.7 overall (or 3.0 in the final sixty semester hours of graded coursework toward the bachelor's degree) and 3.0 in mathematics is required.
- Applicants with a Master's degree in mathematics equivalent to the M .A. degree at Central Michigan University must have a minimum GPA of 3.0 in their graduate work.
- Applicants must arrange for ETS to send an official copy of the general GRE scores. The institution code for Central Michigan University is 1106 and the department code is 0703.
- Applicants must submit contact information of three recommendation letter writers. A link will be sent to each letter writer where the letter of recommendation can be uploaded.
- Applicants must submit a Statement of Purpose of at least 100 words and not to exceed two pages. The Statement of Purpose should explain their relevant academic and professional experiences, discuss motivation for applying to the program, and describe their goals after completing the program.
- Applicants may optionally submit any additional evidence of mathematical ability and promise.
- Both admission to the program and awards of Graduate Assistantships are competitive, with evaluation based on the nature of previous coursework, grades, general GRE scores, and letters of recommendation. The deadline for applying for a Graduate Assistantship is February 15. Application materials received after February 15 are considered on a rolling basis until all positions are filled.
Program Requirements
Successful completion of the Ph.D., including coursework, internship, and dissertation, requires a minimum of 75 semester hours of graduate work beyond the bachelor's degree.
In order to obtain the Ph.D. degree the student must have a GPA of 3.0 (B) or better. Up to 30 hours of relevant graduate coursework may be transferred for students entering with a master’s degree. For this to be approved, the student must complete the Transfer Waiver Form supplied by the Graduate Studies Office.
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Credit Hour Requirements
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Coursework*
(excluding MTH 766 and MTH 898)
700 level or above
600 level or above
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Minimum 57 hours
Minimum 15 hours
Minimum 32 hours
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| *Minimum 17 hours at 600 level or above to be taken at CMU. |
| Teaching Internship (MTH 766) |
6 hours |
| Dissertation (MTH 898) |
Minimum 12 hours |
| Total |
75 semester hours |
Coursework
The minimum hours that are required in each category is specified in parentheses in the program below. An advisor will assist a student in the selection of the courses. Courses in which a student earns or has earned a grade below C (2.0) do not count toward meeting any graduate degree requirements.
Any graduate student having satisfied any of the course requirements prior to entering the program may have this course requirement waived. For this to be approved, the student must complete the Course Requirement Waiver Form supplied by the department. However, the required total credit hours will not be affected.
The two concentrations require a list of Common Core Courses, Internship, Dissertation, and concentration-specific coursework and qualifying exams. The list of coursework below is for students who have an undergraduate degree satisfying the admission requirements.
Program Requirements
Common Core Courses (21 hours)
| MTH 525 | Advanced Linear Algebra | 3(3-0) |
| MTH 623 | Theory of Groups and Rings | 3(3-0) |
| MTH 625 | Theory of Modules and Fields | 3(3-0) |
| MTH 632 | Introduction to Real Analysis and Its Applications | 3(3-0) |
| MTH 636 | Introduction to Complex Variables | 3(3-0) |
| MTH 761 | Methods for Teaching College Mathematics | 3(3-0) |
| MTH 762 | A Survey of Research in Collegiate Mathematics Education | 3(3-0) |
Concentrations
Select one of the following concentrations:
Concentration in Mathematics (36 hours)
Mathematics Core Courses (9 hours)
Must select MTH 534 and MTH 645:
| MTH 534 | Applied Mathematics and Differential Equations | 3(3-0) |
| MTH 633 | Real Variables | 3(3-0) |
| MTH 637 | Complex Variable Theory | 3(3-0) |
| MTH 645 | Algebraic Topology | 3(3-0) |
Core Electives (15-18 hours)
Select 15-18 hours from Core Electives I and Core Electives II.
Core Electives I - Topics in Pure and Applied Mathematics (6-15 hours)
Select from the following:
| MTH 520 | Optimization Theory | 3(3-0) |
| MTH 578 | Combinatorics and Graph Theory | 3(3-0) |
| MTH 627 | Representation Theory of Lie Algebras | 3(3-0) |
| MTH 634 | Fourier Analysis | 3(3-0) |
| MTH 643 | Differentiable Manifolds | 3(3-0) |
| MTH 732 | Functional Analysis | 3(3-0) |
| MTH 734 | Partial Differential Equations and Applications | 3(3-0) |
Core Electives II - Advanced Topics in Mathematics (3-9 hours)
Select from the following:
| MTH 725 | Topics in Algebra | 3-9(Spec) |
| MTH 730 | Topics in Applied Mathematics | 3-9(Spec) |
| MTH 737 | Topics in Analysis | 3-9(Spec) |
| MTH 744 | Topics in Geometry | 3-9(Spec) |
Area of Specialization Courses (6 hours)
| MTH 796 | Special Topics in Mathematics | 1-6(Spec) |
| MTH 797 | Independent Study | 1-9(Spec) |
Other Electives (3-6 hours)
All courses at 500 level or higher, and approved by the advisor.
Concentration in Collegiate Mathematics Education (36 hours)
Mathematics Education Core Courses (18 hours)
| EDU 614 | Advanced Educational Psychology | 3(3-0) |
| MTH 763 | Advanced Perspectives in Collegiate Mathematics Education | 3(3-0) |
| MTH 764 | Qualitative Research Methods in Mathematics Education | 3(3-0) |
| MTH 767 | Seminar in Collegiate Mathematics Education I | 3(3-0) |
| MTH 768 | Seminar in Collegiate Mathematics Education II | 3(3-0) |
| PSY 611 | Research Design | 3(3-0) |
Core Electives I (6 hours)
Select 6 hours from the following:
| MTH 520 | Optimization Theory | 3(3-0) |
| MTH 543 | Curves and Surfaces | 3(3-0) |
| MTH 545 | Introduction to Point-Set Topology | 3(3-0) |
| MTH 578 | Combinatorics and Graph Theory | 3(3-0) |
| MTH 645 | Algebraic Topology | 3(3-0) |
| STA 580 | Applied Statistical Methods I | 3(3-0) |
| STA 584 | Mathematical Statistics I | 3(3-0) |
| STA 585 | Mathematical Statistics II | 3(3-0) |
| STA 590 | Applied Statistical Methods II | 3(3-0) |
| STA 684 | Theory of Statistical Inference | 3(3-0) |
Core Electives II (12 hours)
Select courses from either inside or outside of the department, in consultation with the student's advisor.
Qualifying Examination
In the Ph.D. qualifying examinations, students are expected to demonstrate a broad knowledge of the topics and be able to integrate concepts and explain them at an appropriate level. Qualifying Examinations will be offered in the following subjects, based on the material in the courses listed in the current Graduate Student Handbook of the Department of Mathematics.
- Algebra
- Analysis
- Mathematics Education
Each doctoral student must pass two examinations in two different subjects from those listed above.
- Students choosing the Concentration in Mathematics must pass examinations in algebra and analysis.
- Students choosing the Concentration in Collegiate Mathematics Education must pass examinations in mathematics education and at least one of algebra or analysis.
- If a student decides to switch to a different concentration after completing two qualifying exams, whether s/he will take additional qualifying exam(s) is determined by the Graduate Committee.
Full-time students who entered the Ph.D. program must have passed two qualifying exams at the latest in the exam period just prior to the start of classes of their sixth semester. If the student does not pass both qualifying exams by this time, the student can no longer continue in the Ph.D. program. Part-time students may request additional time from the department.
Internship (6 hours)
Students are required to take 6 hours of a teaching internship.
The teaching internship courses are at the 200 level or above offered in the Department of Mathematics. Students may teach a course lower than 200 level with the approval of the Graduate Committee. Prior to seeking a faculty teaching internship supervisor, the student is required to consult with his/her academic advisor.
The teaching internships must be in two different courses under the supervision of two different graduate faculty members in two different semesters in the Department of Mathematics. Courses with substantial overlap of contents cannot be used as two different internship courses.
The student must earn credits for internships by registering for MTH 766 for teaching internship.
| MTH 766 | Internship: College Teaching | 3-6(Spec) |
Dissertation (12 hours)
Upon successful completion of the qualifying examinations, the student will select a dissertation supervisor. A dissertation supervisor must be a graduate faculty member in the Mathematics Department. The student will form a dissertation committee of at least three graduate faculty members in consultation with the dissertation supervisor. This dissertation committee will be chaired by the supervisor(s) and must include at least two (2) other graduate faculty members. Two members of the dissertation committee must be from the Mathematics Department. A completed doctoral dissertation must be approved by the dissertation committee, and by the Office of Graduate Studies.
Students are required to register for 12 hours of MTH 898 (Dissertation). The dissertation must consist of original work and can combine scholarly, analytical, creative and expository skills. It could consist of research on a topic in mathematics, or research on a topic related to the teaching of collegiate mathematics. Before starting the dissertation work, the project to be undertaken must be approved by the dissertation committee, and by the Office of Graduate Studies.
Upon completion of coursework, qualifying examination, internship, and dissertation, the candidate for the Ph.D. degree must pass a final oral examination which is a dissertation defense in a colloquium format. The student's dissertation committee determines whether the student passes the oral examination.
The dissertation must be prepared according to the regulations prescribed in the Office of Graduate Studies most recent edition of the Preparation Guide to Doctoral Dissertations, Theses, Field Studies, and Plan B Papers and must be submitted to Dissertations Abstracts International.
Total: 75 semester hours