Master of Arts
      Admission Requirements
      Degree Requirements
Master of Arts in Teaching
      Admission Requirements1
      Degree Requirements1
Ph.D. in Mathematics
      Admission Requirements2
      Degree Requirements2
Unspecified Content or Variable Credit Courses
MTH Course Descriptions
STA Course Descriptions

Department of Mathematics website

Sidney W. Graham Chairperson
214 Pearce Hall, (989) 774-3596

Mohan Shrikhande, Graduate Coordinator
201C Pearce Hall, (989) 774-4354

James Angelos, Ph.D., Approximation Theory
Ahmed Assaf, Ph.D., Combinatorics
Esther Beneish, Ph.D., Algebra
Robert A. Chaffer, Ph.D., Algebra
John Daniels, Ph.D., Statistics
Ana Dias, Mathematics Education
Lisa DeMeyer, Ph.D., Differential Geometry
Donna Ericksen, Ph.D., Mathematics Education
Felix Famoye, Ph.D., Statistics
Richard J. Fleming, Ph.D., Functional Analysis
Martha Frank, Ph.D., Mathematics Education
Sidney W. Graham, Ph.D., Number Theory
George Grossman, Ph.D., Applied Mathematics
Arnold Hammel, Ph.D., Linear Algebra and Cryptology
Yury Ionin, Ph.D., Mathematics Education, Combinatorics
Carl Moun-Shen Lee, Ph.D., Statistics
Douglas Lapp, Ph.D., Mathematics Education
Susan Lenker, Ph.D., Statistics
Terry Lenker, Ph.D., Mathematical Analysis
Azita Manouchehri, Ph.D., Mathematics Education
David G. McDowell, Ph.D., Numerical Analysis
Thomas J. Miles, Ph.D., Algebra
Sivaram K. Narayan, Ph.D., Operator Theory
Sing-Cheong Ong, Ph.D., Operator Theory
Leela Rakesh, Ph.D., Applied Mathematics
Richard St. Andre, Ph.D., Topology
Dennis St. John, Ph.D., Mathematics Education
Jungsywan Sepanski, Ph.D., Statistics
Mohan S. Shrikhande, Ph.D., Combinatorics
Ken Smith, Ph.D., Algebra and Combinatorics
Peter J. Vermeire, Ph.D., Algebraic Geometry
Charles Vonder Embse, Ph.D., Mathematics Education
Daniel X. Wang, Ph.D., Applied Statistics

The Department of Mathematics offers the Master of Arts in Mathematics (M.A.), the Master of Arts in Teaching (M.A.T.), and the Ph.D. in Mathematics with a concentration in the Teaching of College Mathematics.

The M.A. degree has an emphasis in the more computational aspects of mathematics for students who are interested in jobs in business, industry and government. The degree program also retains the flexibility to prepare students for teaching mathematics at the undergraduate level or to undertake doctoral work in mathematics. The M.A.T. is designed for secondary school teachers who want to strengthen their preparation in mathematics and teaching.

The Ph.D. degree is a content-based degree designed to develop well-prepared teachers of college mathematics who combine knowledge and skill in mathematics with a desire to teach it effectively. Coursework is broadly distributed across the various areas of mathematics and is intended to help students achieve a level of sophistication in mathematical knowledge that will establish a professional attitude about mathematics. Students would be prepared to do research in traditional mathematics or in areas related to the teaching of collegiate mathematics. Emphasis on pedagogy includes two required courses plus an internship.

The department has an active faculty with particular research strengths in the areas of approximation theory, applied mathematics, number theory, combinatorics and graph theory, functional analysis and operator theory, statistics, mathematics education, algebra, algebra geometry, and differential geometry.

Classes are small, allowing students to receive individual attention. An active colloquium program draws speakers with varied research interests from a wide range of locales. A graduate student seminar gives students the opportunity to explore topics that extend the required coursework as part of their program. The applied mathematics group’s specialty is computational and polymer fluid dynamics. Research groups have strong links with science and engineering departments within Central Michigan University, other universities and industry.

Computing facilities within Pearce Hall, where the department is located, include microcomputer laboratories with Macintosh, IBM PC computers and Sun workstations.

Two types of financial aid are available: graduate fellowships and graduate teaching assistantships. Some of these are specified for doctoral students and carry a higher stipend. A limited number of graduate research assistantships may be available, and are dependent on current grant funding. Additional support is available for members of underrepresented minority groups.

Completed applications for fellowships are due Feb. 6. Completed applications for assistantships must be submitted by March 1, although late applications may be considered if positions are available.
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Master of Arts
Admission Requirements
Admission is dependent upon a student having completed a minimum of 20 semester hours of mathematics including MTH 233 (multivariate calculus) or the equivalent, and one course in either linear or abstract algebra. A grade point average of 2.5 in mathematics is required.

Degree Requirements
The requirements are those that a student with minimal undergraduate preparation would have to fulfill.
Any student having satisfied any of the course requirements prior to entering the program may be excused from that course requirement. However, the 30-hour requirement will not be affected.
If the student elects to write a thesis, it shall be in mathematics.
If a student elects to follow non-thesis Plan B, one or two projects in two fields of mathematics must be completed under the direction of graduate faculty. More detailed information is available in the department office.

Courses (30 credit hours)
A. Analysis:
MTH 533 (3) Advanced Calculus II
MTH 632 (3) Introduction to Real Analysis and Its Applications
MTH 636 (3) Introduction to Complex Variables

B. Algebra:
MTH 525 (3) Modern Algebra II
MTH 623 (3) The Theory of Groups

C. Computational Mathematics:
One course from:
MTH 520 (3) Optimization Theory
CPS 525 (3) Simulation of Continuous Systems
CPS 530 (3) Simulation of Discrete Event Systems
MTH 578 (3) Combinatorics I
MTH 638 (3) Theoretical Numerical Analysis

D. Statistics:
Any statistics course offered by the mathematics department numbered STA 500 or higher.

E. Perspectives in Mathematics:
One course from:
MTH 671 (3) Introduction to the Axiomatic Method
MTH 673 (3) History of Advanced Mathematics 
MTH 694 (3) Practicum in Mathematics

F. Research Requirements (6 credits)
Plan A (6 credits)
Completion of a thesis (MTH 798), including an oral examination over the thesis, OR

Plan B (6 credits)
a. MTH 693 (1) Graduate Seminar in Mathematics and its Applications
b. MTH 698 (1) for Plan B paper 1.
c. MTH 698 (1) for Plan B paper 2.
d. Electives (3 credits). May be chosen from among all graduate level mathematics, statistics, and computer science courses. A student may select up to three hours from a department other than mathematics or computer science. Electives must be chosen with approval of the advisor.
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Master of Arts in Teaching
Admission Requirements1
Admission is dependent upon a student having completed a minimum of 20 semester hours of mathematics including MTH 233 (multivariate calculus) or the equivalent. A grade point average of 2.5 in mathematics is required.

Degree Requirements1
The requirements are those that a student with minimal undergraduate preparation would have to fulfill.

Any student who has satisfied any of the course requirements prior to entering the program may be excused from these course requirements. However, the 20 hours of mathematics and the 30 hour total will not be affected.

If the student elects to write a thesis, it shall be in mathematics education.
If the student elects to follow non-thesis Plan B, one of the two papers shall be in mathematics education and the other shall be in another field of mathematics.

Courses (30 credits)
With the prior approval of the advisor:
A. Two courses in mathematics education:
MTH 658 (1-6 credits), 660, 661, 666

B. Two courses in algebra:
MTH 523, 525, 623, 625, 671

C. One course in analysis:
MTH 532, 533, 545, 632, 633, 636, 637, 645

D. One course in geometry:
MTH 641

E. One course each from two of the following areas:
Applied Mathematics: MTH 578, 586, 638
History of Mathematics: MTH 573, 673
Probability and Statistics: STA 580, 584

F. Cognate Courses ( 0-3 credits)

G. Research Requirements (6 credits)
Plan A (6 credits)
Completion of a masters thesis in mathematics education

OR Plan B (6 credits)
1. MTH 698 (1 credit) for Plan B paper 1.
2. MTH 698 (1 credit) for Plan B paper 2.
3. MTH 692 (1 credit) Graduate Seminar in Mathematics Education
4. Electives (3 credits) courses to be chosen in consultation with advisor.
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Ph.D. in Mathematics
With a Concentration in the Teaching of College Mathematics

Admission Requirements

1. Applicants must meet all College of Graduate Studies admission requirements.
2. Applicants with a Bachelor's degree must have successfully completed 20 semester hours of mathematics including MTH 233 (Multivariate Calculus) or equivalent, and one course in either linear or abstract algebra. A minimum GPA of 3.0 in mathematics is required. (A student entering with the minimum would likely have to take some prerequisite courses before taking the courses required for this program.)
3. Applicants with Master's degrees in mathematics equivalent to the M.A. or M.A.T. degree at Central Michigan University must have a minimum GPA of 3.0 in their graduate work.
4. Applicants must submit GRE examination scores, however, this requirement may be waived by the Department in exceptional cases.

Applicants from non-English speaking countries must achieve a satisfactory score on the Test of English as a Foreign Language (TOEFL); a minimum score of 550 is required for applicants to the graduate college.

The nature of previous coursework, grades, and GRE score will be used by the department in evaluation of candidates for admission. Awards of Graduate Assistantships and Fellowships are competitive, with evaluation based on courses, grades, GRE scores, and letters of recommendation.

Degree Requirements2
Successful completion of the Ph.D. requires a minimum of 90 semester hours of graduate work beyond the bachelor's degree or 60 hours of graduate work beyond the master's degree. In order to obtain the Ph.D. degree the student must have a GPA of 3.0 (B) or better. A student with a bachelor's degree must have earned at least 50 of the total 90 hours at the

600 level or above. Those entering with a master's degree must have earned at least 35 of the 60 hours at the 600 level or above. At least 15 of the last 30 hours must be earned at the 700 level or above, excluding the dissertation and the internship credits.

(1) Coursework
The program requires a minimum of 69 hours of coursework exclusive of internship and the dissertation credit beyond the bachelor's degree or 39 hours of such coursework after the master's degree. These hours are distributed among core courses and courses in area of specialization as given below. The minimum hours that are required in each category is specified in parentheses. 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 student having satisfied any of the course requirements prior to entering the program may be excused from that course requirement. However, the total hour requirement of 69 (or 39) semester hours will not be affected.

Required core courses (27 credit hours)
A. Algebra (9 hours)
MTH 525 (3) Modern Algebra II
MTH 623 (3) The Theory of Groups
MTH 625 (3) Theory of Associative Rings

B. Analysis (12 hours)
MTH 533 (3) Advanced Calculus II
MTH 632 (3) Introduction to Real Analysis
MTH 636 (3) Introduction to Complex Variables
MTH 633 (3) Real Variables OR
MTH 637 (3) Complex Variable Theory

C. Mathematics Education (6 hours)
MTH 761 (3) Methods for Teaching College Mathematics
MTH 762 (3) Research in Collegiate Mathematics Education

Elective core courses (24 credit hours)
Each student is required to take two courses in each of the areas below:
D. Applied Mathematics
MTH 520 (3) Optimization Theory
MTH 586 (3) Operations Research I
MTH 634 (3) Fourier Analysis
MTH 638 (3) Theoretical Numerical Analysis

E. Combinatorics
MTH 578 (3) Combinatorics I
MTH 678 (3) Combinatorics II

F. Statistics
STA 580 (3) Applied Statistical Methods
STA 584 (3) Mathematical Statistics I
STA 684 (3) Theory of Statistical Inference

G. Topology and Foundations of Mathematics
MTH 641 (3) Topics in Geometry
MTH 645 (3) Point-Set Topology
MTH 673 (3) History of Advanced Mathematics

Electives (3-9 credit hours)
Elective courses can be from outside the mathematics department. These elective courses are to be selected by each student in consultation with his/her advisor or dissertation supervisor.

Area of Specialization (9-15 credit hours)
Each student, in consultation with his/her dissertation supervisor, will select at least 9 semester hours of courses in the area of specialization. These courses can be from outside the mathematics department. The areas of specialization include the following: Algebra, Applied Mathematics, Approximation Theory, Combinatorics, Functional Analysis, Mathematics Education, Number Theory, Operator Theory, and Statistics.

(2) Qualifying Examination
In addition to demonstration of competence in the coursework in the above mentioned areas, the student must pass a qualifying examination in three of the areas (A.) Algebra, (B.) Analysis and one from (C., D., E., F., or G.). The format of the exam (oral/written) for each student will be determined in consultation with an examination committee made up of Mathematics Department graduate faculty members. The committee will administer and grade these exams.

The student has a maximum time period of one year or until completion of 12 credit hours after the master's degree, whichever comes later (three years or until completion of 42 credit hours after the bachelor's degree, whichever comes later) to do one of the following: (1) attempt both Analysis and Algebra examinations or (2) pass at least one of the Algebra or Analysis exams. The student has a maximum time period of two years or until completion of 24 credit hours after the master's degree, whichever comes later (four years or until the completion of 54 credit hours after the bachelor's degree, whichever comes later) to pass all three examinations. Two attempts in each area are allowed. A second failure in one area eliminates a student from the Ph. D. program.

(3) Internship (6 hours)
Students are required to teach two courses in mathematics/statistics at the 200 level or above under the supervision of a graduate faculty member in the Department of Mathematics. The student must earn the credits by registering for MTH 766.

(4) Dissertation (15 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 in consultation with the dissertation supervisor. This dissertation committee will be chaired by the supervisor and must include at least three 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 College of Graduate Studies.

Students are required to register for 15 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, an expository or historical examination of a piece of 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 College of Graduate Studies.

Upon completion of (1) through (4) 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 examination.

The dissertation must be prepared according to the regulations prescribed in the College 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.
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Unspecified content or variable credit courses. Click here for additional information regarding these types of courses. The following courses offered through the department are of unspecified content or variable credit: MTH 591, 595, 596, 597, 651, 658, 692, 693, 695, 696, 697, 698 and STA 596, 597.
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