Mathematics, M.A.
Minimum Totals for Graduation: 30 hours
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 requirements are those that a student with minimal undergraduate preparation would need 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, 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.
Admission Requirements, Retention & Termination Standards
Admission Requirement Snapshot
GPA: 2.7 (and 2.7 in major)
Entrance Exam: GRE Recommended
Internat'l Application Deadline: July 1 (Fall), Oct.1 (Spring)
See Admission Requirement Details Below
- Applicants must meet all CMU Graduate Studies admission requirements. International students should take note of any special admission considerations required by the Office of Graduate Studies, including TOEFL requirements.
- Applicants must have successfully completed a minimum of 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). Students missing one or more of these courses may be considered for admission with stipulations. Applicants granted admission with stipulations will be asked to take the missing course(s) when they begin the program. A grade point average of 2.7 overall and a 2.7 in mathematics are required.
- 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.
- Both admission to the program and awards of Graduate Assistantships are competitive. Applicants interested in a Graduate Assistantship position must submit a Graduate Assistantship Application along with General GRE scores and three letters of recommendation directly to the Department of Mathematics. Evaluation for Graduate Assistantships is 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
Algebra Requirements (6 hours)
| MTH 525 | Advanced Linear Algebra | 3(3-0) |
| MTH 623 | Theory of Groups and Rings | 3(3-0) |
Analysis Requirements (9 hours)
| MTH 533 | Advanced Calculus II | 3(3-0) |
| MTH 632 | Introduction to Real Analysis and Its Applications | 3(3-0) |
| MTH 636 | Introduction to Complex Variables | 3(3-0) |
Applied Mathematics Requirement (3 hours)
Select one of the following:
| MTH 520 | Optimization Theory | 3(3-0) |
| MTH 534 | Applied Mathematics and Differential Equations | 3(3-0) |
| MTH 638 | Theoretical Numerical Analysis | 3(3-0) |
Core Electives (6 hours)
Select two of the following:
| MTH 527 | Representation Theory of the Symmetric Group | 3(3-0) |
| MTH 578 | Combinatorics and Graph Theory | 3(3-0) |
| MTH 625 | Theory of Modules and Fields | 3(3-0) |
| MTH 634 | Fourier Analysis | 3(3-0) |
| MTH 637 | Complex Variable Theory | 3(3-0) |
| MTH 543 | Curves and Surfaces | 3(3-0) |
| MTH 645 | Algebraic Topology | 3(3-0) |
| MTH 673 | History of Advanced Mathematics | 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) |
| STA 584 | Mathematical Statistics I | 3(3-0) |
Research Requirements (6 hours)
Select either plan A or plan B.
Plan A (6 hours)
Completion of a thesis, including an oral examination over the thesis.
Plan B (6 hours)
Required Courses (3 hours)
1 hour of MTH 693, plus 1 hour of MTH 698 for Plan B paper 1, and 1 hour of MTH 698 for Plan B paper 2:
| MTH 693 | Graduate Seminar in Mathematics and Its Applications | 1-4(Spec) |
| MTH 698 | Plan B Project | 1-2(Spec) |
Electives (3 hours)
Electives may be chosen from any graduate level course and may be selected from a department other than mathematics. Electives must be chosen with approval of the advisor.
Total: 30 semester hours
Accelerated Master of Arts in Mathematics
Advanced undergraduate students majoring in mathematics may want to consider an option by which they can obtain their Bachelor of Arts or Bachelor of Science in Mathematics and their Master of Arts in Mathematics in five years. The accelerated program requirements are identical to the Major in Mathematics and to the Master of Arts in Mathematics, but allow the student to apply 12 credit hours of graduate coursework toward both the Bachelor of Arts or the Bachelor of Science and the Master of Arts degrees.
Admission Requirements, Retention & Termination Standards
To be eligible for the accelerated program, a student must have completed a minimum of 20 semester hours of mathematics including MTH 233 (Calculus III) or its equivalent, and one course in either linear or abstract algebra. A grade point average of 3.0 overall and a 3.0 in mathematics are required. In addition, students must have completed MTH 332 or its equivalent with a letter grade of at least B and must have completed at least 90 credit hours of undergraduate course work, including all competency requirements and all but 12 credit hours of University Program requirements.
Degree Requirements
During the fourth year, students will complete MTH 632 or MTH 636, MTH 525, MTH 533, MTH 623 to be counted toward both the undergraduate and graduate degrees. Students will complete the Bachelor of Arts or Bachelor of Science degree requirements by the end of the summer term of the fourth year. Students will complete the coursework for the Master of Arts and complete either the Plan A or Plan B option by the end of the summer term of their fifth year.
A sample curriculum for a student who has completed 90 credit hours of undergraduate coursework is given below.
Year 4 - Fall (15 hours)
Undergraduate Courses (9 hours), plus 3 hours each of MTH 525 and MTH 636:
| MTH 525 | Advanced Linear Algebra | 3(3-0) |
| MTH 636 | Introduction to Complex Variables | 3(3-0) |
Note: MTH 525 and MTH 636 apply to both the BA/BS and MA degrees. Students must register for graduate credit in these courses.
Year 4 - Spring (15 hours)
Undergraduate courses (9 hours), plus 3 hours each of MTH 533 and MTH 623.
| MTH 533 | Advanced Calculus II | 3(3-0) |
| MTH 623 | Theory of Groups and Rings | 3(3-0) |
Note: MTH 533 and MTH 623 apply to both the BA/BS and MA degrees. Students must register for graduate credit for these courses.
Year 4 - Summer (4 hours)
Undergraduate courses up to 4 hours.
(BA or BS degree conferred.)
Year 5 - Fall (7-9 hours)
Core Electives (6), plus:
| MTH 693 | Graduate Seminar in Mathematics and Its Applications | 1-4(Spec) |
| MTH 698 | Plan B Project | 1-2(Spec) |
| MTH 798 | Thesis | 1-6(Spec) |
Year 5 - Spring (6-8 hours)
MTH 632, plus:
- For Plan B, a Plan B elective (3 hours), and 1 hour each of MTH 693 and MTH 698.
- For Plan A, students must complete 6 hours of MTH 798 over the course of two semesters.
| MTH 632 | Introduction to Real Analysis and Its Applications | 3(3-0) |
| MTH 798 | Thesis | 1-6(Spec) |
Year 5 - Summer (0-1 hours)
1 hour of MTH 698 or Master Thesis Defense
(M.A. degree conferred in August.)