Mathematics (PhD)

Students who graduate from the Mathematics Ph. D. program will be prepared for a career of research, either in industry or academia. Students who successfully complete this program will be able to:

Recall and apply concepts from core subject areas including Vector Spaces, Analysis, and other topics such as Numerical Methods, Complex Variables and Integration, Probability, and Algebra
Integrate and synthesize knowledge gained from core courses to develop a research program
Use technology to gain insight into mathematical structures
Explain how their research extends knowledge and understanding in their field of specialization
Present mathematical ideas at a level appropriate for the audience
Write mathematics at a level appropriate for publication or dissemination
Navigate the steps of the scientific publishing process, understand disciplinary standards of citation, and award credit to other scholars when appropriate.

Program Policy Document:

Please see the Program Policy Document for more information.

Requirements For The PhD Degree

An outline of the degree requirements for the Ph.D. is as follows.

Meet the coursework requirement (section 3.2.1).
Pass the Preliminary Examination requirement (section 3.2.2).
Pass the Candidacy Examination (see section 3.2.4).
Complete two semesters of experience in teaching undergraduate students, either as teaching assistant or as instructor of record.
Complete 9 credits of MATH 969 (Doctoral Dissertation) in addition to the coursework requirement in 1.
Complete and successfully defend a dissertation (section 3.2.5).

Coursework: There are two options for the coursework requirement: standard and accelerated.

Regardless of which track is taken, credit hours for which the grade is below C-minus do not count toward a graduate degree.

Preliminary Examination Requirement: All students who wish to obtain a PhD degree must complete the Preliminary Exam Requirement. The Preliminary Exam Requirement is divided into two tiers. The first tier consists of two exams and the second tier consists of a single exam. The first tier exams are Linear Algebra (with material related to MATH 672 and its prerequisites) and Analysis (with material related to MATH 600 and multivariable calculus). The second tier exam is to be chosen from the following list: Advanced Analysis (MATH 602), Numerical Methods (MATH 611), Applied Mathematics (MATH 617), Stochastic Processes (MATH 631), and Algebra (MATH 650). The courses help prepare students for preliminary exams, but the syllabi for exams and courses are not identical. It is not required that the course be taken before attempting the exam. Registration for specific exams opens 10 weeks before each session and closes 8 weeks before.

The first tier of the Preliminary Exam Requirement must be completed before the start of the third semester of study. The second tier of the Preliminary Exam Requirement must be completed before the start of the fourth semester of study.

Candidacy Examination: The purpose of the Candidacy Examination is to assess the student’s readiness to undertake and complete a research project for the doctoral dissertation. Each student must pass the Candidacy Examination by the beginning of the student’s sixth semester of study. For students using the accelerated coursework requirement, the Candidacy Exam should be completed before the start of the fourth semester. After passing the exam, students are encouraged to pursue Admission to Candidacy with the Graduate College. A student who fails the Candidacy Examination twice will be eligible for the M.S. degree but not the Ph.D.

Other requirements: The student must maintain a GPA of 3.0 or better; complete two semesters of experience in teaching undergraduate students; select a Dissertation Committee and be admitted to candidacy; complete nine credits of MATH 969 (Doctoral Dissertation) after admission to candidacy; and complete and successfully defend a dissertation. Exceptions to the degree requirements can occur only with the permission of the Graduate Studies Committee.

Dissertation: A student must successfully defend his/her dissertation in front of a committee consisting of the dissertation advisor and no less than three additional members, one of whom must be from outside the department. The dissertation must contain original publishable results.

Standard Track:

Students must complete 48 credits from the below courses. Up to a maximum of 27 credits may count from 600 level MATH courses. Up to a maximum of 12 credits combined may count from MATH 868 and MATH 870.

MATH 600 - Fundamentals of Real Analysis Credit(s): 3
MATH 602 - Measure, Integration and Complex Variables Credit(s): 3
MATH 611 - Introduction to Numerical Discretization Credit(s): 3
MATH 612 - Computational Methods for Equation Solving and Function Min Credit(s): 3
MATH 616 - Modeling in Applied Mathematics Credit(s): 3
MATH 617 - Techniques of Applied Mathematics Credit(s): 3
MATH 620 - Introduction to Mathematical Finance Credit(s): 3
MATH 630 - Probability Theory and Applications Credit(s): 3
MATH 631 - Introduction to Stochastic Processes Credit(s): 3
MATH 637 - Mathematical Techniques in Data Science Credit(s): 3
MATH 650 - Algebra I Credit(s): 3
MATH 672 - Vector Spaces Credit(s): 3
MATH 688 - Combinatorics and Graph Theory I Credit(s): 3
MATH 806 - Functional Analysis Credit(s): 3
MATH 810 - Asymptotic and Perturbation Methods Credit(s): 3
MATH 817 - Introduction to Numerical Methods for Partial Differential Equations Credit(s): 3
MATH 829 - Topics in Mathematics Credit(s): 3
MATH 835 - Evolutionary Partial Differential Equations Credit(s): 3
MATH 836 - Elliptic Partial Differential Equations Credit(s): 3
MATH 838 - Finite Element and Boundary Element Methods Credit(s): 3
MATH 845 - Algebra II Credit(s): 3
MATH 850 - Theory of Probability Credit(s): 3
MATH 868 - Research Credit(s): 1-6
MATH 870 - Reading in Mathematics Credit(s): 1-6
MATH 888 - Combinatorics II Credit(s): 3
Any 600 or 800 level non-MATH courses, up to a maximum of 6 credits. Exceptions may be granted by petitioning the Graduate Studies Committee.

Accelerated Track:

To qualify for the accelerated coursework requirement, the student must successfully complete the first tier of the Preliminary Requirement (section 3.2.2) before the start of the first semester (that is, by passing all required exams on the first possible date). Such an attempt at the exams counts as one of the student’s regular allowed attempts. Additionally, the student must complete the second tier before the start of the third semester.

Students must complete 30 credits from the below courses. Up to a maximum of 9 credits may count from 600 level MATH courses except for MATH 600 and MATH 672. Up to a maximum of 12 credits combined may count from MATH 868 and MATH 870.

MATH 602 - Measure, Integration and Complex Variables Credit(s): 3
MATH 611 - Introduction to Numerical Discretization Credit(s): 3
MATH 612 - Computational Methods for Equation Solving and Function Min Credit(s): 3
MATH 616 - Modeling in Applied Mathematics Credit(s): 3
MATH 617 - Techniques of Applied Mathematics Credit(s): 3
MATH 620 - Introduction to Mathematical Finance Credit(s): 3
MATH 630 - Probability Theory and Applications Credit(s): 3
MATH 631 - Introduction to Stochastic Processes Credit(s): 3
MATH 637 - Mathematical Techniques in Data Science Credit(s): 3
MATH 650 - Algebra I Credit(s): 3
MATH 688 - Combinatorics and Graph Theory I Credit(s): 3
MATH 806 - Functional Analysis Credit(s): 3
MATH 810 - Asymptotic and Perturbation Methods Credit(s): 3
MATH 817 - Introduction to Numerical Methods for Partial Differential Equations Credit(s): 3
MATH 829 - Topics in Mathematics Credit(s): 3
MATH 835 - Evolutionary Partial Differential Equations Credit(s): 3
MATH 836 - Elliptic Partial Differential Equations Credit(s): 3
MATH 838 - Finite Element and Boundary Element Methods Credit(s): 3
MATH 845 - Algebra II Credit(s): 3
MATH 850 - Theory of Probability Credit(s): 3
MATH 868 - Research Credit(s): 1-6
MATH 870 - Reading in Mathematics Credit(s): 1-6
MATH 888 - Combinatorics II Credit(s): 3
Any 600 or 800 level non-MATH courses, up to a maximum of 3 credits. Exceptions may be granted by petitioning the Graduate Studies Committee.

Dissertation:

9 credits required.

MATH 969 - Doctoral Dissertation Credit(s): 1-12

Mathematics (PhD)

Program Policy Document:

Requirements For The PhD Degree

Standard Track:

Accelerated Track:

Dissertation:

Standard Track Credits to Total a Minimum of 57

Accelerated Track Credits to Total a Minimum of 39

Last Revised 2024-2025 Academic Year