Program Structure and Requirements
Overall Program Structure
The PhD in Mathematics consists of a minimum 72 credit hours, distributed as follows: 36 credit hours of coursework, 36 credit hours of PhD Dissertation, two zero credit PhD Seminar courses, as well as PhD Written Qualifying and PhD Research Proposal Examinations. The components of the program are summarized in the table below.
| Category |
Credit Hours |
| Core Courses |
12 |
| Technical Electives |
24 |
| SCIE 702 PhD Research Seminar I |
0 |
| SCIE 703 PhD Research Seminar II |
0 |
| SCIE 795 PhD Written Qualifying Exam |
0 |
| SCIE 796 PhD Research Proposal Exam |
0 |
| PhD Research Dissertation |
36 |
| Total |
72 |
All the courses that the students will take are at PhD level. The students will only be able to attempt SCIE 795 PhD Written Qualifying Exam (WQE) after successfully completing a minimum of 27 credits of formal coursework.
Program Requirements
Students seeking the degree of PhD in Mathematics must successfully complete a minimum 72 credit hours as specified in the program requirements detailed below, with a minimum CGPA of 3.0. Course selection should be made in consultation with the student’s Main Advisor. All courses listed below have a credit rating of three credits each, except for PhD Research Seminar, Written Qualifying Exam, Research Proposal Exam, and the PhD Research Dissertation.
Program Cores (12 credit hours)
Students must complete the core courses listed below.
Core Courses
Program Electives (24 credit hours)
Students must complete a total of eight elective courses (24 credits). Program electives are listed below.
Program Elective Courses
| MATH 701 | Combinatorial Analysis | 3 |
| MATH 702 | Functional analysis | 3 |
| MATH 703 | Finance and Stochastic Calculus | 3 |
| MATH 704 | Matrix Computations | 3 |
| MATH 705 | Mechanics of interacting particles | 3 |
| MATH 706 | Modern Statistical Prediction and Data Mining | 3 |
| MATH 707 | Nonlinear Optimization | 3 |
| MATH 708 | Partial Differential Equations | 3 |
| MATH 709 | Probability and Stochastic Processes | 3 |
| MATH 710 | Selected topics in group theory | 3 |
| MATH 711 | Selected Topics in High Dimensional Statistics | 3 |
| MATH 712 | Quantitative Principles in Biology | 3 |
| MATH 717 | Methods of Mathematical Physics | 3 |
| MATH 725 | Computational Systems Biology | 3 |
| MATH 777 | Mathematical Models for Biology and Epidemiology | 3 |
| MATH 787 | Mathematical Imaging | 3 |
Subject to approval of the Main Advisor and the Program Coordinator, up to three electives (9 credits) may be taken from outside the student’s department, if these courses support the student’s dissertation topic. Suggested courses are listed below.
Elective Courses from Other Departments
Physics
Aerospace Engineering
Electrical and Computer Engineering
| ECCE 732 | Machine Learning and Applications | 3 |
| ECCE 738 | High Performance Computing | 3 |
| ECCE 742 | Advanced Concepts in Stochastic Processes, Detection, and Estimation Theory | 3 |
| ECCE 753 | Computational Prototyping of Dynamical Systems | 3 |
| ECCE 754 | Computational Prototyping of Partial Differential Equations | 3 |
Engineering Systems and Management
| ESMA 710 | Times Series Analysis Modeling and Prediction | 3 |
| ESMA 720 | Advanced Production and Operations Management | 3 |
| ESMA 721 | Stochastic Processes and Applications | 3 |
| ESMA 730 | Complex Network Analysis | 3 |
Mechanical Engineering
| MEEN 703 | Linear and Nonlinear Finite Element Methods | 3 |
| MEEN 721 | Computational Fluid Mechanics | 3 |
| MEEN 722 | Non-Newtonian Fluid Dynamics | 3 |
PhD Research Dissertation (36 credit hours)
Students must complete a Dissertation that involves creative, research-oriented work within the field of mathematics, under direct supervision of a full-time faculty advisor from the Mathematics Department, and at least one other full-time faculty who acts as a co-advisor. The outcome of research should demonstrate the synthesis of information into knowledge in a form that may be used by others. The research findings must be documented in a formal dissertation and defended successfully in a viva voce examination.
Dissertation