Graduate Catalog

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

SCIE 701Research Methods in Science

3

MATH 713Measure Theory

3

MATH 714Real Analysis

3

MATH 715Analytical Foundations of Risk and Optimization

3

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 701Combinatorial Analysis

3

MATH 702Functional analysis

3

MATH 703Finance and Stochastic Calculus

3

MATH 704Matrix Computations

3

MATH 705Mechanics of interacting particles

3

MATH 706Modern Statistical Prediction and Data Mining

3

MATH 707Nonlinear Optimization

3

MATH 708Partial Differential Equations

3

MATH 709Probability and Stochastic Processes

3

MATH 710Selected topics in group theory

3

MATH 711Selected Topics in High Dimensional Statistics

3

MATH 712Quantitative Principles in Biology

3

MATH 717Methods of Mathematical Physics

3

MATH 725Computational Systems Biology

3

MATH 777Mathematical Models for Biology and Epidemiology

3

MATH 787Mathematical 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

PHYS 701Advanced Computational Physics

3

PHYS 702Advanced Quantum Mechanics

3

Aerospace Engineering

AERO 701Nonlinear Structural Dynamics

3

AERO 703Numerical Methods in Aerofluids

3

Electrical and Computer Engineering

ECCE 732Machine Learning and Applications

3

ECCE 738High Performance Computing

3

ECCE 742Advanced Concepts in Stochastic Processes, Detection, and Estimation Theory

3

ECCE 753Computational Prototyping of Dynamical Systems

3

ECCE 754Computational Prototyping of Partial Differential Equations

3

Engineering Systems and Management

ESMA 710Times Series Analysis Modeling and Prediction

3

ESMA 720Advanced Production and Operations Management

3

ESMA 721Stochastic Processes and Applications

3

ESMA 730Complex Network Analysis

3

Mechanical Engineering

MEEN 703Linear and Nonlinear Finite Element Methods

3

MEEN 721Computational Fluid Mechanics

3

MEEN 722Non-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

SCIE 799PhD Thesis Dissertation

36