PhD in Mathematics

Upon completion of the program, graduates will be able to:

• demonstrate mastery of comprehensive, deep and overarching knowledge of at least two main areas of mathematics such as algebra, analysis, dynamical systems and statistics
• apply advanced mathematical skills to solve problems and communicate solutions in precise mathematical language
• design, conduct and defend independent and original research in a specialized area of mathematics
• effectively disseminate and communicate research outcomes to relevant audiences in both written and oral formats
• uphold standards of ethical academic and professional conduct

To qualify for graduation with the PhD-MTH degree, students must successfully complete all the requirements of the program, which consist of a minimum of 54 credit hours with a minimum cumulative GPA of 3.00 as follows:

• a minimum of 24 credit hours of coursework (8 courses)
• doctoral seminar (0 credit hours)
• qualifying examination
• a minimum of 30 credit hours of research work

Required Core Courses

Students must successfully complete the following core courses (12 credit hours), which cover advanced topics in fundamental areas of mathematics and expand on their mathematical knowledge.

• MTH 705 Theory of Ordinary Differential Equations (3-0-3)
• MTH 710 Functional Analysis (3-0-3)
• MTH 711 Measure Theory (3-0-3)
• MTH 733 Commutative Algebra (3-0-3)
• MTH 795 Doctoral Seminar (1-0-0)

Elective Courses

Students must successfully complete a minimum of four courses (for a minimum of 12 credit hours) selected from the following list and subject to the approval of the program coordinator.

• MTH 701 Advanced Probability Theory (3-0-3)
• MTH 706 Analysis of Partial Differential Equations (3-0-3)
• MTH 707 Extreme Values and Financial Risk (3-0-3)
• MTH 715 Operator Theory (3-0-3)
• MTH 735 Nonlinear Algebra (3-0-3)
• MTH 736 Multiplicative Ideal Theory (3-0-3)
• MTH 741 Dynamical Systems and Chaos (3-0-3)
• MTH 751 Algebraic Coding Theory (3-0-3)
• MTH 761 Algebraic Topology (3-0-3)
• MTH 762 Applied Topology (3-0-3)
• MTH 775 Computational Differential Equations (3-0-3)
• MTH 794 Special Topics in Mathematics (3-0-3)