Program Overview

PhD Program Overview

The doctoral program in Mathematical Sciences offers three areas of concentration: computational and applied mathematics, discrete mathematics, and statistics. The program requires advanced coursework beyond the master's degree and successful completion of the Qualifying and Comprehensive Examinations. Students must demonstrate the ability to independently conduct research.

Program Requirements

To complete a doctoral degree, students must complete the following milestones:

• Complete all coursework and research credits
• Pass Qualifying Examination
• Pass Research Proposal Examination
• Prepare and Submit Approved Dissertation
• Pass Final Oral Defense

The minimum credit requirements are as follows:

• Total Credit Requirements:
  • MS-PhD (minimum): 30 Credits
  • BS-PhD (minimum): 60 Credits Individual programs may have higher standards, and students are expected to know their program's requirements.

Concentrations

The PhD degree is offered in the following concentrations:

• Computational and Applied Mathematics
• Discrete Mathematics
• Statistics

Computational and Applied Mathematics

Computational and Applied Mathematics students develop expertise in the theory and application of ordinary and partial differential equations, linear algebra, and computational methods.

• Core courses:
  • MA5501 Theoretical Numerical Analysis
  • MA5510 ODEs
  • MA5565 PDEs
  • MA5627 Numerical Linear Algebra
  • MA5629 Numerical PDEs
• Elective courses (choose two):
  • MA5401 Real Analysis
  • MA5630 Numerical Optimization
  • MA5580 Topics in Applied Mathematics
  • MA6500 Advanced Topics in Applied Mathematics
  • MA6600 Advanced Topics in Computational Mathematics

Discrete Mathematics

Students of Discrete Mathematics study design and coding theory, graph theory, number theory, and algebra.

• Core courses:
  • MA5221 Graph Theory
  • MA5222 Design Theory
  • MA5231 Error-Correcting Codes
  • MA5301 Algebra I
• Elective courses (choose two):
  • MA5201 Combinatorial Algorithms
  • MA5280 Topics in Applied Combinatorics
  • MA5302 Algebra II
  • MA5320 Commutative Algebra
  • MA5360 Number Theory
  • MA6222 Advanced Topics in Design Theory
  • MA6231 Advanced Topics in Coding Theory
  • MA6280 Advanced Topics in Combinatorics, Algebra, or Number Theory
  • MA6300 Advanced Topics in Algebra

Statistics

While providing a broad statistics background, the Statistics program also specializes in statistical genetics, computational methods, and functional data analysis.

• Core courses:
  • MA5711 Mathematical Statistics I
  • MA5712 Mathematical Statistics II
  • MA5731 Linear Models
  • MA5741 Multivariate Statistical
• Elective courses (choose three):
  • MA5702 Statistical Consulting
  • MA5730 Nonparametric Statistics
  • MA5732 Generalized Linear Models
  • MA5750 Statistical Genetics
  • MA5761 Computational Statistics
  • MA5770 Bayesian Statistics
  • MA5790 Predictive Modeling
  • MA5791 Categorical Data Analysis
  • MA6700 Advanced Topics in Statistics
  • MA6701 Probability

Additional Requirements

• Find an advisor and form a PhD dissertation committee, which must include one faculty member from outside of the department.
• Complete at least two 6000-level courses in the chosen concentration.
• Complete the "breadth" requirement by taking two graduate-level courses in other concentrations.
• Pass the qualifying examination, a written exam covering advanced undergraduate material, by the end of the third semester.
• Pass the comprehensive examination, a multi-part exam covering graduate coursework, by the end of the sixth semester.
• Present a dissertation proposal to the satisfaction of the dissertation committee.
• Write a dissertation detailing the results of a substantial and original research project.
• Defend the dissertation with a public presentation and examination by the committee.