Doctor of Philosophy in Natural Sciences: Mathematics
As part of the Natural Sciences Ph.D. program, students in a primary discipline of Mathematics must meet the minimum Ph.D. program requirements. These can be found within the main program page and subsequent requirement pages.
Mathematics
Please see the School of Graduate Studies web page for the contact information for the discipline Coordinator. To view all doctoral and graduate faculty in Mathematics, see this web page.
Admission Requirements
Applicants must meet both the general and the discipline-specific criteria for admission and be recommended for admission by the faculty review group. Upon approval by the graduate dean, students are admitted to the School of Graduate Studies.
Please see the website for updated application deadlines.
Primary Discipline
For full admission, an applicant should have a bachelor's degree or a master's degree in mathematics/statistics (or equivalent) from an accredited college or university. Applicants who do not have a master's degree are expected to provide strong evidence of academic ability and research capability. GRE General score submission is not required, but is recommended.
A student who is admitted to the Ph.D. program while having not completed all of the qualifying/pre-requisite coursework as described below must complete the missing courses with a GPA of 3.0 or better to be deemed qualified to continue in the Ph.D. program.
Secondary Discipline
For full admission, an applicant should have a bachelor's degree in mathematics/statistics from an accredited college or university, or a bachelor's degree in another subject including evidence of a strong performance in at least three mathematics courses beyond Calculus I, II, and III.
Applicants may be provisionally admitted if the above conditions are not fully satisfied at the time of application.
Core Coursework Requirements
Students with a Mathematics primary discipline will complete a minimum of 42 credit hours for the degree. This includes at least 21 credit hours in the primary discipline, 9 hours outside the primary discipline (decided in consultation between the student and primary advisor), and at least 12 hours of dissertation credit in the primary discipline.
Primary Discipline
Mathematics focus:
| Code | Title | Credits |
|---|---|---|
| A minimum of 21 credit hours of coursework, completed with at least a B (3.0) average. | ||
| MATH 5519 | Algebra II | 3 |
| MATH 5521 | Differential Equations | 3 |
| MATH 5523 | Real Variables II | 3 |
| MATH 5542 | Advanced Numerical Analysis | 3 |
| Choose 1 of the following: | 3 | |
| Probability | ||
| Theory of Linear Model | ||
| Choose 2 of the following: | 6 | |
| Algebra I | ||
| Complex Variables I | ||
| Numerical Analysis and Scientific Computing | ||
| Mathematical Methods in Data Science | ||
| Optimization | ||
| Special Topics | ||
| Coursework Outside of Primary Discipline (either in designated secondary discipline or multiple other disciplines) 1 | 9 | |
| Dissertation | 12 | |
| Total Credits | 42 | |
Statistics focus:
| Code | Title | Credits |
|---|---|---|
| A minimum of 21 credit hours of coursework, completed with at least a B (3.0) average. | ||
| STAT 5572 | Multivariate Analysis | 3 |
| STAT 5576 | Probability | 3 |
| STAT 5578 | Advanced Mathematical Statistics | 3 |
| STAT 5588 | Theory of Linear Model | 3 |
| Choose 1 of the following: | 3 | |
| Real Variables II | ||
| Advanced Numerical Analysis | ||
| Choose 2 of the following: | 6 | |
| Mathematical Methods in Data Science | ||
| Statistical Design Of Experiments | ||
| Applied Statistical Analysis | ||
| Time Series Analysis | ||
| Nonparametric Statistics | ||
| Regression Analysis | ||
| Special Topics | ||
| Coursework Outside of Primary Discipline (either in designated secondary discipline or multiple other disciplines) 1 | 9 | |
| Dissertation | 12 | |
| Total Credits | 42 | |
Total Credit Hours: 42
- 1
Minimum of 9 hours with possibility of more required. Decided in consultation with primary advisor.
Secondary Discipline
Students with a Mathematics secondary discipline will complete a minimum of 9 credit hours in the discipline.
| Code | Title | Credits |
|---|---|---|
| At least 9 hours of graduate coursework in Mathematics or Statistics, with at least a B (3.0) average. Up to 3 hours may be at the 400-level. | 9 | |
| Total Credits | 9 | |
Qualifying Exams
The final exams in the core courses will play the role of qualifying exams. A qualifying exam passing score (usually 70% or 80% of the maximum possible grade) is decided by the instructor, who will notify the doctoral students whether they passed the qualifying exam. Students need to have a passing score on at least two qualifying exams within two years from admission into the program. The choice of the two exams to be passed needs to be agreed upon with the advisor. If a student did not pass a qualifying exam the first time, they can re-take once the exam. Re-takes of qualifying exams can only be scheduled twice a year, in the beginning of the Fall, respectively Spring semester.
Comprehensive Examinations
Following the completion of the qualifying examinations, the student is deemed fully qualified to carry out doctoral-level research. At this stage, the student begins his or her doctoral research. Within two years of successful completion of the qualifying examination, the student is required to complete the Ph.D. Comprehensive Examination. The Comprehensive Exam consists of submitting a fully developed proposal of the Ph.D. research topic, together with an oral presentation to the student’s full Ph.D. committee. The exact timing and topic of this written and oral comprehensive exam will be determined by the student and their supervisory committee.
Dissertation and Final Oral Examination
Within two years of admission to Candidacy, the student is required to have completed the necessary research and writing to form the Dissertation. Once this is complete, the student must complete the Final Oral Examination. The Final Oral Examination is a two-hour discussion with the student and the supervisory committee. The student must prepare a presentation that outlines the content of the dissertation. The presentation is a public event, so anyone is free to attend. Following the completion of the presentation, a closed-door session with the student and the Supervisory Committee is held in which the Candidate fields questions and comments regarding the content of the Dissertation. Following successful completion of the Final Oral Examination, the committee will make recommendations for revisions to the dissertation, and the Candidate is required to address these recommendations in order to complete the Ph.D.
Other Requirements
All Ph.D. students with Mathematics as the primary discipline are required to attend the department graduate seminar at least five times per semester.
The student must satisfy all requirements set forth by the School of Graduate Studies.