Mathematics, PhD
for the Doctor of Philosophy in Mathematics
Graduate Degree Programs in Mathematics
for the Doctor of Philosophy in Mathematics
Students working toward a Ph.D. degree usually require from four to six years to complete the requirements. Each student must pass the comprehensive examinations (testing the student's knowledge of basic graduate-level mathematics in algebra, analysis, and other areas) and the preliminary examination (testing the student's ability to begin or continue research in a chosen field). Students must also write and defend a research thesis in their field of mathematics.
For additional details and requirements refer to the department's Guide to Graduate Studies and the Graduate College Handbook.
Requirements
| Code | Title | Hours |
|---|---|---|
| Students must demonstrate competence in five core courses including the following: | ||
| To demonstrate competence, a student must receive a B+ or higher in the course, or pass a written exam on the topic. | ||
| MATH 500 | Abstract Algebra I | 4 |
| MATH 540 | Real Analysis | 4 |
| Plus choose three of the following: | 12 | |
| Intro to Algebraic Geometry | ||
| Differentiable Manifolds I | ||
| Algebraic Topology I | ||
| Algebraic Number Theory | ||
| Analytic Theory of Numbers I | ||
| Complex Variables I | ||
| Dynamical Systems I | ||
| Partial Differential Equations | ||
| Theory of Probability I | ||
| Risk Modeling and Analysis | ||
| Mathematical Logic | ||
| Combinatorial Mathematics | ||
| Master's equivalency | 32 | |
| MATH 599 | Thesis Research (0 min applied toward degree) | 0 |
| Total Hours: | 96 | |
Other Requirements
| Requirement | Description |
|---|---|
| Other requirements may overlap | |
| MATH 405, MATH 406, MATH 415, MATH 444, and MATH 499 cannot be counted toward this graduate degree. | |
| 64 hours in residence | |
| Masters Degree Required for Admission to PhD? | No |
| Comprehensive Exam Required | Yes |
| Preliminary Exam Required | Yes |
| Final Exam/Dissertation Defense Required | Yes |
| Dissertation Deposit Required | Yes |
| Minimum GPA: | 3.25 |
for the Doctor of Philosophy in Mathematics
- Acquire a foundation in abstract algebra at the graduate level.
- Acquire a foundation in real analysis at the graduate level.
- Acquire a suitable breadth of knowledge to provide a foundation for undertaking high-level research.
- Gain a broad understanding of the range of current research in the mathematical sciences.
- Demonstrate depth of knowledge in chosen area of research specialization.
- Gain the ability to conduct independent mathematical research at a professional level.
- Gain experience and competence in the teaching of mathematics at the college level.
for the Doctor of Philosophy in Mathematics
Mathematics Department
Department Chair: Vera Hur
Director of Graduate Studies: Jared Bronski
Mathematics Department website
Mathematics Department faculty
Mathematics faculty research
273 Altgeld Hall, 1409 West Green Street, Urbana, IL 61801
(217) 333-5749
math-grad@illinois.edu
College of Liberal Arts & Sciences
College of Liberal Arts & Sciences website
Admissions
Mathematics Admissions & Requirements
Graduate College Admissions & Requirements