# Mathematics, PhD

*for the Doctor of Philosophy in Mathematics*

**Graduate Degree Programs in Mathematics**

- Actuarial Science, MS
- Applied Mathematics, MS
- Mathematics, MS
- Predictive Analytics and Risk Management, MS
- Enterprise Risk Management
- Financial and Insurance Analytics
- Mathematics, PhD
- optional concentrations:
- Teaching of Mathematics, MS

*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: Yuliy Baryshnikov

Mathematics Department website

Mathematics Department faculty

Mathematics faculty research

273 Altgeld Hall, 1409 West Green Street, Urbana, IL 61801

(217) 333-5749

Mathematics email

**College of Liberal Arts & Sciences**

College of Liberal Arts & Sciences website

**Admissions**

Mathematics Admissions & Requirements

Graduate College Admissions & Requirements