Students who want to pursue a PhD in the area of Algebra/Algebraic Geometry/Number Theory and their applications must try to follow the instructions below.

The research of our faculty is in one of the following areas:

The research of our faculty is in one of the following areas:

- Algebraic Geometry (Curves, Jacobians, Moduli Spaces, Singularities)
- Computational Algebra/Computational Algebraic Geometry
- Coding Theory and Cryptography
- Theta functions and their applications

A student must fulfill all requirements as stated in the catalog. Below we give a guide for all PhD students intending to work in Algebra.

A Master of Science degree in

A Master of Science degree in

has been proposed. If you are interested in this new program we would like to hear from you.

**Courses:**

**Breadth requirements:**

- MTH 571-572: Algebra I, II
- MTH 551: Real Analysis; MTH 555: Complex Analysis
- MTH 613: Statistics and one other graduate course in Statistics

**Required Courses:**7 of the following courses:

- MTH 671: Commutative Algebra
- MTH 672: Algebraic Geometry
- MTH 577: Computational Algebra
- MTH 670: Algebraic Number Theory
- MTH 673: Coding Theory
- MTH 561-562: Algebraic Topology
- MTH 569: Graph Theory
- Theory of Computation
- Combinatorial Optimization

#### PhD qualifying exams

There are two qualifying exams for students working in algebra.

- PhD qualifying exam in algebra (based on MTH 571-572)
- PhD qualifying exam in the area of concentration (to be decided in cooperation with your advisor)

The exam is graded Pass/Fail and is administered by the Algebra Committee which contains three faculty members of the Department from the area of research in Algebra/Algebraic geometry. The student can take the exam only twice.

The PhD qualifying exam in algebra is offered twice a year in May and August of each year. The exam in the area of concentration is offered at the students request.

### PhD oral exam

The oral exam is an oral presentation of the thesis problem by the student in front of the Dissertation Committee. The exam is graded pass/fail. A unanimous decision of the committee is required for the student to pass. After passing the oral exam the student is a PhD candidate.

### Thesis Defense

The thesis defense is done in front of a Dissertation Committee. The first part of the defense is open to the public and it lasts one hour. During the second hour the committee meets with the student in private to discuss certain matters of the scientific content. The exam is graded Pass/Fail. A unanimous decision of the committee is required for the student to pass. The student can take the exam at most twice.