**Note:** *The information and policies contained on this website is for informational purposes only. The Undergraduate Record and Graduate Record represent the official repository for academic program requirements. These publications may be found at http://records.ureg.virginia.edu/index.php.*

*Official requirements for our graduate degrees are listed in the Mathematics section of the Graduate Record.*

*The general rules and requirements governed by the Graduate School of Arts and Sciences can also be found in the Graduate Record under Policies.*

Courses and research amounting to 72 credit hours. Courses must include satisfactory work in two semesters of analysis (MATH 7310, 7340), algebra (MATH 7751, 7752), and topology (MATH 7820, 7800), or the equivalent. Students may take approved courses from other departments. Students entering our program with a masters degree from another institution may get credit for up to 24 hours of coursework.

Passing grades on two General Examinations, chosen from Algebra, Analysis, and Topology. These writen exams cover the following material: Algebra (MATH 7751, 7752), Analysis (MATH 7310, 7340), and Topology (MATH 7820, 7800).

These exams are typically offered twice a year, January and August. Students are expected to attempt two different general examinations by August of their second year, to pass at least one general examination by January of their second year, and to pass both exams by January of the student's third year. A student may repeat the examinations as many times as needed in order to satisfy these requirements.

Current syllabi for the Algebra, Analysis, and Topology General Examinations:

- Syllabus for Algebra General Exam
- Syllabus for Analysis General Exam
- Syllabus for Topology General Exam

Examples of past general exams can be found here.

A passing evaluation on an oral examination covering material from two or three selected second-year courses. Its purpose is to gauge the student's readiness to begin carrying out research in the student's chosen area, and the exact content is determined by faculty in consultation with the student. The exam is normally taken in May of the second year. If problems with the student's readiness are noted, the examining panel will make recommendations on how to fix these and meet again with the student in August.

Successfully teaching and directing discussion sections of undergraduate courses, and participating in the professional training seminars MATH 7000 and MATH 7010. Teaching is evaluated, and a good record is an asset to graduates seeking academic employment.

Written under the supervision of the major advisor, the PhD dissertation must contain original contributions to the field of mathematics. The main results of the dissertation are presented at a public oral defense. A committee consisting of the major advisor and three other faculty members (two from within the Department and one from outside) must approve the dissertation and defense in order for the dissertation to be accepted by the faculty.

The Master of Arts and Master of Science programs are normally completed within two years.

Successful completion of 30 hours of approved courses at the 5000 level or above, which must include MATH 5310, 5330, 5651, 5652, or higher-level substitutes. Students may take approved courses from other departments. With permission, a Masters thesis can be substituted for up to six of the course hours. In addition, the student must pass a master’s exam: either one of the General Exams as described in our PhD program requirements, or an ad hoc exam approved by the graduate committee.

Successful completion of 30 hours of approved courses at the 5000 level or above, which must include MATH 7310, 7340, 7751, 7752, 7800, and 7820, or higher-level substitutes. Students may take approved courses from other departments. In addition, the student must pass one of the General Exams as described in our PhD program requirements.