### PhD in Mathematics

There are two types of graduate oral exams in the School of Mathematics, for students in the PhD program, as described in various places on Georgia Tech websites and in the Catalogue. Here is a synopsis of some key points.

### Oral Comprehensive Exam

The final part of the Comprehensive Examination for the PhD in Mathematics is the oral specialty examination, as described in the degree description.

The Oral Comprehensive Exam is designed to allow a student to show they are ready to work on their PhD thesis and receive input from a committee of experts on the direction of their work. Some key components of the exam are:

- The students will demonstrate that they have mastered enough material in a specialized area of mathematics to begin working on their thesis.
- The students will demonstrate that they can synthesize and critically evaluate research literature in their area of specialization.
- The students will demonstrate that they can formulate and discuss interesting open problems and/or areas in need of development in their area of specialization.
- The students will demonstrate their ability to communicate mathematics ideas orally. This will include providing background, context and motivation for the problems considered as well as being able to express mathematical arguments or ideas in a cogent manner.
- The student will demonstrate their ability to communicate mathematical ideas in a written form through the oral exam proposal.
- The students will receive feedback from the committee members about potential directions their proposed work can take and connections with other parts of mathematics.

**Format:** The oral exam involves approximately a 40 to 45 minute talk on their area of research making sure to address the above issues. This will be followed by 10 to 15 minutes of questions and comments from the audience that will hopefully include constructive ideas about the work and/or their presentation. The general public is allowed in oral exams during the talk portion and can ask questions, but there should be some time for the committee to ask questions and make comments to the student in private. Lastly the committee will meet privately for a few minutes to discuss the performance, vote on whether the student passes or not and fill out the evaluation forms.

Please note that due to the format and purpose of the exam, it is not suitable to just give a seminar talk.

**
Exam proposal:** The oral exam proposal must be completed at least one week before the exam. The proposal should be between one and three pages, preferably typeset with TeX or LaTeX, consisting of the following elements:

- List of the committee members for the exam.
- A brief, but careful and precise, discussion of area and direction of the student's research.
- A list or discussion of the literature read to prepare for the exam.

This material will help the committee provide better feedback to the student, allow the student to practice mathematical exposition, and provide a record of the student's direction of research at one point in time (but this is not meant to limit the direction a student's research ultimately takes).

** Regulations:** Students and committee members should comply with the following regulations.

- Every doctoral student in mathematics shall pass this oral comprehensive exam within 3 years of first enrolling in the doctoral program.
- The oral exam committee consists of the dissertation advisor and two or more members chosen by student and his or her advisor. An additional member is appointed by the graduate coordinator or the graduate committee.
- The oral exam proposal must be submitted to the graduate advisor and all committee members at least one week before the exam.
- The committee members should also receive a copy of or link to this document (pdf version available here) and the Comprehensive oral exam survey so they are fully aware of the parameters of the exam.
- The student should bring one copy of the Oral specialty form and a copy of the Comprehensive oral exam survey for each committee member.
- At the completion of the exam each committee member should fill out the Comprehensive oral exam survey, the students advisor should also complete the Oral specialty form and then collect all the paperwork and deliver it to the graduate advisor.