Prerequisites: To enter the Ph.D. program a student should hold at least a Bachelor's degree in mathematics. The academic record of a student applying to the Ph.D. program should contain substantial evidence that the student will succeed in the doctoral program. In reviewing an applicant's folder, the Graduate Committee gives substantial weight to the applicant's transcripts and letters of recommendation. Requirements: The Ph.D. degree has no rigid course requirement beyond the residency requirement (however, breadth and depth of knowledge are strongly encouraged). It does require: 1. Passing written and oral qualifying examinations. 2. Writing a dissertation embodying the results of original research which is acceptable to the student's dissertation committee. 3. A final oral defense of the dissertation. A student's progress towards the Ph.D. degree is initially supervised by a three-person committee appointed by the Director of Graduate Studies (DGS) and called Preliminary Advisory Committee (PAC). Once the graduate student has passed the written qualifying exams and has chosen a dissertation advisor, the supervising committee consists of the dissertation advisor who chairs the committee, and three or four additional members chosen by the chair after discussions with the student. The Ph.D. Qualifying Examination System consists of two parts. The first part consists of passing three or four Written Qualifying Exams, and the second part consists of an Oral Qualifying Exam. Written Qualifying Exams are offered every year in August before the start of Fall semester classes and in January before the start of Spring semester classes. Study guides and copies of previous qualifying exams are available on the Graduate Program website for students to use in preparing for their Written Qualifying Exams. Written qualifying exams are offered in algebra, complex analysis, numerical analysis, real analysis and topology. There are three possible grades on each exam: pass, master's pass or fail. Each PhD candidate is required to either: (i) attain pass grades on three written qualifying exams or (ii) attain pass grades on two written qualifying exams and master's pass grades on two additional written qualifying exams. The choice of which three or four exams to apply to meet these requirements from the available exams must be approved by the student's Preliminary Advisory Committee. (Tentative) Once a Ph.D. student has passed at least two written exams, the department expects that the student will now be actively looking for a suitable dissertation supervisor. For many students, this happens at the beginning of the fall semester of their second year at UGA. This search might involve for instance taking courses taught by potential supervisors, or requesting to take a reading course with a potential supervisor who is not teaching a suitable graduate course, or attending research seminars also attended by potential supervisors. Until the graduate student has found a suitable dissertation advisor, it is incumbent to the graduate student, before registering for classes in any given semester, to appraise the Director of Graduate Studies of their efforts and progress towards finding a suitable dissertation supervisor. Once the student is matched with a dissertation supervisor, the student turns to preparing for the Oral Qualifying Exam. The Oral Qualifying Exam is based on the student's anticipated area of specialization. In it, the student is expected to present material from a research paper and to answer general questions about their area of specialization. It is typical for students to take their oral exam within 1 year of their passing the Written Qual requirements. (Students who passes Written Quals early will sometimes take additional time to pass the Oral Qual.) To begin preparing for the Oral Qual, a committee of four or five is chosen (including the student's thesis advisor). The student prepares by reading research papers in the area, and the student, advisor, and committee agree upon a body of material for which the student will be responsible. The exam consists of a presentation on the prepared research papers, followed by a question period covering the presentation and the agreed upon body of material. Graduate Guidebook
