Mathematics

The PhD is the highest degree in Mathematics, designed to provide a broad background in the traditional areas of mathematics and also take students to the frontier of research. The program prepares students for careers in research and teaching at the university level, or the equivalent in government and industry. Admission to the PhD program requires a Bachelors or Masters degree in Mathematics or a related discipline.

Candidates for the PhD degree must pass written and oral qualifying exams, write a dissertation embodying the results of original research, and present a final oral defense of the dissertation. They also must demonstrate knowledge of two foreign languages.

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. Knowledge of two "languages" as discussed below.
• 2. Passing written and oral qualifying examinations.
• 3. Writing a dissertation embodying the results of original research which is acceptable to the   student's dissertation committee.
• 4. A final oral defense of the dissertation. A student's progress towards the Ph.D. degree is initially supervised by a three person committee, increasing to four or five members following the written qualifying exams. The student's faculty advisor chooses this committee, and is its chair.

The Ph.D. Qualifying Examination System consists of two parts. The first part consists of four Written Qualifying Exams and the second consists of an Oral Qualifying Exam.

Written Qualifying Exams are offered in Algebra, Real Analysis, Complex Analysis, Topology, Numerical Analysis and Probability. The 8000-level sequences in each area are designed to prepare the student for Qualifying Exams. Written Qualifying Exams are offered every year in August and in January, during the week before the start of classes. Syllabi, and copies of old Exams, are available from the department office for students to use in studying for Exams or can be found on-line from the section for current graduate students.

Each Ph.D. candidate is required to pass four Qualifying Exams, including both Real and Complex Analysis, and either Topology or Algebra.

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 his or her area of specialization. It is to be taken within 1 year of the time the student passes his or her last Written Qual. (A student who passes Written Quals early will be allowed 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.

Ph.D. Language Requirements:  A student must either demonstrate: a reading knowledge of two foreign languages with significant mathematical literature, chosen from French, German, and Russian; OR a reading knowledge of one of the above languages, and sufficient competence with computers to do mathematical research; OR a reading knowledge of one of the above languages, together with sufficient improvement in English, if the student is an international student whose English is initially inadequate.
Language/Research Skills: A student can satisfy the language requirements by passing an appropriate course (French, German, or Russian 2001 or above, FREN 2500, GRMN 3500, or CSCI 7010) with a B-  or better; OR by translating an unfamiliar mathematical paper, using a dictionary, in a reasonable length of time (3-4 hours for a 4 page paper), to the satisfaction of a qualified examiner from the Mathematics faculty; OR  by having native proficiency in one of the languages above, as certified by a qualified examiner; OR doing a computer project to the satisfaction of a qualified examiner from the Mathematics faculty.

• Application for admission
• Application-processing fee
• Transcripts. Documents must be submitted in both Russian and English. Russian documents must bear the original institution stamp. The English translations must bear the original institution stamp or the original stamp/signature of the certified translator.
• 4-5 year Diplom from a recognized institution.. An official copy of the Diplom, which bears the original stamp of the issuing institution. The English translation is required and must bear the original stamp of the issuing institution or the original stamp/signature of the certified translator.
• Entrance test scores
• Letters of recommendation
• Certification of finances forms (international applicants)
• Minimum TOEFL score requirement: overall score of 80 with at least 20 on speaking and writing
• Minimum IELTS score requirement: overall band-width of 6.5, with no single band (score) below 6.0.

Scholarships

The Mathematics Department offers financial support to all PhD students as long as they are making satisfactory progress toward their degrees. Historically, about half of our MA and MAMS students have received financial support; recently, the percentage of supported Masters students has been higher. Available support includes the prestigious Presidential Fellowships at $27,000 for five years, Graduate School Assistantships with no teaching duties for two years, and Departmental Teaching Assistantships. In addition, we support most of our graduate students during the summer.