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The department offers programs leading to the PhD degree in the areas of algebra, analysis, applied mathematics, combinatorics, geometry, mathematical physics, numerical analysis, probability, statistics, and topology. The PhD is a degree of quality not to be conferred in routine fashion after completion of a specific number of courses or after attendance in Graduate School for a given number of years. All applicants are initially enrolled in the pre-PhD program. In the pre-PhD program, you take one or two years of courses (depending on your background) in preparation for the PhD qualifying examination. The decision of whether to spend one or two years in the pre-PhD program is made in conjunction with an advisor with whom you meet when you first arrive. You must take the PhD qualifying examination at the latest at the beginning of your third year (during the week before fall term classes begin). Students with a strong background usually take the examinations at the beginning of their second year. The qualifying examination consists of examinations on two basic 600 level graduate courses, one each from two of the following three categories: (1) algebra; (2) analysis or probability; (3) algebraic topology or differential geometry. Formal admission to the PhD program itself is based on the following criteria: satisfactory performance on the qualifying examination, completion of three courses at a level commensurate with study toward a PhD, and satisfactory performance in seminars or other courses taken as a part of the pre-PhD program. Students who are not admitted to the PhD program because of unsatisfactory performance on the fall term qualifying examination may retake the examination once only at the beginning of winter term. Once you have successfully transferred to the PhD program itself, usually at the beginning of your third (possibly second) year here, you start to take more advanced seminar courses and reading courses, as you begin the process of finding a PhD advisor. You should expect to have found a PhD advisor by the end of the spring term of the academic year in which you pass the qualifying examinations. With your PhD advisor, you then draw up a detailed program of study in preparation for the comprehensive oral examinations, usually taken by June one year later. Once you have passed the oral examination, you begin to work on your PhD dissertation in earnest, which usually takes two further years depending on the student. To complete the requirements for the PhD, you must have passed one language examination, the comprehensive oral examination, submit a dissertation and have it read and approved by a dissertation committee, and defend it orally in a formal public meeting. Language Requirement: The department expects PhD candidates to be able to read mathematical material in a second language selected from French, German, and Russian. The language requirement may be fulfilled by (1) passing a departmentally administered examination, or (2) satisfactorily completing a second-year college level language course. The language requirement should normally be completed after passing the preliminary examination and definitely before taking the oral examination. Comprehensive Oral Examination: This oral examination emphasizes the basic material in the student's general area of interest. A student is expected to take this examination within two years of passing the qualifying examination. At the discretion of the Graduate affairs committee, students who fail the oral examination may be allowed to retake the oral examination at most once. Dissertation: PhD candidates in mathematics must submit a dissertation containing substantial original work in mathematics. Requirements for final defense of the thesis are those of the Graduate School. |
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