No one can earn a doctorate merely by completing a specified course of study; the doctoral candidate must demonstrate high scholarship and the ability to perform significant original research in mathematics.
General requirements: Completion of the Ph.D. requires four full years of graduate study (72 hours), with at least 48 hours spent in residence at Washington University. The student must spend at least one academic year as a full-time student; this requirement cannot be met wholly by summer sessions or part-time study. The student may, with departmental permission, transfer a part of the 72 hours from other universities. The typical load is nine credit hours per semester. A grade point average of "B" or better is required in graduate course work.
Graduate students in mathematics may ordinarily expect up to five years of support. Continuation of support each year is dependent upon normal progress toward the degree and satisfactory performance of duties.
For the well-prepared student, "normal progress" usually means: At the end of his or her second year, the student should have successfully completed the four qualifying exam course sequences; at the end of the third year, the student should have completed the major and minor oral exams and the language requirement; by the end of the fourth year, the student should have completed the 72-hour course requirement, and should be making substantial progress on a thesis. Students must also complete the Teaching Seminar course (L24 597), which prepares them for both TA work and academic teaching duties, which is an integral part of all scholarly activities. The course spans three semesters usually starting in the second semester. Students will have departmental duties (TA, grading, proctoring) of no more than twelve hours per week as teaching assistants.
Please note, however, that the sequence outlined above is for "well-prepared" students. The exact point at which any student enters the sequence depends upon his or her ability and background. When warranted, we will deviate from the normal sequence, and tailor a program that fits the student's ability and background.
Specific course requirements: The 72 hours of course work must include four basic graduate sequences : Math 5021-5022, 5031-5032, 5041-5042, 5051-5052. In exceptional circumstances, departmental permission may be requested to replace one of these sequences with a suitable alternative. The student may also petition the department to waive one or more of the sequences because of work done previously.
It is in each student's best interest to take the four sequences that contain the material covered in the qualifying exams as soon as their individual program allows. Sequels to these courses, at the 500 level, are frequently offered; the qualifying exam courses are generally prerequisites to these 500 level courses.
Language requirement: Most research literature in mathematics is written in English, French, German, or Russian. Consequently the department requires two of these languages for the Ph.D. If the student's native language is English, then he or she must demonstrate competence in one of the other three languages by either:
submitting an undergraduate transcript showing one year of one of these languages passed with a grade of C or better;
taking a one-semester course in one of these languages while a graduate student at Washington University, and passing with a grade of ``B'' or better; or
passing one of the annual written exams given by the department in mathematical French or German or Russian; to pass, the student must translate a passage in the language from a mathematics journal or book.
A student whose native language is not English must demonstrate proficiency in English. The student will also be expected to become fluent in spoken English. In particular, any student who expects to gain teaching experience while pursuing a degree will need to do this as soon as possible.
Ordinarily, otherwise qualified students who score less than 600 on the Test of English as a Foreign Language (TOEFL) are not admitted into the program. If English is not the student's native language, he or she must pass an oral English proficiency exam with a grade of "3" or better. If the student does not score a "3" the first time he or she takes the exam, the director of the English Language Program at the International Office will recommend taking one or more classes to improve reading, writing, pronunciation, listening or speaking skills. After the recommended classes have been completed, the student is required to retake the English proficiency exam. Once the student has demonstrated the ability to handle teaching a class (by scoring a "3" or better on the exam), he or she will qualify for a Teaching Assistantship or teaching duties. All students are expected to fulfill the language requirement during their first two years of graduate study.
Qualifying examinations: The qualifying exam is in two parts. One is a series of four written tests covering a range of topics, and one is an oral exam on two selected topics.
The written tests cover the material in the four basic course sequences: 5021-5022, 5031-5032, 5041-5042, and 5051-5052. Each spring, at the end of each sequence, all students enrolled in the course take a two-hour final exam; this exam usually covers the second half of the sequence. Doctoral candidates take an additional one-hour exam which covers the entire sequence. To pass the qualifying exam in one of the four areas, the student must pass the three hour combined exam.
Because each sequence varies somewhat in content from year to year, it is recommended that the student take each set of exams at the conclusion of the sequence in which he or she is enrolled. No advantage is gained by delaying the exam for a year. It is desirable to make every effort to finish all four exams by the end of the second year of study.
Some students will enter the Ph.D. program with previously acquired expertise in one or more of the four basic sequences. This sometimes happens with students who transfer from other Ph.D. programs, or who come from certain foreign countries. Such students may formally petition the Chairman of the Graduate Committee to be exempted from the appropriate course and from its qualifying exam. The petition must be accompanied by hard evidence (e.g., published research, written testimony from experts, records of equivalent courses, or examinations and the grades achieved on them). The Graduate Committee will make the final judgment on all exemption requests.
Once the written phase of the qualifying process is complete, the student is ready to begin specialized study. The oral component of the qualifying exam is designed to expedite this process. Along with a committee of at least two faculty members, the student selects one major and one minor topic, and a body of literature dealing with each. The student then usually spends a semester studying the selected material. At the end of this period the student demonstrates mastery of each of the two selected topics by means of satisfactory oral expositions to a faculty committee. One member of this committee will in all likelihood become the student's thesis advisor and may have already agreed to be the advisor. The preparatory work for the presentation often becomes the foundation on which the thesis is constructed.
Following the oral and language exams, work on the thesis begins.
The dissertation and final oral exam: The student's dissertation is the single most important requirement for the Ph.D. degree: it must be an original contribution to mathematical knowledge. This is the student's opportunity to conduct significant independent research.
It is the student's responsibility to find a thesis advisor who is willing to guide his/her research. Since the advisor should be part of the major and minor orals committee, the student should have engaged an advisor by the end of the third year of study.
Once the department has accepted the dissertation (on the advice of the thesis advisor), the student is required to pass a final oral examination. Part of this procedure is a question/answer period in which the student is expected to ``defend'' the thesis.
For information about preparing the thesis and its abstract, and about the deadlines involved, please consult the following items from the Graduate School of Arts and Sciences: the 2014 Doctoral Dissertation Guide, the forms page at http://graduateschool.wustl.edu/forms, and the Policies and Guides page at http://graduateschool.wustl.edu/policies-and-guides. For a sample thesis TeX file and style file go to http://wumath.wustl.edu/links.