PART IV Doctoral Degrees in Mathematics
The Department of Mathematics offers graduate work leading to the degrees Doctor of Philosophy and Doctor of Philosophy in Applied Mathematics. An incoming student with a bachelor's degree or its equivalent is usually admitted into a master's program first. Admission to the doctoral program is limited to those applicants who possess a master's degree in mathematics or equivalent preparation as determined by the Director of Graduate Studies. The requirements for the various doctoral degrees are listed below. Please note that credits used to satisfy requirements for a Master’s degree may not be applied toward the requirements for a Ph.D. degree. Students must be enrolled the semester they take the qualifying and comprehensive examinations and the semester they defend their dissertation.
Ph.D. Degree in Mathematics
In order to receive the Ph.D. degree in mathematics the student must:
- Satisfy the qualifying examination requirements.
- Pass the comprehensive examination.
- Take thirty credits of 800-900 level mathematics courses, excluding dissertation credits (Math 999) and core courses in areas in which the qualifying examination requirements are fulfilled. These courses must be approved by the student's guidance committee.
- Satisfy the foreign language requirement.
- Satisfy the seminar requirement.
- Take twenty-four credits of dissertation (Math 999).
- Write and defend a doctoral dissertation acceptable to the student's dissertation committee.
Ph.D. Degree in Applied Mathematics
The requirements are the same as for the Ph.D. in Mathematics with the following additions:
- At least 18 credits of the 30 required in (3) above must be in approved applied mathematics courses and
- The doctoral dissertation must be in an area of applied mathematics.
Dual Ph.D. Degree
The Mathematics Department offers the Dual Ph.D. degree jointly with other programs. For a current program with Quantitative Biology and Modeling Initiative (QBMI), please consult http://www.biomodel.msu.edu/grad_research.php.
Students who are interested in these dual degree programs should contact the Director of Graduate Studies to obtain further information regarding the policies and requirements.
Qualifying Examination Requirements
Written qualifying examinations are given in five areas: (1) Algebra, (2) Differential Equations,(3) Geometry/Topology, (4) Numerical Analysis, and (5) Real and Complex Analysis. These exams are based on syllabi available to the student and are given twice yearly, at the beginning of each semester.
Parallel to these exams the department offers five "core" sequences: (1) Algebra - MTH 818-819, (2) Differential Equations - MTH 848-849, (3) Geometry/Topology - MTH 868-869, (4) Numerical Analysis - MTH 850,851,852, and (5) Real and Complex Analysis - MTH 828-829. See the descriptions for these courses on pages 19-22 of this handbook. While these courses will cover much of the material on the corresponding exam syllabi, the student may need to learn some of this material, independently.
Ph.D. students in mathematics and applied mathematics satisfy the qualifying examination requirements by passing written examinations in three of the following five areas: (1) Algebra, (2) Differential Equations, (3) Geometry/Topology, (4) Numerical Analysis, and (5) Real and Complex Analysis. These requirements must be completed within four semesters of entering the doctoral program. Within this period of time the written exams can be taken at most three times for each area and passed in any order, and all exams do not need to be passed at the same time.
The Comprehensive Examination
The content of the comprehensive exam will be decided by the student's guidance committee and will cover material germane to the students' research interest. The committee chair, with the student, will prepare the syllabus at least three months before the exam . The comprehensive exam will be an oral exam based upon this written syllabus. The purpose of the exam is to determine if the student can do independent research. Consequently, the exam will not necessarily correspond to specific course material. The exam may be taken twice and should normally be completed within one year of completion of the qualifying examinations. If one of the committee members is not available to attend the exam, the student can still be tested and either pass or fail by majority vote.
The content of the exam should be roughly that of a semester course at the 900 level. It should be material known to most researchers in the field. The student should be able to learn the material in about a semester from completion of the qualifying exams. In fact, the content of the exam may overlap with that of graduate courses. Examples of content might be: (1) Schauder theory (in pde), (2) Seiberg-Witten theory (in topology), (3) class field theory (in algebra), (4) one-dimensional dynamical systems (in dynamics).
The comprehensive examination should test both knowledge of material and research promise. The examination itself should be open to any interested student or faculty member.
The Foreign Language Requirement
The Foreign Language Requirement consists of one language from among French, German, and Russian. The requirement for a language may be satisfied in one of the following ways:
- Native fluency.
- Course work: passing approved course(s) in the respective foreign language department at Michigan State University (e.g. French 400, German 400).
- Exam: passing a foreign language test given by a member of the faculty in the Department of Mathematics or by making arrangements for testing with the appropriate language department.
Ph.D. Seminar Requirement
Each Ph.D. student must give at least two fifty-minute seminar talks. The talks, which should be at an advanced level, can be given either in a faculty or student seminar. The completion of this requirement must be certified by a faculty member knowledgeable in the area covered by the talks. A student should be certified as having fulfilled this requirement only if the talks are reasonably good, both in content and form.
Guidance Committee and Dissertation Committee
It is the responsibility of the candidate, in consultation with the Director of Graduate Studies, to form a guidance committee during the first year of doctoral study. The guidance committee is to consist of four faculty members, selected by the Director of Graduate Studies in consultation with the student.
The guidance committee must be chaired or co-chaired by a regular tenure system faculty member currently having at least a 50% appointment in the Department of Mathematics. Furthermore, at least two of the four guidance committee members must satisfy this description.
The responsibilities of the guidance committee are:
- To plan the student's program, taking into account the student's goals and the courses and seminars appropriate to these goals.
- To assess progress, approve program changes, and to offer its best advice.
- To prepare a syllabus for the comprehensive examination.
- To indicate a timetable for the completion of courses, the comprehensive examination, and the language and seminar requirements based on the student's entering level.
- To observe the student’s classroom performance, upon request, and to prepare a teaching letter on behalf of the student for job applications.
It is the responsibility of the student to plan a tentative program and have it approved by his or her guidance committee.
When a student passes the comprehensive examination, the guidance committee for that student will be dissolved. The student will then be expected to find a dissertation advisor. The dissertation advisor has the right to indicate conditions (courses, seminars, specific languages, specialty examinations) under which the student will be accepted by the advisor. The Department does not guarantee the student a dissertation advisor.
A dissertation committee will be formed after a faculty member has agreed to be the student’s dissertation advisor. The dissertation committee is to consist of five members, selected by the Director of Graduate Studies in consultation with the dissertation advisor and the student. These members must agree to be on the committee. In addition, the dissertation committee must be chaired or co-chaired by a regular tenure system faculty member currently having at least a 50% appointment in the Department of Mathematics. Furthermore, at least three out of five dissertation committee members must satisfy this description.
The responsibilities of the dissertation committee include:
1. Assessing the student's progress. 2. Planning the seminar and research phase of the student's work, not excluding additional course requirements in areas deemed appropriate to the student's research. 3. Reading and approving the dissertation.Annual Evaluation
When a student is admitted into our Ph.D. program, it is expected that they progress towards the degree requirements in a timely fashion. The student’s guidance committee and dissertation committee are responsible for evaluating the student’s competency and rate of progress.
To assist in the evaluation progress, each student is required to file an annual progress report in early March. The chair of the guidance committee or the dissertation advisor must sign the progress report and may wish to supply written comments at that time. The student can then add a written response to the professor’s comments. A copy of the progress report and evaluation will be kept in the student’s departmental file and can be accessed by the student or any member of the faculty. The student will meet annually with the Director of Graduate Studies to discuss his/her annual report and his/her progress towards the advanced degree before the end of March.
If a student is not making timely and reasonable progress towards his/her degree in terms of completing coursework or taking the necessary exams, within fifteen days following their annual meeting with the Director of Graduate Studies, the student should receive a letter from the Director specifying the deficiencies and describing the expected steps, with a timetable, to get back in good standing. The student may wish to respond in writing if they disagree with the deficiencies listed or with the steps and timetable for remediation. Any responses will become part of the student’s file.
It is a disservice to permit a student to continue towards the advanced degree without necessary qualifications, a high level of motivation, commitment, and aptitude. Judgment regarding retention is made by the student’s guidance committee or dissertation committee. The committees may consult the Director of Graduate Studies and the department chairperson. If a majority of the guidance committee decides that a student lacks such standards, he/she may be asked to withdraw from the program according to the procedures as defined in the Graduate Students Rights and Responsibilities (http://vps.msu.edu/SpLife/grr1.htm) .
The Dissertation
Every doctoral candidate must write a dissertation acceptable to the faculty. The dissertation is to be an original and significant contribution to mathematical knowledge. It constitutes evidence that the candidate is a well-trained and capable research worker in some specialized area of mathematics. The research on the dissertation is done under the guidance of the dissertation advisor and dissertation committee.
The Dissertation Defense
The final public oral examination in defense of the dissertation is conducted by the dissertation committee and is arranged by the candidate in consultation with the dissertation committee and the Director of Graduate Studies. The candidate must present copies of the dissertation to the committee at least three weeks prior to the date of the defense. It is the responsibility of the candidate to determine that all members of the committee are available on the expected date of the defense. Requests for changes or substitutions in the dissertation committee must be submitted to and approved by the Director of Graduate Studies at least four weeks prior to the anticipated date of the defense. Last minute requests for changes may not be honored.Teaching
Every doctoral candidate is required to complete one year of teaching as part of his or her professional training.
Residency Requirements and Time Limits for all Ph.D. Degrees
One year of residence on the campus after completion of the master's degree or its equivalent is required to permit the student to work with the faculty, and to engage in independent and cooperative research utilizing University facilities. A year of residence is two consecutive semesters, involving completion of at least six credits of graduate work each semester.
The time limit for completion of the requirements for the degree is eight calendar years.