### GENERAL STATEMENT

There are three graduate programs closely affiliated with the Department of Mathematics, namely Mathematics MATH, Applied Mathematics & Statistics and Scientific Computation AMSC, and Mathematical Statistics STAT. The Office of Graduate Studies provides administrative support for all three programs and the Associate Chair for Graduate Studies makes all decisions concerning the awarding and renewal of teaching assistantships. The Graduate Committee of the Department of Mathematics sets broad policies to achieve the basic goals of assuring an effective program providing students the maximum opportunity to earn advanced degrees and maintaining the standards of the degrees. The Committee also serves as an advisory body on admissions, curricula, and eligibility for graduate degrees.

Admission and degree requirements for the AMSC and STAT programs are set by independent committees, and differ in some details from those for the MATH program. During the first year, a graduate student has the privilege of changing between MATH, AMSC, and STAT. After the first year an application must be submitted to the Graduate School.

Some general regulations of the Graduate School are listed on this webpage, as well as specific policies of the Department. Additional information is available in the Office of Graduate Studies and in such Graduate School publications such as the Graduate Catalog, Graduate Student Life Handbook , Graduate Assistant Handbook, and the Schedule of Classes .

### EXPECTATIONS FOR DOCTORAL STUDENTS

Most full-time doctoral students (entering with a bachelor's degree) are expected to graduate in six years or less, according to the following timetable. However, students are urged to aim to graduate in less than 6 years; financial support is not guaranteed in the sixth year.

- Become involved in research activity within the first two years.

- Identify field of speciality and advisor and advance to candidacy within three and one half years.

- Identify a dissertation topic during the fourth year.

- Submit at least one paper for publication before graduation.

- Complete all requirements and graduate within six years.

For a detailed time table regarding qualifying examinations, and candidacy, see Progress to Degree

Graduate students in CMNS doctoral programs normally may expect:

- A wide selection of courses.

- Advice and mentoring by faculty in their program prior to the selection of an adviser.

- From their adviser (or, in some instances the program):

- Regular access and advice during the research and thesis writing process.

- Training in the preparation of oral and written scholarly presentations; in particular, advice and support for the writing of at least one paper for publication.

- Introductions, for example at conferences, to other members of the field.

- Assistance and advice with job searches.

### ADMISSION TO GRADUATE STUDY

Offers of admission are made to applicants selected from those who show promise in mathematics as demonstrated by their undergraduate records. It is required for admission that applicants take the general Graduate Record Examinations and the Subject Examination in mathematics. It should be emphasized that admission to graduate status does not guarantee that a student will be able to earn a degree.

After an applicant is admitted, an official letter is sent by the Graduate School stating for which semester the student is admitted. If the student does not register for the specified semester the admission is canceled and a new application must be submitted. An admission can be deferred for one time only and for up to one year.

The admission status may be terminated if a graduate student's overall average stays below B for an extended period.

### ADVISING, REGISTRATION AND MAINTENANCE OF GRADUATE STANDING

New students admitted for the Fall semester complete advising and registration during the one week orientation program that takes place in August, the week before the start of class. For currently enrolled students, registration takes place through the Office of Graduate studies every October and March for the following semester.

In order to aid students in planning their programs, the Department tries to follow a regular schedule for offering the basic graduate courses. The Department expects to offer the following two-semester sequences every year:

Math 600-601, Math 630-660, Math 730-740, Stat 600-601, Stat 700-701, AMSC 660-661, AMSC 666-667.

In addition, the Department expects to offer the following basic courses every year, as long as they have sufficient enrollment:

Math 631, Math 634, Math 642, Math 712-713, Math 734, Math/AMSC 673-674.

Many other courses will be offered as the need arises. For listings of courses that have been offered in recent years, see this page

Any course may be repeated and the grade on the repeated course replaces the original grade in determining the overall average. As long as the overall average is at least "B" at the time of receiving the degree, grades of "D", "F" and "I" may stand, but "D" and "F" count as 0 quality points in computing averages, and courses in which these grades are received cannot be used to fulfill degree requirements.

The deadline for dropping courses without penalty is normally midway through the semester. After this date all courses dropped automatically receive the grade of F unless the student withdraws from the University. The Schedule of Classes should be consulted for pertinent dates.

A full time graduate student must carry a combination of courses that adds up to at least 48 units each semester (excluding the summer sessions). For graduate assistants this requirement is reduced to a minimum of 24 units. A unit is defined as follows:

- All 400 level courses: 4 units per credit hour;
- All 600/700 level courses (except 799): 6 units per credit hour;
- 799 course: 12 units per credit hour;
- 899 course: 18 units per credit hour.

Students registering for a reading course or any 689/799/899 course should obtain the correct section number from the Administrator of the Graduate Program.

Students are expected to make steady progress toward their degrees. For the M.A. degree, all requirements must be completed within five years from the date of admission. A student admitted to a Ph.D. program must be admitted to candidacy within five years from the date of admission. After admission to candidacy all requirements for the Ph.D. degree must be completed within four additional years. Minimal continuous registration is required of all students who have been admitted to candidacy for the Ph.D. degree.

### GRADUATE STUDENT FINANCIAL AID

Graduate teaching assistantships are the main form of financial aid offered by the Department. In addition to a stipend, graduate assistants receive a tuition scholarship for up to ten credits per semester and are eligible for health insurance benefits.

Graduate teaching assistants usually conduct two three-hour courses each semester and hold a specified number of office hours per week. Occasionally a graduate assistant may have grading or tutoring responsibilities only.

Applicants for the Fall semester who desire financial support should submit their applications to the Graduate Committee by February 1 (December 15 for foreign students). Financial aid applications are only processed once a year.

Renewals of all fellowships and assistantships depend upon both satisfactory performance of teaching assignments and a satisfactory scholastic record in graduate studies. All renewals will be made by March 1 of each year, possibly on a contingent basis, but made final by the end of the spring semester.

A set of current departmental guidelines is available here. Generally, a first year graduate student will be given a renewal for another year if he/she has completed 12 credit hours of course work as well as having performed satisfactorily as an assistant. Subsequent renewals are contingent upon such factors as having passed the written examinations at either the Master's or Ph.D. level or making satisfactory progress on a Ph.D. dissertation.

### WRITTEN EXAMINATIONS

All students in the Ph.D. program and all M.A. students who do not choose the thesis option must take written examinations in two (three for STAT students) fields of mathematics. These examinations are given in January and August during the weeks preceding the start of classes. The sign-up months for the examinations are October and March respectively.

The written examinations for the Ph.D. are given in the following fields: algebra, analysis (real and complex), geometry and topology, probability, statistics, and applied statistics (for STAT students). A MATH student may choose to be examined in any two fields with the following exception: at most one of statistics and probability can be used to satisfy the written exam requirement.

There is no limit on the number of times a student can attempt the examinations, but one examination must be passed by the middle of the student's second year in the graduate program, and all must be passed by the middle of the third year. Most full-time students pass all examinations by the end of the second year.

No special combination of fields is mandatory and students usually prepare for two areas that relate to their field of interest. Detailed syllabi are available here.

The written examinations for the M.A. without thesis are given in the same fields as those mentioned above for the Ph.D. Again, each student takes examinations in two (three for STAT students) different fields. Such students take the same examinations described above that are administered to Ph.D. students and must receive a Master's level pass.

There is no limit on the number of times a student can attempt the examinations, but in order to earn a M.A. degree with the non-thesis option all examinations must be passed by the end of the student's third year in the graduate program. Most full-time students pass all three examinations by the end of the second year or middle of the third year.

### REQUIREMENTS APPLICABLE TO ALL M.A. STUDENTS

** Residence Requirements. **A full-time student must have two semesters in residence, a part-time student four semesters. All requirements for the M.A. degree must be completed within a period of five years.

** Transfer of credit. **Up to 6 credits of graduate level work taken at another regionally accredited institution are permitted providing that:

- The faculty advisor and Associate Chair for Graduate Studies agree that the specific credits are acceptable in the student's program.
- A grade of "B" or better was earned in the courses offered. No courses with pass/fail grades will be accepted.
- The credit was earned within the five year limit imposed for completing the Master's degree at The University of Maryland.
- The course received graduate credit at the institution where it was taken, and has not been used to meet the requirements for any degree previously carried.

** Diploma Application. **Application for diploma/graduation can be done online through Testudo, early in the semester in which the degree is expected. The deadline for the application can be found here.

** Approved Program Form: **A student who has applied for a diploma must complete the Approved Program Form obtained from the Office of Graduate studies before the dead line listed in the Schedule of Classes. This form is returned to the Administrator of the Graduate Program who will forward it to the Graduate School.

** Grade Point Average. **The student must maintain an average of "B" or better in all courses taken, not just those listed on the Approved Program Form. For this purpose, the grades of "D" and "F" count as 0 quality points, and courses with these grades cannot be used for degree requirements.

** Incompletes.** Any grade of incomplete in a course listed on the Approved Program Form must be removed.

### MINIMUM REQUIREMENTS FOR M.A. WITH THESIS

In addition to satisfying the requirements applicable to all M.A. candidates in MATH, the student must have:

- Taken a total of 24 hours of courses carrying graduate credit of which at least 15 are at the 600/700 level; Of these 15 hours at least 12 hours must be in mathematics.
- Taken at least 3 hours in each of two fields of mathematics distinct from the one in which the thesis is written, and obtained a grade of "B" or better in each of these courses. These 6 hours are part of the 12 hours mentioned in (1);
- Taken 6 hours of thesis research in addition to requirements (1);
- Written a satisfactory thesis;
- Passed a final oral examination.

** Thesis. **The M.A. thesis should represent a meaningful piece of independent work which has some novel features, for example, the detailed working out of the application of a general theory or method to some particular case or cases of interest. It must be prepared in the form required by the Graduate School. Each member of the final oral committee must receive a legible typed copy at least one week before the final oral examination. The final thesis must be submitted online by the given semester's deadline.

** Nomination of Thesis or Dissertation Committee Form: **This form obtained from the Office of Graduate Studies, must be completed two months prior to the date of the final oral and in keeping with the deadline listed in the Schedule of Classes. It should be completed in conjunction with the student's thesis advisor and returned to the Administrator of the Graduate Program who will forward it to the Graduate School. This will generate the Report of Examining Committee form sent from the Graduate School to the advisor to be taken to the final oral examination to be signed by all members of the thesis committee and returned to the Graduate School. There is also an equivalent internal form. The student will be examined on the thesis and related topics at the discretion of the examiners. All pertinent information concerning this oral examination should be given to the Office of Graduate Studies two weeks prior to the examination. The information will then be posted as the examination is open to the public.

### MINIMUM REQUIREMENTS FOR THE M.A. WITHOUT THESIS

In addition to satisfying the requirements applicable to all M.A. candidates in MATH (for STAT, see the STAT requirements, the student must have:

- Taken a total of 30 hours of courses carrying graduate credit of which at least 18 are at the 600 or 700 level. Of these 18 hours, no less than 12 hours must be in mathematics;
- Taken parts 1 and 2 of at least two 600/700 level full-year courses in mathematics except that a suitable "Selected Topics" course may be substituted for the second part of one of these full-year courses;
- Passed two written exams at the Master's level and fulfilled the course requirements; see this link for more information;
- Written a satisfactory scholarly paper;
- Passed a final oral examination.

** Scholarly paper. **The student must complete an acceptable scholarly paper of an expository nature. Normally, the topic shall be related to the second semester of one of the year courses. The topic shall normally be agreed upon with the professor of the course, who shall become the student's advisor. If the paper is not written in connection with a course, some other appropriate faculty member may approve the topic and become the advisor. A second reader shall be appointed by the advisor and both readers must approve the paper for it to be accepted. A neat copy of the final approved version shall be provided for the Office of Graduate Studies. The scholarly paper shall be based on substantial use of at least two sources, one of which shall be a journal article, with appropriate references given.

** Final Oral Examination. **The final oral examination shall consist of a presentation of the material in the scholarly paper, plus questioning by the examiners based on the paper and whatever material in the approved M.A. program that has not been covered by the written examination. The examining committee shall consist of the two readers of the scholarly paper.

### THE DEGREE OF DOCTOR OF PHILOSOPHY

To receive the Ph.D. degree in mathematics a student must display a high level of scholarship shown by the ability to do original research and should possess a broad knowledge of the major fields of modern mathematics. It is not necessary to have a master's degree before obtaining the doctorate.

** Residence Requirements. ** The equivalent of at least three full years of graduate study is required of which at least one must be in residence at The University of Maryland campus. At least 18 hours of course work must be taken at The University of Maryland, plus 12 hours of credit research at the Ph.D. level.

** Minimum Requirements. **In order to receive a Ph.D. degree, the student must have:

- Taken at least 36 hours of formal course work (at least 27 at the 600/700 level) with an average of "B" or better. Courses used as part of a master's program may be used in fulfillment of this requirement. At least 18 hours must be taken in the Department of Mathematics. Please note that Math 898 and 899 do not count toward the 36 credit requirement. Grades of "D" and "F" count at 0 quality points and the courses in which they are obtained cannot be used to fulfill degree requirements;
- Taken at least 12 hours of Mathematics 899;
- Passed the written examination requirements (exams and courses);
- Fulfilled specific requirements by the field committee that represents the student's principal mathematical interests. The student must demonstrate that he or she has obtained a sufficient depth of mathematical knowledge and has the ability to write a dissertation on a topic in the field in question.
- Passed an examination in one foreign language;
- Been admitted to candidacy during the semester previous to the one in which the degree is granted or earlier;
- Prepared a dissertation representing an original contribution to existing mathematical knowledge;
- Passed the final oral examination.

** Language Examinations.** A candidate must demonstrate a competent reading knowledge of mathematical material in one foreign language selected from French, German, and Russian. Other languages may be accepted if they are common in the literature of the area of specialization. Competence in a foreign language will consist of passing to the Department's satisfaction an examination prepared by the Department. The student will be required to prepare an acceptable translation of selected excerpts from the mathematical literature within a reasonable period of time. A dictionary may be used. These examinations are given each fall and spring.

** Advisors. **The entire course of study must constitute a unified program, approved by an advisor in the field of the student's major interest.

** Admission to Candidacy.** Before petitioning for admission to candidacy a student must have:

- Completed half of the residence requirements;
- Maintained a B average in formal course work;
- Passed the written examinations at the Ph.D. level;
- Satisfied the specific requirements of the field committee governing the field of principal interest, including passing the oral candidacy examination;
- Obtained the consent of a faculty member who will accept the responsibility of directing a dissertation.

After fulfilling these requirements, the student should complete the Admission to Candidacy form available in the Office of Graduate Studies. This form will be forwarded to the Graduate School. The dates pertaining to the Admission of Candidacy form are always posted on the Office of Graduate Studies bulletin board.

** Dissertation. **The dissertation must represent an original contribution to existing mathematical knowledge. It must follow the format given in the "Style and Policy Manual for Theses and Dissertations" written by the Graduate School and available in the Office of Graduate studies. Often the dissertation or some modification thereof will be submitted to a mathematical journal for publication.

** Final Oral Examination**. The final oral examining committee must consist of five members, one whom is on the graduate faculty of a department other than mathematics. Each member of the committee must be given a copy of the dissertation at least ten days prior to the examination.

The Nomination of Thesis or Dissertation Committee form is obtained from the Office of Graduate Studies and must be completed and returned to that office three months prior to the final oral and in accordance with the deadline listed in the Schedule of Classes. Details governing the structure of the committee are on the back of the form. This form will generate the Report of Examining Committee form sent from the Graduate school to the advisor which must be taken to the Graduate School. There is also an equivalent internal form.

All pertinent information concerning the oral examination should be given in the Office of Graduate Studies two weeks prior to the examination. The information will then be posted as this examination is open to the public.

No final oral may be scheduled until the language examination has been passed.

The final oral examining committee will examine the candidate on the research work incorporated in the dissertation, review attainments in the major and minor fields and then vote on the candidate's qualifications for the degree. In order to justify a finding of failure, at least two negative votes must be cast.