University of Washington Applied Mathematics
UW Department of Applied Mathematics
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Valid from academic year 2006-07 on.

Degree Requirements & Operating Guidelines

INTRODUCTION

These guidelines are intended to help familiarize graduate students with the policies governing the graduate programs leading to the degrees of Master of Science (M.Sc.) and Doctor of Philosophy (Ph.D.) in Applied Mathematics. This material supplements the official University Catalog which contains further Graduate School regulations and degree requirements. Students should also be familiar with this Catalog.

INITIAL ADVISING APPOINTMENT

All new graduate students should make an appointment to see a designated faculty advisor before registering for the first quarter of study. During the initial advising appointment, the student will be assisted in the selection of courses for the first quarter of study; the advising procedures for subsequent quarters will also be explained at this time. Since an integral part of the Applied Mathematics program of study is an applications field, it is suggested that each new student give some thought to identifying this field. Of course, the selected applications field may change as the student's interest evolves after exposure to different topics.

THE MASTER OF SCIENCE PROGRAM

The M.Sc. Program is intended to give the student a working knowledge of several areas of Applied Mathematics and a specific area of application. The Graduate School and the Department require a minimum of 36 credits for the M.Sc. degree. The following are the requirements to be met:

In addition, the student is expected to develop some experience in scientific computation. The required core, applications and additional courses must be taken for a grade, and the overall GPA in these requirements must be at least 3.2 on a 4.0 maximum scale. Exceptions will be granted only by petition to the Graduate Committee.

REQUIREMENTS

(1) Basic Course List

Usually, the following three (3) core courses are taken by M.Sc. students: AMATH 567 (Complex Variables), 568 (Ordinary Differential Equations), 569 (Partial Differential Equations). The 3 other core courses consist of (i) 2 of the following 4 courses: AMATH 506 (Applied Probability and Statistical Inference), 581 (Scientific Computing), 584 (Applied Linear Algebra and Introduction to Numerical Analysis), or 585 ( Numerical Analysis of Boundary Value Problems), and (ii) one of AMATH 507 (Calculus of Variations) or 515 (Fundamentals of Optimization). Alternative program elements may be substituted, subject to the approval of the Applied Mathematics Graduate Committee. At the discretion of the Graduate Program Coordinator and consistent with the Graduate School Requirements for a M.Sc. degree, up to 18 credits at the 400-level may be used to substitute for the requirement at the 500-level. For example, AMATH 401 for AMATH 567, AMATH 402 for AMATH 568 and AMATH 403 for AMATH 569.

(2) Field of Application

In general, this requirement is satisfied with a coherent sequence of two (2) graduate (500 level) graded courses in a given field. Other alternatives may be appropriate. For example, at most three (3) credits may be in a 400 level course if the student receives a minimum grade of 3.0 in this course. The following courses offered by the Applied Mathematics Department are also designated as Applications Courses: AMATH 503, 504, 505, 521; AMATH 422, 423, 441. In any event, the courses selected in the field of application must be approved by the student's advisor and the Graduate Committee.

Traditional fields of application include all branches of engineering, the physical sciences, biological sciences, computer science, economics and management science, and certain areas of medical science. Other fields may be approved by the Graduate Committee where appropriate. Mathematics and statistics are not fields of application.

(3) Applied Mathematics Seminar/Clinic

All students must register for two (2) quarters of AMATH 501 (Applied Mathematics Seminar) and two (2) quarters of AMATH 502 (Applied Mathematics Clinic/Journal Club).

(4) Final Examination for Master's Degree

In this department, the Graduate School requirement for the Final Examination can be satisfied in two ways:
- by an oral presentation by the candidate in the presence of his or her Graduate Committee on a current topic of interest from the literature or the results of original research . At least two members of the Committee must sign the Master's Application (warrant), after they are satisfied that the various requirements for the degree are met and that the presentation is of high quality.

- by obtaining a M.Sc. level pass (or higher) on the department's preliminary examination. In that case the student's Graduate Committee consists of the examiners of the preliminary examination. At least two members of the Committee must sign the Master's Application (warrant), after they are satisfied that the various requirements for the degree are met and that the examination is passed at a sufficiently high level.

(5) Program Plan

The student will be assigned a faculty advisor. In order that studies progress satisfactorily and the degree requirements are met, a Program Plan must be filled out by the student, signed by the advisor, and approved by the Graduate Committee. The Graduate Committee is a faculty committee consisting of the Graduate Program Coordinator (GPC) plus other members appointed by the GPC. For full-time students, a Program Plan must be on file no later than the end of the third quarter of registration. Part-time students should file their Program Plan prior to the end of their first three quarters of registration. The Plan may be revised as the focus of studies changes, in which case, a new Plan should be submitted for approval.

SATISFACTORY PROGRESS IN THE M.SC. PROGRAM

The student is expected to maintain at least a 3.2 grade point average for satisfactory scholarship. In addition, full-time students (whether self-supporting or under full-scholarship or assistantship support) are normally expected to complete the requirements for an M.Sc. Degree in one year and should not exceed two years. Exceptions will be granted only by petition to the Graduate Committee. Note that regardless of whether a student is enrolled in full- or part-time study, the Graduate School requirement is that the M.Sc. Degree be completed in less than six (6) calendar years of Graduate study.

In accordance with Graduate School guidelines, students whose cumulative GPA since entering the program falls below 3.0 will receive a warning during the next quarter, and final probation in the second quarter thereafter if their cumulative GPA remains below 3.0.

It is the student's responsibility to make certain that all deadlines set by the Graduate School are met in order to graduate at the expected completion of study.

SUGGESTED ACADEMIC WORKLOAD

Full-time students in the M.Sc. Program are expected to register for somewhere between twelve (12) and eighteen (18) quarter credits. The course-load beyond nine (9) credits (exclusive of AMATH 501) may be taken as Independent Study, AMATH 600, for which a faculty advisor is selected. The purpose of the independent study is to gain further familiarity with the chosen field of application as well as to identify potential areas of research for future study. However, an entering student with some deficiency in any of the required areas may elect independent study in this area to strengthen his/her background. In all cases, the number of credits that are taken in AMATH 600 is to be determined by the selected faculty advisor not to exceed (10) credits per quarter, and is based on the scope of the study. If the student is preparing a Master's thesis, (s)he should register for AMATH 700 (not to exceed (10) credits per quarter) in place of AMATH 600. After passing the Preliminary Examination and having been admitted into the Ph.D. program, a student is considered to be working toward a doctoral thesis and should register for AMATH 800 credits in addition to their regular courses, being expected to take a total of (15) credits per quarter. The number of AMATH 800 credits is to be determined by the Chairman of the student's Supervisory Committee, not to exceed (10) quarter credits.

THE DOCTOR OF PHILOSOPHY PROGRAM

The Doctor of Philosophy (Ph.D.) Degree in Applied Mathematics is primarily a research degree, and is not conferred as a result of course work. The granting of the degree is based on proficiency in Applied Mathematics, and the ability to carry out an independent investigation as demonstrated by the completion of a doctoral dissertation. This dissertation must exhibit original mathematical contributions in a significant area of application. In particular, a thesis on a mathematical topic with no demonstrable application is not acceptable, nor is it appropriate to study some application using mathematical techniques which are only routinely used in that application.

ADMISSION TO THE PH.D. PROGRAM

A graduate student is considered for admission to the Ph.D. program by the Graduate Committee after completing AMATH 567, 568, and 584 with a grade of 3.4 or better in each course and passing the Preliminary Examination.

COURSE REQUIREMENTS FOR THE PH.D. PROGRAM

The courses required for the Ph.D. are as follows: It is strongly recommended that students take AMATH 567, 568, 569, and AMATH 584, 585, 586 during their first year of academic study. Journal club credits may be substituted for AMATH clinic credits. Students with exceptional preparation who are going on into the Ph.D. program may waive some core courses with the agreement of the Graduate Program Coordinator. If a student fails the Preliminary Examination, then appropriate courses may be taken starting Winter Quarter so that the student may finish the M.Sc. by Spring Quarter. The student will be notified of the committee's decision of admittance to the Ph.D. program in the Spring Quarter after passage of the Preliminary Examination. Therefore new graduate students are usually first admitted to the M.Sc. program, even if their intended degree is the Ph.D. instead of the M.Sc.

The Preliminary Examination is given by the Department during the first week of Winter quarter, and again the first week of Spring quarter. Entering students generally take it following the first quarter of full-time study. Full-time students who do not take or pass the Preliminary Examination after at most two attempts are expected to complete an M.Sc. degree by the end of their second year (NOTE: Continued funding is not guaranteed for the second year in this case). This general rule does not hold for students on a part-time program of six credits or less per quarter. Exception to the general rule may be granted upon request to the Applied Mathematics Faculty.

The Preliminary Examination consists of three written, two-hour exams, covering a core of undergraduate material necessary for successful completion of the Ph.D. program. These core areas are: Old preliminary exams are collected here.

The outcome of a student taking the preliminary exams is (i), (ii) or (iii):

(i) Ph. D. pass:
A student passes the preliminary examination by passing all three area examinations at the Ph.D. level in one sitting .

(ii) M.Sc. pass:
A student passes the preliminary examination by passing two out of all three area examinations at the M.Sc. level in one sitting. If a student chooses to retake the preliminary examination, the results of that retake cannot void the already received M.Sc. pass.

(iii) Retake
If a student is not satisfied with his/her result on the preliminary exams he/she may choose to retake the preliminary exams once. If a student does not obtain a Ph.D. pass on the examination the first time, but receives an outstanding result on one of the three parts of the examination he/she may be excused from retaking this part.The possible outcomes of a retake are (i), (ii) or (iv), see below.

(iv) Fail:
The student is judged as not demonstrating satisfactory understanding of the examined materials on a retake of the preliminary exams. The student will not be allowed to enroll in the Ph.D. degree program. However, the student may finish the M.Sc. degree upon completing all the appropriate requirements.

In every case, a thorough assessment is made by the Applied Mathematics Faculty. Factors other than the examinations can be taken into consideration to the benefit of the student. If there are questions regarding the written performance, an oral examination can be administered by the graduate program coordinator and the examiners during the first two weeks following the written examination.

SUPERVISORY COMMITTEE

As soon as possible, and no later than the end of the Spring quarter of the first year, a student should form a supervisory committee. Initially, the supervisory can consist of only a advisor. At this stage, the Supervisory Committee plays an advisory role in designing a course of study appropriate for the student's research interests, and in formulating a dissertation topic. A full Supervisory Committee should be formed no later than four months prior to the student's General Exam. All names of committee members must be submitted to Graduate School via its on-line form.

The Supervisory Committee should have a minimum of three (3) regular members plus the Graduate Faculty Representative (see below), and will be constituted with at least two (2) faculty members from Applied Mathematics, one of whom is to be the Chairman of the Committee. If the proposed dissertation advisor is a member of the Applied Mathematics faculty, then the advisor will be the Chairman. In special cases, the dissertation advisor may be from another department, and is then also a member of the Supervisory Committee.

One additional faculty member from an appropriate area will be appointed by the Graduate School to be Graduate Faculty Representative (GFR); faculty suitable for this position may be suggested by the student. The GFR should have some familiarity with the anticipated area of research and may not be from the Applied Mathematics faculty. Thus, the minimum number per committee is four. In the event that not all three members, exclusive of the GFR, are familiar with the proposed area of research, it is advisable to select additional faculty so that a Dissertation Reading Committee, consisting of three members, may be formed from the Supervisory Committee. Two members of the Dissertation Reading Committee must be from the Applied Mathematics faculty.

CANDIDACY REQUIREMENTS

The student in the Ph.D. program attains the status of Candidate for the Doctor of Philosophy degree upon

AREAS OF SPECIALIZATION, COURSE REQUIREMENTS, FORMULATING THE DOCTORAL RESEARCH

Every candidate for the Ph.D. Degree is expected to demonstrate proficiency in at least two distinct areas of mathematical specialization which are relevant to his/her doctoral research. This requirement is partially satisfied by passing twelve (12) graded credits in 500 level Applied Mathematics or Mathematics courses beyond the courses used to satisfy the M.Sc. Degree requirements. S/NS grades will not be acceptable for this twelve (12) credit requirement. Principal specialization areas include:

The student's proficiency in his/her two chosen areas of specialization will be further examined during the General Examination.

While the principal source of guidance during the process of choosing specialization areas and a research topic is the thesis advisor, it is strongly advised that the student maintain contact with all members of his/her Supervisory Committee. It is expected that the student meet with the Supervisory Committee at least once a year to discuss his/her progress until the doctoral thesis is complete. During this process the student formulates a research topic which has the potential of leading to original mathematical contributions in a significant area of application. It is suggested that a brief thesis proposal outlining this work be prepared and given to all members of the Supervisory Committee prior to the General Examination.

THE GENERAL EXAMINATION

The General Examination is administered after the student has passed the Preliminary Examination and sometime before the end of the student's second year. The purpose of this examination is threefold:

  1. To determine whether the student has acquired the necessary mathematical background (including two areas of specialization) as well as an applications background appropriate for his/her proposed research,

  2. To determine whether the student is able to draw on this background to make progress in the proposed research,

  3. To determine whether the proposed research topic and approach have the potential of leading to an acceptable dissertation.
The General Examination is an oral exam. Its duration is approximately one and a half hours and it has the following two components:
  1. A thesis proposal consisting of thirty minute (maximum) presentation on the topic of the dissertation.

  2. The thesis proposal is followed by an oral examination testing on the thesis topic area of application and two areas of specialization taken from the list above.
The student will receive a pass of fail depending upon their performance. The General Examination can be taken up to a maximum of two times.

THE FINAL EXAMINATION

The preparation of a dissertation brings the student to the Final Examination. This consists of an oral presentation of the completed research in a seminar open to the public. After the seminar, the student is expected to defend his/her contributions and results by responding to questions directed by members of the Supervisory Committee and any interested graduate faculty.

RESIDENCE REQUIREMENTS

The candidate for the Ph.D. degree is required to spend at least two years in residence as a graduate student at the University of Washington, one of which is full-time residence.

SATISFACTORY PROGRESS IN THE PH.D. PROGRAM

As noted, the first measure of satisfactory progress is the Preliminary Examination which is taken before the end of third quarter of study, with the exception of part-time students. Furthermore, it is expected that the General Examination will be attempted no later than the end of the second academic year of study and passed no later than the first quarter of full-time study. If the candidate has not attempted the General Examination within this period, the Supervisory Committee shall meet to determine if satisfactory progress is being made. The Committee must determine if justifiable reasons for postponement exist and advise the GPC of these reasons.

If the student's Final Examination has not yet been scheduled after four years of full-time study from the date that the Preliminary Examination was passed, then the Supervisory Committee will formally meet and re-examine the candidate's ability to complete a Ph.D. dissertation. The examination will focus on the candidate's progress, understanding, and contributions to the dissertation. The two possible conclusions of this examination are: (1) a reasonable conclusion of the dissertation can be foreseen and a specific time limit will be established, or (2) a reasonable conclusion of the dissertation is not expected and the student will be informed that the Graduate Committee advises the Graduate School that the student is not making satisfactory progress toward the degree. In such event, the student is referred to the Graduate School Memorandum No. 16 which deals with unsatisfactory progress and low scholarship.

Note that regardless of whether a student is enrolled for full- or part-time study, the Graduate School requirement is that the Ph.D. degree be completed in less than ten (10) calendar years of graduate study. In the event that this time limit is exceeded, the student must petition the Graduate School for an extension. This petition must be supported by the Department which is required to review all the courses that the student has taken for credit to ensure that the current equivalents of these courses are not significantly different. In the event that a needed course has been substantially updated, the student is required to retake this course.

SUGGESTED ACADEMIC WORKLOAD

After successful completion of the Preliminary Examination, the full-time student is expected to continue to register for at least fifteen (15) quarter credits. These credits may initially include course work related to the specialization areas, or other areas suggested by the Supervisory Committee. If the dissertation advisor is not on the Applied Mathematics faculty, the Doctoral Dissertation credits will be equitably distributed between AMATH 800 and the advisor's departmental 800 registration.

During the dissertation research, it is expected that the candidate will show personal dedication and incentive in accomplishing his/her stated research goals.

ANNUAL PROGRESS REPORT

After admission to the Ph.D program, a student is required to submit an Annual Progress Report to his/her Supervisory Committee by the end of the Winter quarter each year.

FINANCIAL ASSISTANCE

Financial support for Doctoral studies is limited to five (5) years after admission to the Department of Applied Mathematics. In unusual circumstances support for an additional year can be granted upon approval of a petition, endorsed by the student's thesis supervisor, to the GPC.

Time Table to Ph.D. Degree

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