The objective of the department’s Ph.D. program is to produce graduates who are broadly educated in Applied Mathematics and Statistics and who can work at the current research frontiers of their specialized disciplines.
A student should demonstrate mathematical comprehension in two stages:
A main objective is to help those students with the desire and background to do so, to get an earlier start on initial research-type activities. These activities would not necessarily be in the same area as the ultimate doctoral research, and typically would not have the same degree of intensity and commitment as that later work; for example they would involve interaction with the student’s faculty “mentor” rather than an official “dissertation advisor.” One role of the Introductory Exam is to gauge readiness for such activity.
The current University Catalog contains a detailed description of the department’s courses, programs, and requirements and a list of the current faculty and their interests. The purpose of this handbook is to present supplemental information; it should be read along with the departmental listing in the Catalog.
In addition to fulfilling the University requirement of a minimum of two consecutive semesters of registration as a full‑time resident graduate student, the student must accomplish the following to obtain departmental certification for the Ph.D. More detailed information on these items in provided in the following sections.
The most common way for students to gain the knowledge and skills to succeed in the Ph.D. program is through coursework. The relevant courses for the Ph.D. are of three types
Basic Courses: All students are encouraged to master basic material in:
Normally, a student will have completed at least eight basic courses by the end of the fourth semester of residence.
Specialized Courses: Each student takes advanced courses appropriate to the proposed area of dissertation research. Sample programs in the areas of probability/statistics, operations research/optimization, discrete mathematics, and numerical mathematics are given below, but a student with different goals is free to propose an appropriate program meeting the approval of the research advisor.
Prior to passing the Introductory Exam, students should take the normal course load of at least nine credit hours in courses at the 600 level and above, not counting the department seminar. Students conducting research should also register for the appropriate number of credits for 553.800 Dissertation Research that when combined with the course credit hours will total at least 20 credit hours per term. Students who have not passed the real analysis part of the Introductory Exam are required to take EN.553.701 Real Analysis: Preparation for the PhD Introductory Examination at the first opportunity. Students must also register for and attend the weekly department seminar 553.801. (Students enrolled part-time in this stage of the PhD program may have different registration requirements and should seek guidance from the Academic Program Coordinator and their faculty advisor.)
Students must complete, with grades of B- or better (or equivalent level of performance in “pass-fail courses”) at least 12 one-semester courses of graduate work in a coherent program approved by the faculty advisor. All 600-level and 700-level courses (with the exception of seminar and research courses) are satisfactory for this requirement. Certain courses in other departments are also acceptable, and must be approved by the student’s advisor in advance. WSE courses listed as 1- or 2-credit courses count only as one-half course. Approved KSAS graduate courses count as one-half course if the number of meeting hours per week is 1 or 2 and count as a full course otherwise. The 12-courses requirement is a minimum. Students are encouraged to take courses throughout the duration of the program. Students who enter the PhD program after completing a Master’s degree may be permitted to count up to three courses taken during their Master’s program toward this requirement. A student’s advisor will consider requests for approval and notify academic staff accordingly.
Students conducting research should register for the appropriate number of credits for 553.800 Dissertation Research which, when combined with course credit hours, will total at least 20 credit hours per term. Students must also register for and attend the weekly department seminar 553.801. (Students enrolled part-time in this stage of the PhD program may have different registration requirements and should seek guidance from the Academic Program Coordinator and their faculty advisor.)
In consultation with his or her advisor, each student will develop a program of proposed coursework. This program should not be thought of as a firm contract but as a basis for planning; typically it will need to be updated from time to time.
Familiarity with computing is essential to applied mathematics, and students should aim for practical problem-solving capability for computing in applied mathematics. Thus, every department graduate should possess a working knowledge of the utilization of computers and the fundamentals of scientific computing. This includes, but is not limited to, such topics as: computer programming (e.g., FORTRAN or C++), numerical software packages (e.g., MATLAB), symbolic computations (e.g., MAPLE), technical word processing (e.g., LaTeX), and professional presentation (e.g., PowerPoint).
The requirement below is a minimal one, aimed at ensuring that students demonstrate some ability at using the computer for problem-solving through homework assignments and projects.
It is expected that students discuss their plans to meet this requirement with their faculty advisors. As early as possible, students and advisors should agree on a program of work whose satisfactory completion would meet the computing requirement. Students with no previous background in computing should first acquire basic competence during their first year of residence, either by independent study, or by participation in an elementary course. It is recommended that students meet this computing requirement within their first year of residence, and certainly no later than six months before graduation.
Students meet this requirement typically by receiving a grade of B- or better in taking an approved AM&S department course. The list of approved courses together with the years in which versions of these courses can be used to meet the requirement can be found here.
The Introductory Exam is a written exam and tests (at no higher than the 400-level) for an understanding of the basic areas listed below, and for general proof-writing and integrative skills. This exam is designed to be taken and passed early in a student’s graduate academic career.
The Introductory Exam will be offered just prior to each semester. It may be taken no more than four times (including a first try before the student’s first semester). A student is required to pass the exam before beginning the fourth semester of study in order to continue in the Ph.D. program. In anticipation of the possibility of not passing the exam students are advised to plan for completion of the Master’s degree during the student’s second and final year in the department.
The Introductory Exam will consist of three separate exams in linear algebra, real analysis, and probability. All three must be passed to pass the Introductory Exam.
Syllabi for these topics are given on this page:
The faculty intend to design the exam so that a student can complete each portion in two to three hours. The exam is a closed-book exam.
Clear thinking and writing are important on the Introductory Exam, and the student’s grade will reflect this. Exams will be graded as pass/fail, with 66 2/3% generally considered passing.
Students who have not passed the real analysis part of the Introductory Exam are required to take EN.553.701 Real Analysis: Preparation for the PhD Introductory Examination at the first opportunity.
Click here for Past Introductory Exams with Solutions
After passing the Introductory Exam, the student begins to formulate the syllabus for the Ph.D. Candidacy Exam. The Candidacy Exam must be taken before beginning the student’s seventh semester, which provides at least three semesters after passing the Introductory Exam. (For a student passing the Introductory Exam upon entrance into the program, the Candidacy Exam may come as late as six semesters after the Introductory Exam.) A student is given at most two chances to pass this exam, with the opportunity to retake the exam left at the discretion of the examining committee. Should a student be given such a second opportunity, the second try must take place within 4 months of the first attempt.
A student may receive from the examining committee a grade of unconditional pass, conditional pass (with conditions specified by the examining committee), or fail. A (strict) majority of votes in favor of either pass or conditional pass is needed for the student not to fail the exam.
For each Ph.D. student who has successfully passed the Ph.D. Candidacy Examination, a post-Candidacy supervision committee consisting of three faculty members will be formed to oversee the student’s research progress until the completion of his/her doctoral study. This committee, which consists of the thesis advisor and two other members recommended by the advisor, is formed when the thesis advisor is selected by the student; this should occur no later than the end of the semester in which the student passes the Ph.D. Candidacy Exam. Two members of this committee shall be the departmental examiners in the student’s Graduate Board Exam. The committee will evaluate and report the student’s performance at the end of each semester in the same way as in course evaluation. Ideally, the membership of the student’s post-QE supervision committee shall remain unchanged until his/her dissertation research is completed; however, it may be reconstituted if necessary.
One to three months after the Ph.D. Candidacy Exam, the student should request that the department schedule the Graduate Board Oral Examination. (Faculty from other departments, perhaps corresponding to the student’s elective courses, will be among the examiners.) Prior to the scheduling of the GBO (and with no timing constraint relative to the Ph.D. Candidacy Exam), a student should prepare a written dissertation proposal, which will be submitted along with the form to start the GBO scheduling process.
The examination panel will evaluate the student’s preparedness and potential to carry out the proposed research program. Before taking the Graduate Board Oral Examination, the student should have completed at least one of the elective courses outside the department. The rules of the Graduate Board state that the purpose of the examination is “to test the depth and breadth of the student’s knowledge and reasoning abilities”, and that the scope of the examination is not to be sharply defined but rather is to be set by the examination committee on the basis of the student’s course record and the specific departmental requirements.
The Gradual Board Oral Examination Committee is comprised of two members from within the AMS Department and three members outside of the AMS Department. Graduate Board policy requires that committee members be selected by the Department Chair. Students are not to contact potential examiners about their willingness to serve until the examining committee has been formed by the Department Chair. Please click on Ph.D. Student Forms in the menu, to access the form necessary to begin the Graduate Board Oral scheduling process.
A Ph.D. candidate’s program of original research and the written dissertation to which it leads are the highlight and culmination of doctoral study. The dissertation is the written documentation of the findings of the research program, and is required by the University to constitute a “significant contribution to knowledge worthy of publication in scholarly journals.” Not only the research but also the exposition, grammar, and style must be of the highest order.
The dissertation defense is a public presentation and discussion of the findings of the research program, conducted before a committee of members of the faculty (not necessarily all from this department). It is open to attendance by all members of the University community. The dissertation defense is the climax of the Ph.D. program.
The following procedures are consistent with this interpretation of dissertation research, manuscript, and defense.
A Readers’ Report must be received for all students receiving a Ph.D., or a Master’s Degree with essay.
Dissertation Readers are to be selected and appointed by the sponsoring department or committee. Any duly appointed member of a department or committee sponsoring Ph.D. candidates and holding the rank of assistant professor or higher (including visiting professors, but excluding lecturers) is eligible for selection as a Reader without prior approval. Readers from outside the University structure, or from any non-Ph.D. sponsoring department, laboratory, or institute within the University, must be approved by the Graduate Board Office. Such approval will be forthcoming only when such an appointment is justified in writing by the chair of the department or committee making the request.
Two Readers are required for Ph.D. students and one for Master’s students.
Readers’ Reports, in order to qualify for acceptance by the Graduate Board, must certify that the dissertation is a significant contribution to knowledge worthy of publication in its present form or with appropriate modifications, and that it is worthy of acceptance in partial fulfillment of requirements for the Ph.D. degree. Readers’ Reports must show the academic rank or title of each Reader and the department and school (or University) with which he or she is associated. The report must also be dated, give the student’s full name, and give the full title of the dissertation or essay. The title must be correct since the transcript and graduation program show this title.
This report must be in the Graduate Board Office by the deadline date for that period and the date must precede the date of the departmental certification.
The original and one copy of the Readers’ Report are sent to the Secretary of the Graduate Board.
The primary source of advice and counseling about a student’s progress is the faculty advisor.
When a student first enters the department, the student is assigned (even before passing the Introductory Exam) an academic advisor. The academic advisor assists the student in selecting courses and other administrative tasks, and provides general career guidance.
After a student has passed the Introductory Exam, the student is assigned a mentor. The mentor is chosen in an area in which the student is proficient (and, it is hoped, interested). The purpose of the mentor is to guide the student in choosing a research area. The mentor does this by giving the student papers and other material to increase the student’s depth. The mentor suggests depth courses. The mentor may offer or make the student aware of research opportunities. The mentor may guide the student to faculty who share the student’s research interest. The mentor may eventually become the student’s dissertation advisor, but this is not a certainty.
Students are expected to find a research advisor and begin mentored research by the end of their fourth semester. Any full-time PhD student who has failed to do so will be placed on probation and, if this requirement is not met by the end of the probationary semester, will ordinarily be terminated from the program. Only in exceptional circumstances will petitions be considered to extend the probation. PhD students registered part-time are subject to a similar requirement to find a research advisor in a timely fashion.
Of course, a student’s research guidance need not come only from the research advisor. The entire faculty of the department, indeed of the whole University, is available to each student to provide advice and assistance.
The department conducts regular reviews of all graduate students, and notifies each student in writing annually (usually in early February) of his or her status.
At the end of each academic semester, faculty instructors for each of a student’s courses (even those outside the department) are asked to complete a written evaluation of the student’s performance. If a student is a teaching assistant, the supervising faculty member is asked for a written performance evaluation also.
At the annual graduate student evaluation meeting, the faculty considers each student’s grades, written evaluations, passage of Introductory, Candidacy and Graduate Board Examinations, satisfaction of the computing requirement, research progress, and departmental citizenship. The evaluation letter characterizes the student’s progress, provides advice, and states the faculty’s expectations for the student’s performance during the following year.
A full-time Ph.D. student who fails, in a given semester before passing their Introductory Exam, to receive a grade of B- or better in at least two courses in the program will be placed on Academic Probation. For a full-time Ph.D. student on Academic Probation, failure to pass at least two courses with a B- or better in any semester in the program is grounds for dismissal. Also, in any given semester, whether or not a student is on Academic Probation, they may be dismissed if they do not receive any grades of B- or better in their program.
All full-time PhD students are required to maintain funding status as either a teaching assistant, research assistant or externally-funded fellow during the program (with possible waivers only in exceptional circumstances). Although students are usually offered teaching assistant status with a specified period, loss of this status may occur at any time, even during the specified period, due to unsatisfactory performance. Loss of status will always be preceded by a warning to the student concerning their performance and will usually result in a one-semester probationary period, but egregious misbehavior may lead to immediate termination. Students who lose their teaching assistant status without finding a research assistant position will be terminated from the program.
While enrolled in the PhD program, students should take steps to ensure that, if for whatever reason they are unsuccessful in their attempt to earn a PhD degree, they have something to show for the effort they have put in. To this end, students are advised to pay close attention to the department’s MSE requirements, and take steps to earn a Master’s degree as they pursue the PhD. Such a degree can be important for a student’s future career.
Students in the Applied Mathematics and Statistics PhD program may also apply to the AMS Financial Mathematics Master’s program. However, a student cannot be admitted to this program and cannot take any of the three required semesters of 550.647/553.847 Financial Mathematics Masters Seminar until they have passed the Introductory Exam.
Some of the department’s graduates will enter academic professions where formal teaching is part of their responsibility, while others will embark upon consulting, governmental, or business careers and do no formal teaching at all. Every graduate will, however, have to “teach” in the sense that his or her ideas will have to be imparted to others. By itself, this would suggest that some formal teaching experience is valuable for every graduate, but there is another reason as well. Everyone who has ever taught anything has learned something; the very act of organizing information for someone else’s benefit helps one to understand it better. This is particularly valuable for a graduate student trying to organize a body of knowledge for self benefit. Finally, prospective academic employers usually request recommendations which evaluate the student’s promise for teaching as well as for research, and it is helpful to have some teaching performance upon which to base such recommendations. For these reasons the department requires some supervised teaching experience for each student. This requirement may be fulfilled either by leading a discussion class in section or by being the instructor of record in an intersession, summer or academic year course.
The Department Seminar meets weekly for the presentation and discussion of current research work. Both University scholars and invited guests appear, and a wide variety of topics is covered in the course of a year. All resident department graduate students are required to register every semester and to attend.
The Applied Mathematics and Statistics Department makes a long-term full-support commitment to Ph.D. students. Per WSE policy, AMS Ph.D. students are fully funded (tuition, health insurance and 9-month stipend) for the duration of their Ph.D. program while they are in a full-time resident status.
As a part of the Ph.D. educational program, full-time Ph.D. students will receive an assignment as a Teaching Assistant or Research Assistant each term. Teaching Assistants provide teaching and grading assistance and are expected to spend up to 15 hours per week for 15 weeks per semester. All TAs with full-support commitments receive the same level of funding as any other fulltime, resident PhD student, regardless of financial need or varying assignments.
Research Assistants work with individual faculty members who have research grants or contracts. The selection of RAs is made by the faculty member providing the funds, subject to approval by the Department Head. All RAs with full-support commitments spend up to 15 hours per week for 15 weeks per semester on assigned research and receive the same level of funding as any other fulltime, resident PhD student, regardless of financial need or varying assignments.
Finally, some students may be supported 50% as RAs and 50% as TAs, with the teaching assignment reduced by half to help balance the time commitment.
Outstanding eligible candidates may be nominated by the Department for certain diversity-focused Fellowships awarded competitively by the Engineering School. These also carry a full-support commitment.
Fulltime resident PhD students are expected to successfully complete at least twelve graduate courses before the completion of their degree, pass the various examinations required in the program, and start working with an advisor on research in a timely manner.
Fully supported Ph.D. students are provided with a sufficient stipend to support their living expenses and allow them to devote fulltime effort to their studies. These students should not be employed outside the department during the academic year. The department reserves the right to adjust/reduce internal support to a student found to be in violation of the above stipulations so as to account for any external funding. There also may be academic/research performance ramifications to a student found to not be making satisfactory progress and also in violation of the above stipulations.
All students supported as TAs are expected to satisfactorily complete their teaching duties as directed by the course instructors. If needed, they are also expected to make appropriate efforts to enhance their language and communication skills so as to be the most effective teacher possible, which may require participating in training and improvement courses offered by the university.
Applied Mathematics and Statistics graduates elect one or two graduate student representatives early each Spring semester. The representatives attend all department faculty meetings (except where confidential matters are discussed) to provide the students’ point of view on issues being discussed. The representatives also provide a means for other students to raise issues, voice concerns, or propose changes anonymously.
The Milton S. Eisenhower Library has extensive resources of books and journals and can draw freely on large nearby collections such as the Library of Congress. The department maintains a small reference library of books and journals. Resident full‑time Ph.D. candidates are assigned office space in Whitehead Hall. The facilities of the University Computing Center are available to all students for research and instruction. The Department also has high‑capability computing resources for graduate students and faculty research in its quarters in Whitehead Hall.
The computing resources of the Johns Hopkins University Department of Applied Mathematics and Statistics exist to meet the computing needs of the Department’s faculty and graduate students for the purposes of instruction and research, and to provide access to relevant information and services of the Internet computer network.
We distinguish between operation (otherwise known as system management or administration) and administrative oversight. Operation is considered to consist of those tasks related to the maintenance of software, hardware, user accounts, and any other tasks which directly affect the status and performance of the physical resources. Administrative oversight will consist of the establishment and maintenance of software licenses, procurement of equipment, establishment of policies, and all other tasks not related to operation.
The computing resources of the Department are to be operated by one or more designated graduate Computer Assistants, possibly in collaboration with members of the faculty. The administrative oversight of the computing resources is the responsibility of the Departmental Research and Facilities Committee.
The computing resources of the Department will be available to those who are eligible for accounts on the Departmental server(s), as described below, for tasks consistent with the conditions of usage described under Acceptable Usage below.
All faculty, staff, and graduate students of the Department are eligible for computer accounts on the Departmental server(s). Accounts for faculty and graduate student users will be maintained through the end of the first full semester after the user’s departure. Accounts for staff members will be maintained at the discretion of the Research and Facilities Committee after the staff member’s departure
Undergraduate students, students from other departments, and former students from the Department of Applied Mathematics and Statistics, or any other person not specifically eligible as per above may obtain accounts or extend accounts past the normal termination date, as follows. The requester must have the sponsorship of a member of the Departmental faculty. The sponsoring faculty member should present the request to the Research and Facilities Committee and Department Chair for approval, whereupon the operator(s) will be instructed to create or maintain the account as specified.
If resource quotas are enforced, those users with accounts under special dispensation as described above may be required to observe resource limits different from those of eligible Departmental users.
The Department Chair is ultimately responsible for all decisions to create or terminate accounts on the Department’s server(s). The Research and Facilities Committee recommends actions on these matters to the Department Chair. Users will be notified by e‑mail two weeks prior to termination, in order to have time to properly clean out the account.
The users of the Department’s computing resources are responsible for adhering to all Johns Hopkins usage requirements, as well as all local, state, federal, and international laws.
Users are expected to observe the following:
2. Publication (mail and Web usage)
3. Network security
The reasons for these restrictions should be clear. Further information and suggestions are available online. Interested users may, for example, consult the Netiquette guide on the World Wide Web.