Graduate Degree Programs & Requirements

Getting Started

Admission Process

Admission to the Graduate School of Arts & Sciences depends on a candidate's ability and promise of achievement. To demonstrate both, applicants must submit undergraduate records showing above-average performance at a recognized school, and letters of recommendation from people thoroughly familiar with their abilities. Graduate Record Examination general scores and the subject test are required. For information about admission schedules and procedures, please consult the Graduate School of Arts and Sciences.

An entering graduate student should display competence in analysis and algebra, equivalent to the content of Washington University's Math 411-412 and 429-430 courses. PhD candidates will also find a knowledge of topology (Math 417-418) to be very helpful. A student lacking in one or more of these prerequisites may have difficulty conforming to the expected timetable for the qualifying exams; time may be allowed to complete this preparation when appropriate.

International students must be proficient in English. Entering students whose native language is not English are expected to perfect their speaking and writing skills before beginning studies at Washington University. A student arriving at the University with an inadequate command of English may be required to take remedial English instruction at his or her own expense. It is best for all foreign students to arrive at Washington University in the early summer, several months before the fall semester begins at the end of August, to ensure that these language requirements are met. 

Program Overview

Doctoral students at Washington University are required to demonstrate proficiency in algebra, real analysis, complex analysis, and geometry. Most students satisfy these requirements by taking a yearlong (two-semester) course in each subject, capped by a final exam that serves as a "qualifier." Students with strong backgrounds may be excused from some of these courses.

Typically, it takes two years for a student to complete the written qualifying exam phase of the program. By the end of the second year, the student usually has some idea of which area of specialization to choose. By that time the student is also acquainted with several faculty and feels comfortable asking one to direct his/her research.

Once the qualifying exams are passed and a thesis advisor engaged, the next step in the program is for the student to prepare a "minor oral presentation" and a "major oral presentation." Topics for these orals are chosen in consultation with their thesis advisor, and culminate in two public lectures. These should be completed by the end of the year following completion of the written qualifying exams as well as satisfying their language requirement.

After these preliminaries, the essential part of a student's graduate work – the thesis – begins. This thesis may range from fifty to a few hundred pages and is the formal record of the student's achievement in the graduate program. The final official step is for the student to defend the thesis in a public lecture followed by questions from a panel of appointed faculty members of the University in a closed session.

Students typically complete the PhD program in five years. A student who comes here with advanced preparation may finish in less time. In special cases, the time schedule may be lengthened accordingly. Students should plan to develop a close relationship with their thesis advisors so that they may have a realistic idea of their progress.

The Extended Graduate Orientation

The Extended Graduate Orientation is strongly recommended for new graduate students in mathematics. The program is run by the Department of Mathematics and Statistics and has proven very beneficial for all involved. The purpose is twofold: to introduce incoming students to the style and pace of graduate courses, so as to have everybody up to speed when fall classes begin; and to foster a cohesive and supportive social environment of graduate students, faculty, and staff, in which all can work most effectively and productively.

The Extended Graduate Orientation takes place in mid-August. The program mainly consists of lectures and discussions in mathematical topics, and meeting with faculty and support staff. A program schedule is given to participants in late June.

The AM in Mathematics

General Requirements

The minimum residence requirement is one full academic year of graduate study. Thirty-six semester hours of graduate-level course work is required, with or without thesis, but six units may be for thesis research. If the department consents, a student may transfer up to six hours from other universities. A grade point average of "B" or better must be maintained in graduate course work.

Course Requirements

There are four basic graduate course sequences in pure mathematics: 5021-5022, 5031-5032, 5041-5042 or 5043, and 5051-5052. A candidate for the AM in Mathematics must include two of these sequences (12 hours) in the required 36 hours. The student, in consultation with his or her advisor, will select the remaining 24 hours according to the student's interests and needs.

The AM Examination

Candidates for the AM degree must pass at least four of the 9 semester long PhD qualifying exams. Under exceptional circumstances, the Graduate Committee may allow the student to substitute the PhD. Qualifying exams mentioned above with a comprehensive examination on the contents of Math 411-412, 417-418, and 429-430.

The AM in Statistics

General Requirements

36 units of coursework and an optional thesis by discretion of the Statistics Committee. Three units may be for thesis research.  The minimum residence requirement is one full academic year of graduate study. A grade point average of "B" or better must be maintained in graduate course work.

Optional Thesis Requirements

To be eligible for the thesis option, a student must maintain a cumulative grade point average of 3.5 or above in the first two semesters (or 18 units) of course work satisfying the program requirements. A maximum of 3 units may be used for thesis research.

Course Requirements

The student must take the following six required courses in mathematics or their equivalents: Math 493 and 494 (Probability and Mathematical Statistics) or 5061 and 5062 (Theory of Statistics); Math 4392 (Advanced Linear Statistical Models); Math 439 (Linear Statistical Models); Math 459 Bayesian Statistics; and 475 (Statistical Computation) or a suitable substitute elective approved by the department.

In the case that an equivalent course has been taken and also proficiency in the course material has been demonstrated, other 400-level and above electives may be substituted in consultation with the advisor. Knowledge of Linear Algebra at the level of Math 429 is required for many courses. Students may petition to waive the Math 429 requirement based on previous course work. In such circumstances, students may be required to take a Linear Algebra placement exam at the beginning of the first semester. Satisfactory performance on this placement exam will allow students to waive Math 429; otherwise Math 429 will be an additional required course which must be taken during the first semester.

Additional 400-level or higher electives will be chosen by the student in consultation with his or her advisor to make up the 36 units. Typically, at most three electives shall be chosen from outside the Mathematics Department. If not taken before, a course in C programming is strongly recommended but cannot be included among the courses used to satisfy the 36 units requirement.

Electives

MATH 449 Numerical Methods (F)
MATH 4111 Introduction to Analysis (F) 
Math 4121 Introduction to Lebesgue Integration (S)
Math 420 Experimental Design (SE)
Math 4121 (S) Introduction to Lebesgue Integration
MATH 4301 Multilevel Modeling (POLI SCI 584C) (F)
MATH 434 Survival Analysis (FO)
MATH 4392 Advanced Linear Statistical Models (SO)
Math 449  Numerical Applied Mathematics (F)
Math 456 Financial Mathematics
Math 460 Multivariate Statistical Analysis
MATH 495 Stochastic Processes (SO) 
MATH 5061-62 Theory of Statistics I / II (F)/(S) 
MATH 523C Information Theory and Statistics (ESE 523) 
MATH 5021 - Complex Analysis I (F)
MATH 5022 - Complex Analysis II (S)
MATH 5031 - Algebra I (F)
MATH 5032 - Algebra II (S)
MATH 5041 - Geometry I (F)
MATH 5042 - Geometry II (SE)
MATH 5051 - Measure Theory and Functional Analysis I (F)
MATH 5052 - Measure Theory and Functional Analysis II (S)
MATH 551 - Advanced Probability I 
MATH 552 - Advanced Probability II
B62 FIN 538 Stochastic Foundations for Finance (1.5 credits) 
B62 FIN 539 Mathematical Finance (1.5 credits)
BIO 4181 Population Genetics 
BIOL 5483 01 Human Linkage and Association Analysis 
BIOL 5495 01 Computational Molecular Biology 
CSE 514A Data Mining
CSE 515T Bayesian Methods in Machine Learning
CSE 517A Machine Learning
Econ 513 Introduction to Econometrics
Econ 5145 Advanced Theoretical Econometrics
Econ 5161 Applied Econometrics
Econ 5175 Structural Microeconometrics
ESE 545 Stochastic Control
ESE 522 - Random Variables and Stochastic Processes II
MEC 670 - Seminar in Econometrics 
 

Please note: Not all courses are offered each year. 
Courses are listed in numerical order. The letters in parentheses after the name of a course mean:

  • F = offered each fall

  • FO = offered each fall in odd-numbered years

  • FE = offered each fall in even-numbered years

  • S = offered each spring

  • SO = offered each spring in odd-numbered years

  • SE = offered each spring in even-numbered years

Math courses listed without one of these codes are offered based on demand.

Accelerated AB/AM Program

About the Program

It usually takes 3-4 additional semesters to complete a master's degree (AM) after earning the bachelor's degree (AB). The Graduate School of Arts & Sciences has an accelerated AB-AM program in which highly qualified undergraduate majors can earn both the AB and AM degrees with two additional semesters work (usually a total of 5 years). The department offers the AM degree in mathematics or statistics. 

Note that this program is only for WU undergraduates who, if they participate, must do so in the academic year immediately following graduation (no deferments).  According to the Graduate School, eligibility requires having completed the AB degree from Arts & Sciences (which would rule out, for example, a second major who degree is from the Engineering School). 

Some students might find a master's degree earned through this program useful. However, students planning to enter a PhD program in mathematics or statistics usually do so directly after completing the AB degree rather earning an AM degree first.  Majors should talk with their advisors early about whether this program would have any advantage for them. 

Majors who are interested in the program should

  • look at the general Information in the Bulletin (graduate School of Arts & Sciences). The description for the Accelerated AM program appears several paragraphs down on that page.
  • read the Department's requirements for the AM in Mathematics and for the AM in Statistics.
  • The application deadline (subject to change by the Graduate School)  is the August 1 prior to beginning the AM program in the fall semester following completion of the WU AB degree. Note that the application is made through the Department, which forwards it to the Graduate School. Since relevant people in the Department might not be available much during the summer months, it's best to complete the application by the end of the semester's classes.

The program allows participants to count up to 15 units of 400-500 level coursework earned during the 4 years of undergraduate study (with grades of B or better) toward the AM course requirements.  (The point of the 15 unit limit is to avoid having majors push so much specialized work into the AB years that they limit their opportunities to do the exploration outside of the major that an undergraduate should do.) Counting these 15 units makes it possible to finish the master's requirements in one additional year, but the program is still fast-paced and requires a lot of intense work and some careful planning.

Careful course selection throughout the undergraduate program is required. Usually, the Department will not recommend that the Graduate School admit a major to this program unless the 15 applicable units of 400-500 level work will be completed by the time of graduation. In addition, the Department expects applicants to have backgrounds comparable to students admitted to our regular master's programs. The total number of master's candidates that the Department can accept at a given time may be limited. 

For more information about graduate program requirements, contact the Department's Director of Graduate Studies,  Professor Brett Wick.

Applying to the Program

The Department of Mathematics asks that interested majors apply to the program by the end of the fall semester in the senior year.  If accepted, they must begin the program in the fall semester immediately after graduation: no deferred admissions are allowed by the Graduate School.

Students should fill out the Application Form and make an appointment to meet with the Administrative Assistant for the Department's graduate programs, Ms. Mary Ann Stenner, in Cupples I, Room 100.  She will clarify the rest of the procedure for you: submitting the application for Department consideration and getting the required signatures from the Department Chair and Chair of the Graduate Committee.  If the Department approves the application, then Ms. Stenner will submit it to the Graduate School which will make the final decision.

International Students: 

For students in the US on a visa as undergraduates: staying on to complete an AM creates a change in visa status, which will involve reapplication paperwork. Be sure to check on the details with an international student advisor at the Office for International Students and Scholars.

The PhD in Mathematics

General Requirements

Completion of the PhD 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 (24 graduate credits for a Ph.D. and only 6 credits for a Master's). 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 the second year, the student should have successfully completed the specific course requirements and passed six qualifying exams; at the end of the third year, the student should have completed the candidacy 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 Assistant to the Instructor (AI) 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 (AI, grading, proctoring) of no more than fifteen hours per week as Assistants to the Instructor (AI).

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 their ability and background. When warranted, deviation from the normal sequence is permissible and a tailored program that fits the student's ability and background will be followed.

Specific Course Requirements

The 72 hours of coursework must include eight of the following nine courses: Math 5031-5032 (Algebra I and Algebra II), Math 5051-5052 (Real Analysis and Functional Analysis), Math 5021-5022 (Complex Analysis I & II), Math 5041-5042 (Smooth Manifolds and Differential Geometry) and Math 5043 (Algebraic Topology).  Students may omit one of the following classes when satisfying the course requirement: Math 5022, 5042, or 5052.  To satisfy the breadth requirement one must pass the required courses with a B or better.  The classes are typically offered in the following time frame:

  • Fall:                 Algebra 1, Real Analysis, Complex Analysis I, Algebraic Topology, Differential Geometry
  • Spring:             Algebra II, Functional Analysis, Complex Analysis II, Smooth Manifolds

In exceptional circumstances, Departmental permission may be requested to replace required courses with a suitable alternative. The student may also petition the Department to waive one or more of these courses because of work done previously.

It is in each student's best interest to take the courses 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

All students must demonstrate proficiency in English.

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 Assistant to the Instructor or Course Instructor duties.

Qualifying Examinations and Candidacy Requirements

The qualifying exam is a series of six written tests covering a range of topics and the candidacy requirement is an oral presentation and thesis proposal.

The written tests cover the material in one semester of the courses: 5021, 5022, 5031, 5032, 5041, 5042, 5043, 5051, and 5052. To satisfy the written exam requirement, the student must pass six out of the nine possible qualification exams, with the requirement that two be from Math 5021, 5022, 5051 or 5052, two in Math 5041, 5042, or 5043, and two in Math 5031 and Math 5032.  To satisfy the qualification examination requirement the student must pass the final exam for the course with an A- or better.

Because each course varies somewhat in content from year to year, it is recommended that the student take the exams at the conclusion of the course in which they are enrolled. No advantage is gained by delaying the exam. It is required to finish all six qualification exams by the end of the second year of study.

Some students will enter the PhD program with previously acquired expertise in one or more of the required courses. This sometimes happens with students who transfer from other PhD 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.  By the third year of studies, the student must complete the candidacy requirement.  The student must form a preliminary thesis committee comprising the advisor and at least two other faculty members.  In discussion with the advisor and preliminary thesis committee, the student will select a topic and body of literature related to this topic.  The student will prepare a one-hour oral presentation related to these topics and a two-page thesis proposal related to these topics to demonstrates mastery of the selected topics.  The oral presentation is designed to expedite specialized study and provide guidance toward the thesis.  The preparatory work for the thesis proposal often becomes the foundation on which the thesis is constructed.

Following the candidacy requirement work on the thesis begins.

Dissertation and Thesis Defense

The student's dissertation is the single most important requirement for the PhD 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 candidacy requirement, the student should have engaged an advisor by the beginning of the third year of study.

Once the Department has accepted the dissertation (on the recommendation of the thesis advisor), the student is required to defend their thesis through a presentation accompanied by a question/answer period.

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 Doctoral Dissertation Guide, the Forms page, and the Policies and Procedures page.

The PhD in Statistics

Degree Requirements Summary

Total of 72 graduate units required, consisting of:

  • 24 required coursework units total in fundamental topics and exam fields
  • 12 elective coursework units
  • 3 qualifying exams: 2 in statistics, 1 in mathematics
  • Graduate School Teaching Requirement for Ph.D. Students
  • Oral presentation
  • Dissertation research, thesis preparation, and defense (30 coursework units)

General Requirements

Completion of the PhD 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 (24 graduate credits for a Ph.D. and only 6 credits for a Master's). 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 statistics 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. Teaching experience is an increasingly important component of graduate education for students who seek academic employment. The Ph.D. in Statistics program provides the opportunity for students to be Assistants to the Instructor (AI) and to learn how to teach technical topics to students with a wide range of backgrounds.

For the well-prepared student, normal progress usually means: At the end of his or her second year, the student should have successfully passed the two statistical qualifying exams associated to Math 5061-5062 and Math 439-4392, the mathematical qualifying exams associated to Math 5051-5052, and completed the courses Math 459 and Math 475;  at the end of the third year, the student should have completed the candidacy 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 Assistant to the Instructor (AI) 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 (AI, grading, proctoring) of no more than fifteen hours per week as Assistants to the Instructor (AI).

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 their ability and background. When warranted, deviation from the normal sequence is permissible and a tailored program that fits the student's ability and background will be followed.

Specific Course Requirements

 The 72 hours of course work must include two basic graduate-level sequences in statistic: Math 5061 Theory of Statistics I - Math 5062 Theory of Statistics II, Math 439 Linear Statistical Models - Math 4392 Advanced Linear Models; the following statistics courses: Math 459 Bayesian Statistics and Math 475 (Statistical Computation); and the following graduate-level mathematics sequence Math 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.

Prerequisites, if needed, are advanced undergraduate courses in abstract linear algebra and real analysis. Such courses would count as 0 credits towards the degree.

It is in each student's best interest to take the three 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.

Prior to finding a research advisor, students are welcome to take any of the Department of Mathematics 400- and 500-level statistics electives, and may also take reading courses with statistics faculty members (Math 500 / Math 590). Statistics electives offered by the Department include:

  • Mathematics 420, Experimental Design
  • Mathematics 434, Survival Analysis
  • Mathematics 449, Numerical Applied Mathematics
  • Mathematics 456, Financial Mathematics
  • Mathematics 459, Bayesian Statistics
  • Mathematics 460 Multivariate Statistical Analysis
  • Mathematics 461 Time Series Analysis
  • Mathematics 462 Mathematical Foundations of Big Data
  • Mathematics 475, Statistical Computation
  • Mathematics 495, Stochastic Processes
  • Mathematics 551, Advanced Probability I
  • Mathematics 552, Advanced Probability II
  • Mathematics 523C, Information Theory and Statistics (ESE 523)
     

Prior to finding a research advisor, students may submit a request to the Graduate Committee to take a course outside the Department. A decision on such requests will be made in consultation with statistics faculty members. 

Students are encouraged to take reading courses with Department faculty to learn about the research interests of potential advisors. After the student has found a research advisor and research topic, the advisor may suggest that the student takes some additional courses from other departments which may be useful for the student's research program.

Elective courses taken in other departments allow students to supplement their statistics coursework with other topics that may be helpful for their research and professional development.  Some popular elective courses offered by other departments include:

  • Electrical and Systems Engineering 405, Reliability and Quality Control
  • Electrical and Systems Engineering 407, Analysis and Simulation of Discrete Event Systems
  • Electrical and Systems Engineering 415, Optimization
  • Electrical and Systems Engineering 425, Random Processes and Kalman Filtering
  • Electrical and Systems Engineering 428, Probability
  • Electrical and Systems Engineering 520, Probability and Stochastic Processes
  • Electrical and Systems Engineering 521, Random Variables and Stochastic Processes I
  • Electrical and Systems Engineering 522, Random Variables and Stochastic Processes II
  • Electrical and Systems Engineering 523, Information Theory
  • Computer Science & Engineering 511A, Introduction to Artificial Intelligence
  • Computer Science & Engineering 514A, Data Mining
  • Computer Science & Engineering 517A, Machine Learning
  • Computer Science & Engineering 519T, Advanced Machine Learning
  • Computer Science & Engineering 541T, Advanced Algorithms
  • Biostatistics M19-550, Randomized Controlled Trials
  • Biostatistics M21-623, Advanced Topics in Biostatistics
  • Economics 5145, Advanced Theoretical Econometrics

Language Requirement

All students must demonstrate proficiency in English.

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 Assistant to the Instructor or Course Instructor duties.

Qualifying Examinations and Candidacy Requirements

The qualifying exam and candidacy requirement constitute two separate requirements.  The qualifying exam is a series of three written tests covering a range of topics, and the candidacy requirement is an oral presentation coupled with a thesis proposal.

The written tests cover the material in the two basic statistics course sequences: Math 5061-5062, Math 439-4392, and in the mathematics sequence Math 5051-5052. Each spring, at the end of the Math 5061-5062 and Math 439-4392 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, the student must pass the three-hour combined exam.  In the case of the Math 5051-5052 sequence, to satisfy the qualification examination requirement the student must pass the final exam for the course with an A- or better.

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 three 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 candidacy requirement 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 presentation, work on the thesis begins.

The Dissertation and Thesis Defense

The student's dissertation is the single most important requirement for the PhD degree: it must be an original contribution to the knowledge of statistics, probability, and/or applied probability. 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 oral committee, the student should have engaged an advisor by the beginning of the third year of study.

Once the Department has accepted the dissertation (on the recommendation of the thesis advisor), the student is required to defend their thesis through a presentation accompanied by a question/answer period.

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 Doctoral Dissertation Guide, the Forms page, and the Policies and Procedures page.

PhDs for Applied Mathematicians

About the Program

Prospective PhD students with previous degrees in mathematics or applied mathematics who are interested in PhD studies and research with applications to engineering are encouraged to apply for PhD studies in Systems Science & Mathematics or Electrical Engineering & Mathematics.

The mathematics faculty contact for this option is Professor Ari Stern.  The engineering faculty contact is Arye Nehorai.