Doctoral Qualifying Examinations
January 2024 Qualifying Exams:
Foundation exams: Thursday, January 18; Time: 9:00 AM - 1:15 PM; Location: Physics,
Room P-117
Area Specific exams: Friday, January 19; Time: 9:00 AM - 1:00 PM; Location: Physics,
Room P-122
Comp Bio oral exams: Date: TBD, Time: Individual Scheduling, TBD; Location: TBD
A Ph.D. student must pass the qualifying examinations to be allowed to continue toward the Ph.D. degree. The Doctoral Qualifying Examinations include the “Foundation Exam” and the “Area-Specific Exam.” The exams are designed to test the student's preparation to do research. Every Ph.D. student must pass both examinations in his/her declared area of concentration – computational applied mathematics, operations research, computational biology, statistics, or quantitative finance – to be allowed to continue toward the Ph.D. degree. The exams are given twice each year, in January and May. All Ph.D. students are expected to take the Foundation Exam by the end of the first year of study and to take the Area-Specific Exam by the end of the second year of study. A student can take the Foundation Exam and the Area-Specific Exam in any order, but will usually take the Foundation Exam first. If a student fails an exam in the first attempt, a second attempt is allowed if done so within one year of the failure.
In order to take either one of the qualifying exams, a student must register for the exam with the Graduate Program Coordinator at least one month before the exam. An M.S. student can register for the Foundation Exam in his/her area only if the student has received a grade of B+ or above in all of the courses covered on the exam, except for AMS 510, which may be substituted by a higher-level course upon the approval of the track advisor. Similarly, an M.S. student can register for the Area-Specific Exam in his/her area only if the student has received a grade of B+ or above in all of the required courses covered on the exam, as specified below. A Ph.D. student must take the Foundation Exam before the end of the first year of study and take the Area-Specific Exam before the end of the second year of study. A Ph.D. student who did not take either part of the qualifying exam by its designated deadline will be considered to have failed the exam. A student may cancel the registration for an exam if done so at least one week before the exam. If a student registers for an exam, does not cancel the registration at least one week before, and does not show up to take the exam at the scheduled exam time, the exam will count as a failure for the student. Exceptions can be made only with written approval from the Track Advisor and the Graduate Program Director.
Foundation Exams
A Foundation Exam is a four-hour exam with two parts. The first part is common to
all the tracks, and takes two hours. The student is expected to do three problems
each in linear algebra and advanced calculus at the level of AMS 510: Analytical Methods for Applied Mathematics and Statistics .
In the second part, the student is expected to solve problems from various courses,
depending on the student’s track (CAM/OR/QF/STAT/CB). There are three categories of
problems, depending on the track. The CAM category requires doing three problems from
each of AMS 501: Ordinary Differential Equations and AMS 526: Numerical Linear Algebra. The OR/QF/STAT category involves doing three problems from AMS 507: Introduction to Probability. The Computational Biology (CB) category requires doing three problems from AMS 535: Computational Structural Biology.
No calculator is allowed during the Foundation Exam.
The problems within each part are equally weighted. The first part (Part A) accounts
for half of the total grade of the Foundation Exam, and the second part accounts for
one half. A student must, in general, perform reasonably well on both parts in order
to pass the Foundation Exam.
Organizers:
Foundation (Part A): Prof. Xiaolin Li
CAM category (Part B): Prof. Roman Samulyak
CB category (Part B): Prof. Robert Rizzo
OR/QF/STAT category (Part B): Prof. Eugene Feinberg
Area-Specific Exams
Computational Applied Math (CAM) Area Exam: Organizer - Prof. Xiaolin Li
This is a closed-book exam that lasts four hours. Students are expected to solve eight
problems:
4 problems out of the following 5 problems: 2 or 3 from AMS 502 and 2 or 3 from AMS
503.
4 problems out of the following 5 problems: 2 or 3 from AMS 527 and 2 or 3 from AMS
528.
An M.S. student must have taken at least three of AMS 502, 503, 527 and 528 and received
B+ or above in all of these classes in order to register for this exam.
The problems are equally weighted for grading. No calculator is allowed in the CAM
Area Exam. A student must perform reasonably well in both parts in order to pass the
exam.
Computational Biology (CB) Area Exam: Organizer -TBD; CB Area Exams: TBD.
This is an oral exam based on the student's specific course sequence. The student
is examined by a panel of at least three faculty and must answer questions from those
courses the student has covered in each of these three key areas: fundamentals of
applied mathematics; fundamentals of biology and/or biochemistry; methods and applications
in computational biology, as well as in the particular elective courses the student
has taken. The oral format is chosen to allow greater flexibility in dealing with
a range of students having different focus areas and in assessing the student's understanding
of biological systems. Students should consult with the examination committee well
in advance of the exam in order to determine which areas/courses will be emphasized.
An M.S. student must have taken AMS 533, AMS 537 and CHE 541 and received B+ or above
in each of these classes in order to register for this exam.
Operations Research (OR) Area Exam: Organizer - Prof. Esther Arkin
This is a closed-book exam that lasts four hours. Students are expected to solve seven
problems:
2 out of 3 questions on AMS 540
2 out of 3 questions on AMS 550
3 out of 10 questions: 2 questions each from AMS 544, 545, 546, 553, 556, 569.
An M.S. student must have taken AMS 540 and 550 plus at least two of AMS 544, 545,
546, 553, 556, 569 and received B+ or above in each of these classes in order to register
for this exam.
The problems are equally weighted for grading. No calculator is allowed on the OR
Area Exam.
Quantitative Finance (QF) Area Exam: Organizer - Prof. Stanislav Uryasev
This is a closed-book 4-hour comprehensive exam covering material from:
- AMS 511: Foundations of Quantitative Finance
- AMS 512: Capital Markets and Portfolio Theory
- AMS 513: Financial Derivatives and Stochastic Calculus
- AMS 517: Risk Management
Students are expected to solve eight problems:
- 2 out of 3 questions from AMS 511
- 2 out of 3 questions from AMS 512
- 2 out of 3 questions from AMS 513
- 2 out of 3 questions from AMS 517
An M.S. student must have taken AMS 511, 512, 513 and 517 and received B+ or above
in each of these classes in order to register for this exam.
The problems are equally weighted for grading. No calculator is allowed in the QF
Area Exam.
Statistics (STAT) Area Exam: Organizer - Prof. Wei Zhu
This is a 4-hour exam with two parts:
- Math STAT Exam: A 2-hour closed-book exam consists of four problems from AMS 570 and AMS 571. The student is expected to solve them all. No calculator is allowed.
- Applied STAT Exam: For January 2023, 2-hour open-book exam consists of four problems from AMS 572, 573, 578, or one of AMS 580, 582, 586. For May 2023 and beyond, a 2-hour open-book exam consists of four problems from AMS 572, 573, 578, and 580. The student is expected to solve three of the four problems. Four textbooks, four notebooks, and a calculator are allowed, but no computer, phone, or other electronic device is allowed.
An M.S. student must have taken AMS 570 plus at least three of AMS 571, 572, 573, 578, and (580, 582, 586) and received B+ or above in each of these classes in order to register for this exam.
Preparing for the Qualifying Exams
To prepare for the qualifying exams, students are strongly encouraged to take the
courses that are covered on the exams, even if a similar course has been taken elsewhere.
The qualifying exams typically cover the more advanced materials taught in these courses.
Students are urged to earn A’s in the courses covered on the Foundation Exam. Ph.D.
students who have strong background in mathematics and have excelled in the assessment
test for AMS 510 may opt to audit AMS 510 instead of taking it for credit; however,
every student should learn to solve the course homework problems to prepare for the
Foundation Exam. For the Area-Specific Exams, it is strongly recommended for the students
to earn at least an A- in each course.
Students are encouraged to study the past qualifying exam problems. A collection of
past exam questions can be accessed by clicking here: Past Qualifying Exams.