Ph.D. Comprehensive Exam: Policy and General Information

Ph.D. Comprehensive Exam

Policy and General Information for the comprehensive examination

The comprehensive exam ensures students have sufficient background to undertake Ph.D. research.

Ph.D. students must take a written comprehensive examination as a requirement for admission to Ph.D. candidacy.

The examination is to be taken at the beginning of the 3rd semester of enrollment as an essential part of MATH 699 (Seminar).

4
Components
3h
Per Component
70%
Minimum Score
2
Attempts Max
Comprehensive Exams Course Directory

The examination has 4 components. It covers four graduate-level courses from the list below, including at least two courses from GROUP I.

Group I
1 MATH 521 General Topology
2 MATH 531 Real Analysis
3 MATH 533 Complex Analysis
4 MATH 550 Linear Algebra
5 MATH 551 Abstract Algebra
Group II
1
MATH 525 Graph Theory
or
MATH 645 Combinatorics
2
MATH 565 Advanced ODE I
or
MATH 568 Advanced PDE I
3
MATH 571 Numerical Analysis of ODE
or
MATH 572 Numerical Analysis of PDE
4
MATH 580 Convex Analysis
or
MATH 582 Advanced Linear Programming
5
MATH 527 Differential Geometry
or
MATH 556 Algebraic Geometry
6
MATH 563 Probability Theory
or
MATH 601 Stochastic Differential Equations
7 MATH 535 Functional Analysis
Exam Timeline
3rd
First Attempt — 3rd Semester
All components taken at the beginning of the semester. This is the standard timing for the comprehensive examination.
4th
Retake (if needed) — 4th Semester
Only failed component(s) may be retaken at the beginning of the 4th semester. This is the final chance.
Important Notes
1

An updated list of topics and references will be provided for each component.

2

The minimum passing score for each component is 70%. A student passes the comprehensive exam upon passing all four components.

3

If a student fails one or more components on the first attempt, a severe warning will be issued. The Graduate Committee will advise the student to retake only the failed component(s) at the beginning of the 4th semester (final chance).

4

The duration of each component is 3 hours.

5

The exam is administered by the Department Graduate Committee. Each component is prepared and graded by at least two examiners appointed by the Chairman upon recommendation of the Graduate Committee; examiners' names are confidential, and percentage scores are reported to the Committee.