Ph.D. Comprehensive Exam: Policy and General Information

  • The comprehensive exam is intended to ensure that students have sufficient background in their subject area to undertake Ph.D. research.
  • Ph.D. students are required to take a written comprehensive examination as one of the requirements for admission to Ph.D. candidacy.
  • This examination is to be taken by students at the beginning of the 3rd semester of enrollment as an essential part of MATH 699 (seminar).
  • The examination will have 4 components. Currently, the examination is expected to cover 4 graduate level courses from the following including at least 2 courses from group I:
Group I Group II
MATH 521 General Topology I MATH 525 Graph Theory
MATH 531 Real Analysis MATH 565 Advanced Ordinary Differential Equations I
MATH 533 Complex Analysis MATH 566 Fractional Differential Equations
MATH 550 Linear Algebra MATH 568 Advanced Partial Differential Equations I      
MATH 551 Abstract Algebra MATH 571 Numerical Analysis of Ordinary Differential Equations
  MATH 580
      or
MATH 581 		Convex Analysis
 
Advanced Linear Programming

 

  • An updated list of topics and references will be made available to the students for each component.
  • The minimum passing score for each component is 70%. A student is declared to have passed the comprehensive exam when she/he has passed all four components.
  • If a student fails one (or more) component(s) of the comprehensive exam is the first attempt, she/he will be given a severe warning and the Graduate Committee will advise the student to retake the examination for the component(s) failed at the beginning of the fourth semester of enrollment. This will, however, be the final chance for the student to pass the comprehensive exam.
  • The duration of each component of the comprehensive exam is 3 hours.
  • The comprehensive exam shall be administered by the Department Graduate Committee. Each of the four components shall be prepared and graded by at least two examiners with expertise in the relevant component. The examiners are appointed by the Chairman of the Department upon recommendation of the Graduate Committee. They shall report the students’ percentage scores to the Graduate Committee. The names of the examiners shall be kept confidential.