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Qualifying Review Exams

Schedule of QR Exams 2016-17

September 2016

  • Saturday, September 3 - Topology
  • Monday, September 5 Algebra [Labor Day]
  • Monday, September 5* Applied Analysis [Labor Day]
  • Tuesday, September 6 Classes Begin
  • Saturday, September 10 Analysis
  • Tuesday, September 13 Results Meeting
  • Friday, September 16 Inform Students

January 2017

  • Tuesday, January 3 Algebra
  • Tuesday, January 3* Applied Analysis
  • Wednesday, January 4 Classes Begin
  • Saturday, January 7 Analysis
  • Sunday, January 8 Topology
  • Wednesday, January 11 Results Meeting
  • Friday, January 13 Inform Students

May 2017

  • Friday, April 27 Last day of finals
  • Wednesday,  May 3 Algebra
  • Wednesday, May 3* Applied Analysis
  • Thursday, May 4 Analysis
  • Friday, May 5 Topology
  • Tuesday May 9 Results Meeting
  • Friday May 12 Inform Students

*If a student wishes to take both algebra and applied analysis, alternate accommodations will be made

QR General Description

Each Mathematics Ph.D. student must pass the Qualifying Review. This consists of written examinations, a course requirement, and a survey by the Doctoral Committee of the student's record as a graduate student in the Department. The purpose of the Review is to ensure that students have a good knowledge of core graduate mathematics and to evaluate the chances that a student will be able to complete a Ph.D. degree.

The Qualifying Review Examinations are a written set of examinations offered three times a year in early January, May, and September. They cover applied analysis and each of the three major areas of pure mathematics---algebra, analysis, and geometry/topology.  The syllabus for the Examination in each area is the same as that for the corresponding core courses: 

Algebra: Math 593, 594
Analysis: Math 596, 597
Applied Analysis: Math 556, 572
Geometry/Topology: Math 591, 592

Students are responsible for the material in the syllabus even when it is not covered in a particular core course. Please find the complete description of the QR requirements here on page 2.

Completing the QR Requirement

There are a few ways to satisfy the QR Requirement.

  1. Students who pass the Qualifying Review Exams in two of the pure areas, algebra, analysis, or geometry/topology, must also pass the two core courses in the third pure area, or one core course in each of the remaining two areas, with at least a B average and no grades C+ or lower. Such students must also successfully complete one further course in an area outside the pure core areas, for example, in algebraic geometry, applied mathematics, combinatorics, differential geometry, logic, mathematical physics, number theory, numerical analysis or probability. An applied core course may be used for this purpose. With the permission of the Chair of the Doctoral Committee, a student may substitute a more advanced course in the same immediate area for a core course. For example, the student may substitute a more advanced complex analysis course for the complex analysis core course, but not for the real analysis core course.
  2. Students who pass the Qualifying Review Exam in Applied Analysis and one other area must pass one core course in each of the remaining two areas, with at least a B average and no grades of C+ or lower. Such students must also successfully complete one additional course in algebra, pure analysis, geometry, topology, or discrete mathematics.
  3. Students who pass the Qualifying Review Exams in three of the four areas must also pass a course in an area outside of the pure core areas for example, in algebraic geometry, applied mathematics, combinatorics, differential geometry, logic, mathematical physics, number theory, numerical analysis or probability. An applied core course may be used for this purpose.

Retesting and Requirement Deadline: Students are encouraged to take the QRs as soon as possible. The QR can be taken as many times as necessary with the only stipulation that a student must pass the exams in one area by the beginning of the fourth term in the program, and must complete the entire Review by the beginning of the sixth. The Department expects the entire Qualifying Review to be completed by the end of the fourth term, and requires that it be completed by the start of the sixth term. Thus, for example, a student entering the Doctoral Program in the Fall of 2013 must pass the Examination in at least one area by early January 2015 and the whole Review by no later than early January 2016.