Qualifying Review-Mathematics Ph.D.

The following information about the Mathematics Ph.D. Qualifying Review (QR) can be found on this page:

QR Examination Schedule

2017-2018 (PDF)

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 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.

Please find the complete description of the QR requirements here on page 2.

QR Syllabi

All syllabi provided are PDF documents.

Algebra

Algebra I Syllabus
Algebra II Syllabus

Analysis

Complex Analysis Syllabus
Real Analysis Syllabus

Applied Analysis

Methods of Applied Analysis Syllabus
Numerical Methods Applied Analysis Syllabus

Topology

Algebraic Topology Syllabus
General Topology Syllabus (for September 2015 exam)
General Topology Syllabus (for January 2016 exam)

Past QR Exams

All exams provided are PDF documents.

Algebra

QR Exam (Jan 2017)
QR Exam Solutions (Jan 2017)

QR Exam (Sept 2016)
QR Exam Solutions (Sept 2016)
QR Exam (May 2016)
QR Exam Solutions (May 2016)
QR Exam (Jan 2016)
QR Exam Solutions (Jan 2016)

QR Exam (Sept 2015)
QR Exam Solutions (Sept 2015)
QR Exam (May 2015)
QR Exam Solutions (May 2015)
QR Exam (Jan 2015)
QR Exam Solutions (Jan 2015)

QR Exam (Sept 2014)
QR Exam Solutions (Sept 2014)
QR Exam (May 2014)
QR Exam Solutions (May 2014)
QR Exam (Jan 2014)
QR Exam Solutions (Jan 2014)

QR Exam (Sept 2013)
QR Exam Solutions (Sept 2013)
QR Exam (May 2013)
QR Exam Solutions (May 2013)
No Jan 2013 Algebra Exam Held

QR Exam (Sept 2012)
QR Exam Solutions (Sept 2012)
QR Exam (May 2012)
QR Exam Solutions (May 2012)
QR Exam (Jan 2012)
QR Exam Solutions (Jan 2012)

QR Exam (Sept 2011)
QR Exam Solutions (Sept 2011)
QR Exam (May 2011)
QR Exam Solutions (May 2011)
QR Exam (Jan 2011)
QR Exam Solutions (Jan 2011)

QR Exam (Sept 2010)
QR Exam Solutions (Sept 2010)
QR Exam (May 2010)
QR Exam Solutions (May 2010)
QR Exam (Jan 2010)
QR Exam Solutions (Jan 2010)

QR Exam (Sept 2009)
QR Exam Solutions (Sept 2009)
QR Exam (May 2009)
QR Exam Solutions (May 2009)
QR Exam (Jan 2009)
QR Exam Solutions (Jan 2009)

QR Exam (Sept 2008)
QR Exam Solutions (Sept 2008)
QR Exam (May 2008)
QR Exam Solutions (May 2008)
QR Exam (Jan 2008)
QR Exam Solutions (Jan 2008)

QR Exam (Sept 2007)
QR Exam Solutions (Sept 2007)
QR Exam (May 2007)
QR Exam Solutions (May 2007)
QR Exam (Jan 2007)
QR Exam Solutions (Jan 2007)

Analysis (Real and Complex)

Analysis QR Exam (May 2017)
Analysis QR Exam Solutions (May 2017)
Analysis QR Exam (Jan 2017)

Analysis QR Exam (Sept 2016)
Analysis QR Exam (May 2016)
Analysis QR Exam (Jan 2016)

Analysis QR Exam (Sept 2015)
Analysis QR Exam (May 2015)
Analysis QR Exam (Jan 2015)

Analysis QR Exam (Sept 2014)
Analysis QR Exam (May 2014)
Analysis QR Exam (Jan 2014)

Analysis QR Exam (Sept 2013)
Analysis QR Exam (May 2013)
Analysis QR Exam (Jan 2013)

Analysis QR Exam (Sept 2012)
Analysis QR Exam (May 2012)
Analysis QR Exam (Jan 2012)

Analysis QR Exam (Sept 2011)
Analysis QR Exam (May 2011)
Analysis QR Exam (Jan 2011)

Analysis QR Exam (Sept 2010)
Analysis QR Exam (May 2010)
Analysis QR Exam (Jan 2010)

Analysis QR Exam (Sept 2009)
Analysis QR Exam (Jan 2009)

Analysis QR Exam (Sept 2008)
Analysis QR Exam (May 2008)
Analysis QR Exam (Jan 2008)

Analysis QR Exam (Sept 2007)
Analysis QR Exam (May 2007)
Analysis QR Exam (Jan 2007)

Applied Analysis

Applied Analysis QR Exam (May 2014)
Applied Analysis QR Exam (Sept 2013)
Applied Analysis QR Exam (Sept 2012)
Applied Analysis QR Exam (May 2005)
Applied Analysis QR Exam (Jan 2005)

Topology

Topology QR Exam (May 2017)
Topology QR Exam (Jan 2017)

Topology QR Exam (Sept 2016)
Topology QR Exam (May 2016)
Topology QR Exam (Jan 2016)

Topology QR Exam (Sept 2015)
Topology QR Exam (May 2015)
Topology QR Exam (Jan 2015)

Topology QR Exam (Aug 2014)
Topology QR Exam (May 2014)
Topology QR Exam (Jan 2014)

Topology QR Exam (Sept 2013)
Topology QR Exam (May 2013)
Topology QR Exam (Jan 2013)

Topology QR Exam (Sept 2012)
Topology QR Exam (May 2012)
Topology QR Exam (Jan 2012)

Topology QR Exam (Sept 2011)
Topology QR Exam (May 2011)
Topology QR Exam (Jan 2011)

Topology QR Exam (Sept 2010)
Topology QR Exam (May 2010)
Topology QR Exam (Jan 2010)

Topology QR Exam (Sept 2009)
Topology QR Exam (May 2009)
Topology QR Exam (Jan 2009)

Topology QR Exam (Sept 2008)
Topology QR Exam (May 2008)
Topology QR Exam (Jan 2008)

Topology QR Exam (Sept 2007)
Topology QR Exam (May 2007)
Topology QR Exam (Jan 2007)