Written Qualifying Exam

A 6 hour exam (3 2-hour exams on Algebra, Complex Analysis and Advanced Calculus, and Real Analysis and Elementary Point Set Topology, respectively) usually taken after the first semester in the program or at the beginning of the 2nd year of studies.

Ph.D. Requirements - Written Qualifying Exam

Syllabus for the Written Exam In PDF
Sample exam in current format In PDF

Below is when the next set of Written Qualifying Exams will be offered.

ALGEBRA - Tuesday, 8/30/22, 3:00pm-5:00pm, COMPLEX ANALYSIS - Wednesday, 8/31/22, 3:00pm-5:00pm, and REAL ANALYSIS - Thursday, 9/1/22, 3:00pm-5:00pm.  All exams given in Hill Center Room 705.

Our two-week orientation program "SPP" will take place from Monday, August 22, 2022 through Friday, 9/2/2022 (no weekend days).  It has not yet been decided as to whether it will in-person or online.  For those that are unable to make it here by 8/22/22, we will provide an online option for students who cannot be physically present.

The Mathematics Ph.D. program at Rutgers includes two qualifying examinations, a written exam and an oral exam. The written exam is taken first and covers advanced calculus, elementary topology (metric spaces, compactness, and related topics), linear algebra, and the material of 501 (real analysis), 503 (complex analysis), and 551 (algebra). It is offered twice a year, near the beginning of each semester.

The syllabus represents a common core of material required of all Rutgers Ph.D.'s. In particular, the exam is designed with the goal that a pass on this exam shows a level of mathematical knowledge and ability appropriate for teaching the central undergraduate classes in mathematics.

The exam is a six hour written exam broken up into three exams, each of which is two hours long. The three exams cover, respectively, algebra, real analysis and elementary point set topology, and complex analysis and advanced calculus. Each of these two hour exams consists of two parts. Part I has 3 problems, each of which is mandatory, and part II has 2 problems, of which the student is expected to do one. Each student is expected to submit solutions to all 3 problems in part I, and 1 out of the 2 problems in part II.

Each student is required to take the exam by the beginning of the student's second year, and pass all the exams by the beginning of his or her fourth semester; the program director may allow a student who has entered with less preparation than the norm to take the exam a specified number of semesters later. Students who do not pass the exam on their first attempt do not need to retake individual components which they have already passed.

Students who fail this exam may take it again during the semester following the one in which the exam was failed. During any attempt (except for the "free" attempt for entering students), students are expected to take each of the three portions which they have not already passed. Students who fail on the second attempt or who do not take the exams on schedule (as determined by the program director) will not be allowed to continue in the Ph.D. program.

"Free" attempt for entering students: Students beginning graduate work at Rutgers may take the written qualifying exam at the beginning of their first semester in the program. If such a student fails the exam, this will not count as one of the two attempts that the student is normally allowed; the student will be allowed two additional attempts at the exam.

A complete solution to the August 2016 exam is posted here to serve as a model for students to learn how much justification and detail one should strive to provide --- these solutions are not worked out in a timed setting as the solutions to the real exams are, so can afford to contain more complete arguments; students can get full or close to full credits when their solutions contain all the key ingredients, with perhaps less detail than those contained here. A complete solution to the January 2011 exam, which is in the older format, is posted here.

Please note that this exam, like all exams before Summer 2014, followed a different format. A sample exam in the current format, culled from problems of earlier exams, can be found here in pdf format .

Prior versions of the exam (New format)

Spring 2022 PDF

Fall 2021

Spring 2021 PDF
Fall 2020 PDF
Spring 2020 PDF
Fall 2019 PDF
Spring 2019 In PDF
Fall 2018 In PDF
Spring 2018 In PDF
Fall 2017 In PDF
Spring 2017 In PDF
Fall 2016 In PDF
Spring 2016 In PDF
Fall 2015 In PDF 
Spring 2015 In PDF 
Fall 2014 In PDF 
Prior versions of the exam (Old format)
Spring 2014 In PDF 
Fall 2013 In PDF 
Spring 2013 In PDF 
Fall 2012 In PDF 
Spring 2012 In PDF 
Fall 2011 In PDF 
Spring 2011 In PDF 
Fall 2010 In PDF 
Spring 2010 In PDF 
Fall 2009 In PDF 
Spring 2009 In PDF 
Fall 2008 In PDF 
Spring 2008 In PDF 
Fall 2007 In PDF 
Spring 2007 In PDF 
Fall 2006 In PDF 
Spring 2006 In PDF 
Fall 2005 In PDF 
Spring 2005 In PDF 
Fall 2004 In PDF 
Spring 2004 In PDF 
Fall 2003 In PDF 
Spring 2003 In PDF 
Fall 2002 In PDF 
Spring 2002 In PDF 
Fall 2001 In PDF 
Spring 2001 In PDF 
Fall 2000 In PDF 
Spring 2000 In PDF 
Fall 1999 In PDF 
Spring 1999 In PDF 
Fall 1998 In PDF 
Spring 1998 In PDF 
Fall 1997 In PDF 
Spring 1997 In PDF 
Fall 1996 In PDF 
Spring 1996 In PDF 
Fall 1995 In PDF 
Sample exam (1993) In PDF