Written Qualifying Exam

This comprises 3 two-hour exams on

1) Algebra

2) Complex Analysis and Advanced Calculus

3) Real Analysis and Elementary Point Set Topology

These exams cover the material contained in Math 16:640:551, 16:640:503, and Math 16:640:501, respectively.

Ph.D. Requirements - Written Qualifying Exam

Syllabus for the Written Exam

Sample exam in current format


The Written Qualifying Exams are offered twice a year, in late August and January.  The next sitting of these exams is as follows. Students have 2.5 hours to complete the exam within this time frame - 8:00am-5:00pm (online via CANVAS).

Algebra - Monday, 8/26/24

Complex Analysis - Tuesday 8/27/24

Real Analysis - Wednesday, 8/28/24

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 2024 PDF
Fall 2023 PDF
Spring 2023 PDF

Fall 2022

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Fall 2021

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Prior versions of the exam (Old format)
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Sample exam (1993) In PDF