Overview of Degree Requirements

General requirements for graduate degrees at Rutgers are governed by the rules of the Graduate School - New Brunswick and are listed in the current catalog. These include how and when credit can be transferred and how many credits can be taken each semester.

Course Requirements

Course Requirements for the Ph.D. Program

Students must complete 72 credits, of which at least 24 must be research credits.  The remaining credits should be of approved coursework in Mathematics and related disciplines.  There is no minimum number of credits for approved coursework. The normal minimum grade for graduate courses is B, though a small number of courses with grades of C or C+ may be approved.

The program of courses should be chosen to provide the student with both breadth and depth in mathematics and/or its applications.

The courses 16:642:527-528 (Methods of Applied Mathematics), 16:642:550 (Linear Algebra and Applications), and 640:642:593 (Mathematical Foundations for Industrial and Systems Engineering) are intended as service courses for students in other graduate programs and are not approved for the Ph.D. program in mathematics.

Requests for transfer credit for courses taken at other universities are handled on a case-by-case basis, according to the rules of the department and the university.

Core Courses for the Ph.D. Program

The requirements for a Ph.D. in Mathematics include successful completion of an approved program. To be approved, a program should normally include the following five core courses:

  • 640:501 Theory of Functions of a Real Variable I (Offered every fall) (Outline of topics)
  • 640:502 Theory of Functions of a Real Variable II (Offered every spring)
  • 640:551 Abstract Algebra I (Offered every fall) (Outline of topics)
  • 640:552 Abstract Algebra II (Offered every spring)
  • 640:503 Theory of Functions of a Complex Variable I (Offered every fall) (Outline of topics)

Except in special circumstances, as approved by the graduate program director, first year students should take the five core courses during their first year. Much of the syllabus of the written qualifying exam comes from 640:501,640:503 and 640:551 Besides teaching specific mathematical content, these courses are aimed at giving you considerable experience writing mathematical proofs at a level expected of graduate students. We attempt to give you considerable feedback on your proofs.

Preparing for the core courses

New students - please go to this link Course Selection for Entering PhD Students (rutgers.edu) for information about the preparation expected of students entering - 640:501, 640:503 and 640:551. Students are encouraged to review this material in the months before the semester begins. Textbook information can be found on this link also.

Exemptions from taking core courses

A few entering students have already covered the material from one or more core course in sufficient detail that they may be exempted from taking the course. Students who wish to be granted such an exemption should contact the graduate program director (), explaining the reason for the requested exemption. Normally the reason for requesting an exemption is that you've taken a comparable course elsewhere. In this case, you would include with your request a syllabus for the course (including textbook, chapters covered and topics covered) as well as the grade received for the course. In evaluating such an exemption, we try to judge whether the mathematical content of the course taken is comparable to our core course, whether the course was taught at a level comparable to ours, and whether the course gave you sufficient mastery of writing proofs at the level expected of graduate students. You may be asked to provide some samples of written work (homework and/or exams) when you arrive at Rutgers, so please bring such material with you if you are requesting an exemption.

Receiving an exemption from a core course does not give you degree credit towards the 72 credits. There is a separate process for applying for transfer credit for graduate work completed elsewhere .

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, 1/8/24

Complex Analysis - Tuesday 1/9/24

Real Analysis - Wednesday, 1/10/24

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 2023 PDF

Fall 2022

Spring 2022



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 



Teacher Training Seminar

Satisfactory completion of the teacher training seminar during the Spring semester of the first year. While not required for the Ph.D., it is required for appointment to a TA position after the first year of studies.

Read more ...

Oral Qualifying Exam

An Oral Qualifying Exam (80 to 120 minutes in length) administered by a committee of four faculty on a specialized syllabus selected by the student in consultation with the Committee. Each student must select an Oral Qualifying Exam Committee Chair within one (1) calendar year of passing their Written Qualifying exams. In consultation with their Oral Exam Committee Chair, each student is strongly encouraged to schedule their Oral Qualifying Exam as early in their program as possible and no later than March 1 of their 6th semester in the program. The Oral Exam Committee Chair will usually become the student’s Research Advisor after passing the Oral Qualifying Exam and being admitted to Candidacy. Please see the Graduate Administrative Assistant for an Oral Qualifying Exam application packet. Return the completed application and exam syllabus to the Graduate Administrative Assistant in Hill 306 no later than one month before the exam.

Read more ...

Advancing to Candidacy

A student is designated a "Candidate for a Ph.D. degree" upon application to the graduate school, after completing the written, oral and foreign language exams (if required by the program; our program no longer has a foreign language requirement). This marks the official beginning of the student's dissertation work. A total of 72 credits with a minimum being 24 Research credits are required to receive a PhD degree.

Read more ...

Thesis Committee

The doctoral dissertation (or thesis) is completed under the direction of a thesis advisor, who must be a member of the Mathematics graduate faculty.

Read more ...


A written dissertation based on original research in Mathematics, completed under the direction of a member of the graduate faculty

Read more ...

Masters Degree Options

Traditional Option

For the traditional option, 30 credits of course work are required, chosen with the approval of the Graduate Director. At least 18 of these credits must be in courses offered by the Graduate Program in Mathematics. Specifically required are (i) one of the courses 16:640:501 Theory of Functions of a Real Variable I, 16:640:503 Theory of Functions of a Complex Variable I, 16:640:515 Ordinary Differential Equations, and 16:642:516 Applied Partial Differential Equations, (ii) 16:640:551 Abstract Algebra I and (iii) a course in computer science, statistics, or some area of applied mathematics within the department.

A master's essay is required, as well as a Final Master's Comprehensive Exam. There is no residency requirement.  The School of Graduate Studies doesn't require for you to submit your essay to their office.  With approval from the Graduate Director, you can use the passing of your Written Quals in place of writing an essay in Option 2, Section B.

Requests for transfer credit toward their degree for courses taken at other universities are handled on a case-by-case basis, according to the rules of the department and the university.

General requirements for graduate degrees at Rutgers are governed by the rules of the Graduate School - New Brunswick and are listed in the current catalog. These include how and when credit can be transferred and how many credits can be taken each semester.

Math Finance Option

For information about the Math Finance Option, please refer to their website: http://finmath.rutgers.edu/academics-finmath/degree-requirements-finmath