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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.  The normal minimum grade for graduate courses is B.

The School of Graduate Studies expects all students to maintain satisfactory academic progress at all times.  Failure to maintain satisfactory academic progress may affect the student’s eligibility for financial support and awards, prolong the time to degree, and, if not remedied, may lead to academic warnings and possible dismissal. Programs must conduct periodic reviews of academic performance, including courses completed and grades, no less frequently than once per semester.  Academic review includes written warnings to any student who may not be maintaining satisfactory academic progress.    

Satisfactory academic progress requires all of the following:

  • GPA of 2.5 or higher for students who have attempted 12 or fewer credits
  • GPA of 3.0 or higher for students who have attempted 13 or more credits
  • No more than one grade of “U” in courses that are graded S/U
  • No more than two Incompletes that have been on record for two semesters, unless there are documented and acceptable reasons for the Incompletes along with a plan to complete the work.
  • No more than two Permanent Incompletes on the transcript.
  • No more than 9 credits of C or C+ may be used to meet degree requirements.

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 16:642:593 (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 requirements:

Students should complete the following 3 core courses during their first semester:

Click here  https://mathanalysis.pages.dev/notes for comprehensive and self-contained lecture notes for Math 501 (Real Analysis I) and Math 503 (Complex Analysis).

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. Students who pass a Written Qualifying Exam in Algebra, Real Analysis, or Complex Analysis with a sufficiently high score may continue to request an exemption from taking the corresponding first semester required course (640:501, 640:503, or 640:551), which must be approved by the Graduate Program Director.

Students should complete 3 courses from a menu of additional courses within their first two academic years and not all chosen from the same area (Algebra or Analysis or Applied Mathematics or Geometry & Topology). The current Menu of Additional Courses is

Algebra

  • 640:535 – Algebraic Geometry I
  •  640:550 – Lie Algebras
  • 640:552 – Abstract Algebra II
  • 640:561 – Mathematical Logic
  • 640:571 – Number Theory I

Analysis

  • 640:502 – Theory of Functions of a Real Variable II
  • 640:504 – Complex Analysis II
  • 640:507 – Functional Analysis I
  • 640:515 – Ordinary Differential Equations
  • 640:517 – Partial Differential Equations I

Applied Mathematics

  • 642:561 – Introduction to Mathematical Physics I
  • 642:573 – Numerical Analysis I
  • 640:577 – Introduction to Mathematical Probability Theory I
  • 642:581 – Graph Theory
  • 642:582 – Combinatorics I
  • 642:583 – Combinatorics II (does not require 642:582 – Combinatorics I as a prerequisite).

Geometry and Topology

  • 640:532 – Introduction to Differential Geometry I
  • 640:540 – Introduction to Algebraic Topology I
  • 640:548 – Differential Topology
  • 640:549 – Lie Groups

Courses in the menu of additional courses have formal requirements that go beyond attendance (such as regularly assigned and graded homework or midterm exam(s) or a final exam or a final paper). Each menu course has explicit prerequisites to ensure that students have the required background for that course, and prerequisites for each course can be found under Course Descriptions www.math.rutgers.edu/academics/graduate-program/course-descriptions. Students with appropriate background may request approval from the Graduate Program Director  to instead take alternative courses that are not on the menu.

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 .