This page provides information about planning for and selecting your first year courses. You should also consult your faculty mentor, who will be assigned to you sometime during the summer.
While it's worth thinking about what you will take over the summer, there is no need to formally register for classes until you arrive at Rutgers. Although continuing PhD students should register courses as soon as the registration is open, almost all incoming mathematics Ph.D. students register online during the days just before classes start.
Course requirements
The requirements for a Ph.D. in Mathematics include successful completion of an approved program consisting of 72 credits, of which at least 24 must be research credits. To be approved, a program should normally include the following three core courses in the first semester:
- 640:501 Theory of Functions of a Real Variable I (Offered every fall) (Outline of topics)
- 640:551 Abstract Algebra I (Offered every fall) (Outline of topics)
- 640:503 Theory of Functions of a Complex Variable I (Offered every fall) (Outline of topics)
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.
Selecting your courses
Sometimes an entering student is concerned that he or she may not be ready to take one or more of the core courses. Such students should contact the graduate program director (preferably during the summer) so that we can make an appropriate plan for the student's first semesters here.
The normal course load for first year students is three courses for students holding a TA position or having other outside obligations, and three or four courses for students on fellowship.
For international students: When you arrive, you will be tested in English, and may be required to take an English course for one or more semesters. Further information about this will come from the international student center and the graduate school.
Moving forward, 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.
Preparing for the core courses
Here are links to 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 for the core courses can be found from the course pages.
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 not only whether content of the course taken is comparable to the core course, but also that the course was taught at a high enough level. 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 48 credits. To apply for transfer credit for graduate work completed elsewhere, you should consult with the graduate program director sometime during the first semester.