## 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 (graddir@math.rutgers.edu), 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 48 credits. There is a separate process for applying for transfer credit for graduate work completed elsewhere .