The Mathematics Ph.D. program at Rutgers includes two qualifying examinations, a written exam and an oral exam . The written exam is taken first and covers advanced calculus, elementary topology (metric spaces, compactness, and related topics), and the material of 501 (real analysis), 503 (complex analysis), and 551 (algebra). It is offered twice a year, near the beginning of each semester.

The syllabus represents a common core of material required of all Rutgers Ph.D.’s. In particular, the exam is designed with the goal that a pass on this exam shows a level of mathematical knowledge and ability appropriate for teaching the central undergraduate classes in mathematics.

Each student is required to take the exam by the beginning of the student’s second year; 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 fail this exam may take it again during the semester following the one in which the exam was failed. 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.

The exam is a six hour written exam, taken over two days. Each day, the exam consists of two parts. Part I has 3 problems. and part II has 6 problems, and each student is expected to submit solutions to all 3 problems in part I, and 3 out of the 6 problems in part II.

Prior versions of the exam.

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