Program

The Department of Mathematics and Computer Science at Rutgers University-Newark offers the Doctor of Philosophy (Ph.D.) degree in Mathematical Sciences. The graduate faculty provides research opportunities in many fields of specialization, including algebra, 4-manifolds, geometric group theory, Kleinian groups and Teichmüller theory, low-dimensional topology, differential geometry, algebraic geometry, mathematical physics, number theory, and representation theory in pure mathematics. Joint with the Cognitive and Data Science (CoDaS) Lab at Rutgers University- Newark, our program also offers advanced research training in machine learning and modern Artificial Intelligence(AI).

The program is designed to provide students majoring in pure mathematics with a broad and deep knowledge of both classical and modern methods in the mathematical sciences and provide students majoring in data science with research training in machine learning and Artificial Intelligence. In addition, students gain experience in applying this knowledge to problems in the sciences and engineering.

Individuals entering with a bachelor's degree normally spend their first two years in coursework and in preparation for the Ph.D. qualifying examination. They take that examination no later than the fall semester of their third year. Students are encouraged to take a range of courses in both pure and applied mathematics to help decide the research direction they will pursue.

The Ph.D. curriculum is divided into two options: pure mathematics and applied mathematics. The applied mathematics program is administered by the New Jersey Institute of Technology. Students in the pure mathematics track are required to take 26:645:611 Real Analysis I, 26:645:612 Real Analysis II, 26:645:621 Complex Variables I, 26:645:631 Algebra I, 26:645:632 Algebra II, 26:645:641 Topology I, 26:645:642 Topology II, and 26:645:643 Differentiable Manifolds. The above course requirements may be waived for students with advanced degrees who have completed equivalent coursework.

Additionally, all students are required to take at least 12 credits of advanced elective courses. These electives are chosen in consultations among the student, the student's adviser, and the advisory committee, and with the permission of the graduate program director.

The Ph.D. qualifying examination for students choosing the pure option consists of three parts, with each part covering the basic topics in a particular subdiscipline. Part A consists of real and complex analysis, Part B tests a student's knowledge of algebra, and Part C covers topology and geometry. After successful completion of the exam, students begin their doctoral research under the direction of a faculty member. All students are required to take at least 24 credits of doctoral dissertation research. Upon completion, the dissertation is presented to a thesis committee, which conducts a final oral examination.

More information about the program, the department, and the faculty may be obtained by visiting the program's website at https://www.gsn.newark.rutgers.edu/mathematical-sciences.

General information related to the Graduate School's Academic Policies and Procedures and Degree Requirements can also be found within this catalog.