Programs of study in mathematics that are offered lead to the degree of doctor of philosophy (Ph.D.) and master of science (M.S.). The M.S. degree comes in two options. The primary option is an M.S. with a concentration in mathematical finance, which is described in a separate listing in this catalog. There is also a standard option for the M.S., offering a more traditional mathematics program, but it is used infrequently.
Possible areas of specialization within the Ph.D. program include algebra and algebraic geometry, applied analysis, discrete mathematics, geometry and topology, Lie theory, logic, mathematical physics, nonlinear functional analysis, number theory, partial differential equations, variables, dynamical systems, and mathematical biology.
The program in mathematics is housed in the Hill Center for the Mathematical Sciences, a seven-story building on the Busch Campus. Hill Center and the adjoining CoRE Building house the computer science and statistics departments, the Center for Discrete Mathematics and Theoretical Computer Science, and the Mathematical Sciences Library. The library contains more than 27,000 volumes and subscribes to more than 300 research journals in pure and applied mathematics. Office space is provided to all full-time graduate students in mathematics. The graduate programs in biology, chemistry, physics, and engineering are located nearby.
Applicants to the Ph.D. programs must have a strong undergraduate background in mathematics and must submit scores from both the general tests and mathematics subject tests of the Graduate Record Examination (GRE). Financial aid through fellowships and teaching assistantships is available to qualified doctoral students.
The standard master of science program is a very small program, and students are accepted only in special circumstances. Students who are interested in this program are advised to contact the graduate program director (grad-director@math.rutgers.edu) before applying in order to determine whether their interests and circumstances are appropriate for the program.
It also is possible to apply for admission as a nondegree student. The GRE is not required for these applicants. As many as 12 credits of coursework taken as a nondegree student can count toward a degree if the student is subsequently admitted to a degree program.
All doctoral students must pass a two-stage qualifying examination before officially commencing work on their thesis. The first examination, a written one, is designed to ensure that Ph.D. graduates know certain basic material. Normally, it is taken at the beginning of the student's second year. The second examination, which is oral, normally is taken by the end of the first semester of the student's third year.
Students pursuing a Ph.D. in mathematics must take 48 credits in approved courses. Normally, this curriculum will include 16:640:501,502 Theory of Functions of a Real Variable, 16:640:503 Theory of Functions of a Complex Variable I, and 16:640:551,552 Abstract Algebra. Students should choose a program that gives them knowledge in a broad range of mathematics and/or its applications. In addition, students in the sequence must take 16:640:616,617 Seminar in Mathematics; acquire a reading knowledge of French, German, or Russian; complete 24 credits of research; and submit a doctoral dissertation. There is no residency requirement. Ordinarily, 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 not approved for the Ph.D. program in mathematics.
For the standard M.S. in mathematics, students select, with the approval of the graduate director, 30 credits of coursework. At least 18 of these credits must come from courses offered by the graduate program in mathematics. Specific requirements are: (1) one of the following courses: 16:640:501 Theory of Functions of a Real Variable I, 16:640:503 Theory of Functions of a Complex Variable I, 16:640:515 Ordinary Differential Equations, and 16:642:516 Applied Partial Differential Equations; (2) 16:640:551 Abstract Algebra I; and (3) a course in computer science, statistics, or some other area of applied mathematics offered by the department. There is no residency requirement, but a master's essay is required.
The graduate program offers about 25 graduate courses each semester from the list of graduate courses in this chapter. Courses are scheduled based on program needs, student demand, and faculty availability.
