NYU Courant Institute Columbia APAM

PhD Training


One of the main goals of this research and training group is to provide PhD students with a direct experience in all ingredients of scientific software and the underlying numerical analysis and mathematical models, from construction of mathematical models and development of numerical methods, to analysis of the likely computing environments and high-performance software design.

RTG-supported PhD students enroll in one of the 3 participating PhD programs:

and are expected to complete all program requirements.

RTG fellowships include an 11-month stipend ($25,000 in 2006/7), for three years, conditional on successfully passing an annual review of academic and research progress.

Students are expected to complete teaching requirements of their PhD programs.


Each RTG-supported graduate student will be assigned two faculty mentors whose combined expertise covers both applied and computational mathematics and scientific software. These faculty members will guide the student in formulating his/her program of studies and research agenda and in choosing a research advisor. Both mentors are expected to remain in close touch with the student and his/her work throughout the rest of the student's graduate career.


Each student follows an individualized curriculum, designed in cooperation with student's mentors, and approved by the RTG graduate program director at student's school. A selection of courses most closely related to RTG goals can be found at the RTG Web site.

In addition to the courses and exams required by each PhD program, for RTG-supported students will be strongly encouraged to take courses in fields such as biology, physics, neural science, chemistry, mechanical engineering, and electrical engineering. A cross-registration program is already in place so that students can benefit from course offerings at Columbia and NYU.

Research training and Internships

The structure of the expected research training for students is based on our goal of enhancing the two-way flow between the mathematical sciences and scientific software. Since the quality of such software depends on the underlying mathematics, the research of all students must contain an analytical component.

Similarly, students are expected to have substantial involvement in a research project in scientific computing, with personal responsibility for a significant part of high-quality research software. A variety of options are available for students for either type of research; a specific option is selected by the students with the help from the mentors.

Each RTG-supported Ph.D. student will be expected to have at least one summer internship at a government laboratory or in industry. The senior personnel will help to arrange these internships through their professional contacts.

Students are expected to attend a student research seminar and give at least one presentation a year.