Because of the diversity of the Columbia environment, students in all programs have a wide range of research options. Course requirements for each graduate student are determined individually. Previous training and specialized research interests are weighed. First-year students work with an assigned advisor until they choose a research sponsor, who also serves as permanent advisor. Sponsors are selected from among the department faculty, joint faculty members, and other engineering and science faculty.
All students take a written qualifying examination at the end of the first year.
In addition, an oral examination is required, usually before the end of the second year. As part of the oral examination, applied physics and applied mathematics candidates formally present their thesis proposals. Course work for the doctorate is generally completed during the first two years. Research work is begun during or at the end of the first year. Doctoral candidates are expected to complete degree requirements and defend their theses within five years of residence at Columbia.