A strong background and ability in mathematics are important for successful completion of the program. A minimal mathematics prerequisite for entering PhD students is a thorough working knowledge of the material covered in a two-semester introductory calculus sequence.
The entering student must be able to use mathematics as a language, translating verbal descriptions of phenomena into the appropriate mathematical framework. Students with some background in linear algebra, the elements of optimization, and probability and statistics will be better prepared for required course work.
Residence and Course-Credit Requirements
To maintain good standing as a PhD candidate, a student must be registered for two terms out of three during the trimester academic year, although once involved in research toward a thesis, students are generally expected to be in residence in all three terms. Satisfactory completion of 20 full-time courses is required for the PhD degree. The exact number and selection of courses is determined by the student in consultation with faculty members in the major field.
Normal course loads during the autumn and spring terms are four to five courses per term; summer-term course loads are generally lighter, with heavier emphasis on research work. Students receiving financial aid often serve as teaching or research assistants; a maximum of two assistantships per term is allowed. PhD candidates are allowed, but not encouraged, to take one in five courses for R (registration) credit. The other courses must be taken for letter grade credit (H = honors; HP = high pass; P = pass; LP = low pass; F = fail). Students are expected to take courses in their major fields for letter-grade credit.
Up to 10 courses of relevant graduate work completed at Columbia or at another university may be credited toward the course requirement for the degree. If a student has completed more than 20 graduate courses at Columbia before entering the PhD program, he or she may be granted a maximum of 15 courses of advanced standing. The advanced standing granted depends on the assessment by the Doctoral Committee of the quality and relevance of the work. Credit for advanced standing is not conferred until the PhD student has successfully completed at least one term in the program.
Students must satisfy requirements in the following areas:
- Breadth Requirements
- Field Examination
- Oral Examination
Students entering the doctoral program with only a bachelor’s degree are required to take two courses from the other divisions of the Business School: Accounting; Decision, Risk and Operations; Finance and Economics; Management; and Marketing. For students entering the program with a graduate-level degree other than an MBA or its graduate equivalent, this requirement may be waived, subject to approval of the doctoral coordinator. Students holding an MBA or its equivalent are automatically exempt from the breadth requirement.
The student demonstrates proficiency in the major field by passing comprehensive written examinations.
In the oral examination, a student’s preparation to do independent research is evaluated, in-depth knowledge within the major field is examined, and ability to relate basic knowledge from other areas to the major field is tested. The student will present a dissertation proposal and must answer questions not only on the proposal but also on relevant background.
The oral examination is normally held within one year after the written major field examination. The oral examination committee is usually composed of four faculty members. At least two committee members are chosen from the student’s major field.