입학 요건 Columbia University
Admission to the PhD program in Decision, Risk, and Operations is highly competitive. Superior academic performance is expected, and a strong background in and facility with mathematics are essential for the successful completion of the program.
The entering student must be able to use mathematics as a language, translating verbal descriptions of phenomena into the appropriate mathematical framework(s). Students with some background in linear algebra, the elements of optimization, and probability and statistics will be better prepared for required course work. At a minimum, a thorough working knowledge of a two-semester introductory calculus sequence is required.
Application Materials
Essay
The Decision, Risk and Operations Division is interested in your reasons for pursuing doctoral studies. Please describe them in an essay that is less than 1000 words.
Research Paper
Applicants are encouraged to submit a research paper as part of their application, if they have one. The application form provides the option to submit a research paper under Essays.
Recommendation Letters
Two letters of recommendation are required. However, a total of four may be submitted.
Transcripts
A bachelor's degree or the equivalent (i.e., a four-year course of study in an accredited college or university) is required for admission. A master's degree is not required, although many applicants have a master's degree in such fields as management, economics, psychology, sociology, and statistics. Superior academic performance is expected.
GMAT or GRE
The GMAT or GRE is required for all applicants to the Decision, Risk, and Operations Division.
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Further information
If you aren't eligible for the above entry requirements, you might ant to explore pathway options at Columbia University. If you want to find out more, speak to our counsellors.