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Language Requirement

Doctoral candidates in the Department of Mathematics must pass a language exam in one of the following languages: Chinese, French, German, or Russian. Native speakers of the language and students who have spent two or more years in a country in which the language is commonly spoken may request an exemption from the requirement.

The exam in each language is offered once a year. A faculty member chooses a few pages of mathematical text in the language, and the student must write down an English translation within a two-hour period. The mathematical content of the text is to be accessible to a first-year graduate student; samples are provided below, but the actual text of each semester's exam is revealed only at the exam. The student may bring a dictionary to use during the exam.

The purpose of the requirement is not to require fluency in any of the languages, but to encourage students to develop the minimal skills needed to read the mathematical literature in a language other than English.

Sample Texts