Mathematics Ph.D. Degree

The doctoral program prepares students for a career in research and teaching at the university level or in basic research in a non-academic setting.

Admission and Entry

1. Application requirements:
   • Deadlines: March 1 (Fall, Summer), February 15 (Spring) September 15 (Winter). Apply online.
   • Entrance examinations: General and Math Subject GRE. Every applicant whose native language is not English is required to take the Test of English as a Foreign Language (TOEFL).
   • Three letters of recommendation.
2. Prerequisites:
   • Undergraduate degree in mathematics or its equivalent.
   • One year of mathematical analysis (or advanced calculus).
   • One year of abstract algebra, including linear algebra.

Requirements for Degree

1. Credit Hours (54): Minimum 36 coursework hours in mathematics courses numbered 600 or above with a grade of B or better in each plus 18 dissertation hours (Math 799R). No credit is given for mathematics courses with numbers lower than 510.
2. Required Courses: Complete at least 3 hours each in algebra, analysis, applied mathematics, and geometry/topology.
3. Examinations:
   1. Written Examinations: At the beginning of the second year after admission to the Ph.D. program, the student is required to pass examinations in three of the four areas of algebra, analysis, applied mathematics, and geometry/topology. Four hours are allotted to each examination. A failed examination may be repeated once at the beginning of the winter semester of the student's second year, after which permission must be obtained from the department graduate committee to retake the examination. Passed examinations need not be repeated. Syllabi are available for each examination.
   2. Oral Examination: A student must pass an oral qualifying examination covering the background necessary for research in a specific area. The student, having chosen a research area and having a dissertation advisor approved, will, with the advisor, outline suitable examination topics. These topics must be approved by an examination committee of three (including advisor) appointed by the department graduate committee, which conducts the examination.
   3. Defense of Dissertation: A final oral defense of the dissertation is conducted by a faculty committee consisting of the student's research advisor, two other readers of the dissertation (one of whom may be an outside examiner), and two other members of the faculty.
4. Language Requirement: Demonstrate proficiency in an approved foreign language that is currently in major use in the mathematical literature. The approved languages are French, German, Russian, Italian, Japanese, and Chinese. In certain cases another language may be substituted for one of these if the department graduate committee approves. The committee will consider the current usage in the student's specialty area. The preferred avenue for the completion of the language requirements is the intensive reading course offered by the language department involved (such as French 121).
   
   Two other alternatives are considered suitable:
1. Course credit for the standard undergraduate sequence at the level of the GE math/foreign language requirement (or exam credit at the same level).
2. Exam of mathematics translation with occasional use of a dictionary. The examinations are prepared and offered by the Mathematics Department on a by request basis. They are designed to test a student's ability to translate foreign mathematical literature into scientifically correct English.
5. Dissertation

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