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Requirements for the PhD in Mathematics at the School of Engineering are primarily qualitative rather than quantitative. That being said, you must satisfy certain credit and course obligations. The number of graduate units usually associated with graduation from this PhD program equals 75 credits, with each course worth 3 credits. You must select them from a well-balanced program in 1 major and 2 minor fields. We encourage you to choose minor fields outside the Department of Mathematics, such as those in applied mechanics, financial engineering, control theory, computer science, traffic engineering, or electrical engineering.

Thirty-nine credits of coursework and at least 21 credits of thesis are required. You must earn a grade of B or better for a non-core course to satisfy degree requirements (core-courses require a grade of A). You must also be able to read mathematical text written in French, German, or Russian.

Required Core Courses (12 Credits)

You must take the following courses and receive a grade of A in each. You may repeat them, if necessary.


You are required to pass the following:

  • A Part 0 written examination covering fundamental topics
  • A Part 1 written examination covering real and complex analysis, as well as linear and abstract algebra
  • A Part 2 oral examination on topics chosen by you and your thesis adviser


After passing the Part 2 examination, you must write a dissertation under the supervision of a faculty adviser. You must pass a public oral exam on your dissertation as the final requirement of the PhD degree.