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Q&A Grad School Experience Year II Part III
This article is part of a series of articles where I repurpose some of the questions I have answered on Quora about being a Ph.D. student and what graduate study in mathematics is like. The previous installment is located here. Note that these responses are largely reflections of my personal experience and are only partially based on fact.
What are the preliminary examination requirements for your doctoral degree?
My program (math Ph.D., University of Tennessee) technically has two sets of these exams.
The first is called the diagnostic, and tests proficiency of certain undergraduate-level mathematics courses upon entry. There was one examination on one-variable real analysis (no Lebesgue theory), and one examination on linear algebra (finite-dimensional vector spaces). Both exams were reasonable in my opinion, and fit the scope and level of difficulty of 300-level real analysis and linear algebra courses I took as an undergraduate at Carnegie Mellon. Students who don’t pass upon entry take honors undergraduate level real analysis and linear algebra during their first year and retake the diagnostic thereafter. Each exam is scored and evaluated individually, so it’s possible to pass one and fail the other.
The second, more difficult and broad exams are the preliminary exams (abbreviated…