The Qualifying Exam

The qualifying exam is designed to measure the breadth of students’ knowledge in mathematics. While some students are able to pass the qualifying exam in one try, passing the exam early is mainly an indication that a student has attended an undergraduate university with a broad undergraduate program in mathematics. It is not a good predictor of the quality of the eventual PhD dissertation.

Students are required to take the qualifying examination at the beginning in the first term. The exam may prove a useful diagnostic in helping to identify areas in which a student’s knowledge is weak. There is no stigma attached to taking the exam several times, but students are expected to pass the examination by the second year in residence in order to begin more specialized study leading to research work.

The department runs tutorials and offers several introductory graduate courses (e.g. Math 212a, 213a, 230a, 231a, and 232a) to help students acquire the necessary broad basic background in mathematics to pass the exam.

The exam consists of three, three-hour papers held on consecutive afternoons. Each paper has six questions, one each on the subjects: Algebra, Algebraic Geometry, Algebraic Topology, Differential Geometry, Real Analysis and Complex Analysis. Each question carries 10 points. In order to pass each subject, students must obtain at least 20 of the 30 points in that subject. Students are considered to have passed the qualifying exam when they have passed in all six subjects (120 of 180 points) in one sitting, or they have passed at least four subjects in one sitting and obtained an A or A- grade in the basic graduate courses corresponding to the subject(s) not passed. Students are expected take the recommended course(s) at the first opportunity.

Once students have passed the qualifying exam, they no longer need to take math courses for a letter grade and may elect to receive the grade (EXC) excused. Students should inform the instructor at the beginning of the term if they elect to take (EXC) as a grade.