Passing grades on two General Examinations, chosen from Algebra, Analysis, and Topology. These written exams cover the following material: Algebra (MATH 7751, 7752), Analysis (MATH 7310, 7340), and Topology (MATH 7820, 7800). The Analysis exam is split into two parts: Complex and Real, which are taken and graded independently.
These exams are typically offered twice a year, January and August. A student may repeat the examinations as many times as needed in order to satisfy the following requirements:
Old policy (applies to students who started their graduate program before August 2025): Students are expected to attempt two different general examinations before the beginning of the third semester, to pass at least one general examination before the beginning of the fourth semester, and to pass both exams before the beginning of the sixth semester.
New policy (adopted in April 2025, applies to students who started their graduate program in August 2025 or later): Students are expected to attempt two different general examinations before the beginning of the third semester, to pass at least one general examination before the beginning of the fourth semester, and to pass both exams before the beginning of the fifth semester.
Syllabi for the Algebra, Analysis, and Topology General Examinations:
Below are old exams and study materials for each of the subfields.
Here is an updated Review Guide for algebra general exams (includes old exam problems sorted by topics up to and including Jan 22 exam).