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. Students are expected to attempt two different general examinations by August of their second year, to pass at least one general examination by January of their second year, and to pass both exams by January of the student's third year. A student may repeat the examinations as many times as needed in order to satisfy these requirements.
Current 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).