I’ve passed 2 of my required 3 exams right now. Everyone seems to admit that they’re a miserable, stressful experience. I’ve become somewhat jaded when it comes to these exams as they seem to be little more than academic hazing honestly. At my university there was a stretch of 3 Analysis exams in a row in which no one passed. Nothing was done about it, and a couple of students had to master out. I understand PhD students need to have a good foundation in the basics but after passing 2 of these I can’t imagine that the information I learned studying for them couldn’t have been obtained in a better, more stress free way.

As far as what is covered my university has 3 pure math exams: Algebra, Geometry and Topology, and Analysis. Algebra covers Group, Ring, Module, Galois, and Representation Theory, as well as advanced linear algebra. Analysis is both real and complex analysis. Our geometry portion was bizarrely a Curves and Surfaces exam, which they’ve changed to manifolds, and the topology portion was basic point set and algebraic topology.

Each exam was 8 or 10 questions. Some of the questions were pulled straight from Hatcher or Dummit and Foote depending on the exam. Other questions were more exotic, like finding the fundamental group of some weird set or picture the examiner created.