Questions from Past Qualifying Exams

The following list has links to the questions from past Qualifying Examinations, arranged by topics. The first link is to a ps version of the file. If you click on it you should be able to view it using your navigator (or a ps viewer attached to it, such as ghostview). The second link is to the raw TeX file that generated the ps version. It is a plain TeX file. You are welcome to download it for personal use in preparing for your Qualifying exam. By clicking on the link, your viewer should prompt you for a filename to download it to. Once you have it locally, invoke TeX (not LaTeX) to get the .dvi file.

If you have taken your Qualifying exam and you have questions that do not appear here (especially if they are for some of the topics with few questions, or from a topic we do not have covered yet), or if you have any comments or questions, let the MGSA know.

Here's the index of the Qual questions files; the number in brackets is how many questions are currently in the file.

• Algebraic Geometry [52]: PS Version and TeX Source file.
• Algebraic Topology [42]: PS Version and TeX Source file.
• Banach Spaces and Spectral Theory [21]: PS Version and TeX Source file.
• $C^*$ and von Neumann algebras [13]: PS Version and TeX Source file.
• Combinatorial Game Theory [10]: PS Version and TeX Source file.
• Combinatorics and Combinatorial Algorithms [20]: PS Version and TeX Source file.
• Commutative Algebra [57]: PS Version and TeX Source file.
• Complex Analysis [44]: PS Version and TeX Source file.
• Computation Complexity [12]: PS Version and TeX Source file.
• Differential Topology [33]: PS Version and TeX Source file.
• Dynamical Systems (Symbolic and Otherwise) [7]: PS Version and TeX Source file.
• Fields and Galois Theory [36]: PS Version and TeX Source file.
• Fluid Mechanics [5]: PS Version and TeX Source file.
• Foundations and Set Theory questions, from the Logic Quals [58]: PS Version and TeX Source file.
• General Algebra [3]: PS Version and TeX Source file.
• General Topology [9]: PS Version and TeX Source file.
• Geometry, Riemannian and Symplectic [40]: PS Version and TeX Source file.
• Group Theory [45]: PS Version and TeX Source file.
• 3-manifolds, 4-manifolds, knots [59]: PS Version and TeX Source file.
• Measure Theory and Real Analysis [14]: PS Version and TeX Source file.
• Non-commutative Ring Theory [18]: PS Version and TeX Source file.
• Number Theory [51]: PS Version and TeX Source file.
• Numerical PDE's and ODE's [8]: PS Version and TeX Source file.
• Ordinary Differential Equations [4]: PS Version and TeX Source file.
• Partial Differential Equations [8]: PS Version and TeX Source file.
• Probability [12]: PS Version and TeX Source file.
• Representation Theory, Lie Groups, Lie Algebras [14]: PS Version and TeX Source file.
• Semigroups [8]: PS Version and TeX Source file.
• Universal Algebra and Category Theory [13]: PS Version and TeX Source file.

Other resources (all LaTeX):

• Danny Calegari's annotated low-dimensional topology syllabus is here
• Danny Calegari's sample low-dimensional topology questions with solutions is here
• Douglas Squirrel's problems in Algebraic Geometry, Number theory and Complexity theory with solutions is here

To the MGSA's homepage.

Last Modified: July 28, 1999