Problem bank
Beginning with the September 2025 exam, all problems will be drawn from a public "problem bank." This bank contains two types of problems: template problems and pool problems.
Template problems
Template problems are generally computational with easily adjustable specifics. These types of problems are especially prevalent in linear algebra. Examples include problems such as:
- analyzing a geometrically-given linear transformation for specific properties such as eigenvalues or diagonalizability; e.g., see March 2025 (Problem 5) or Spring 2019 (Problem 1)
- counting the number of morphisms between two specific group; e.g., see Spring 2017 (Problem 4) or Fall 2015 (Problem 1)
Template problems are available below:
- Template problems in linear algebra
- Template problems in group theory
- Template problems in ring theory
Pool problems
Pool problems make up the rest of the problem bank, and include all problems that are not easily adjustable. These problems, when chosen, will usually be asked as is.[1]
Pool problems are available at the links below:
Related pages
Home for the Algebra Qual
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Past exams
Changelog
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