Algebra Qualifying Exam

Here is some assorted material related to the Algebra Qualifying Exam. This page has been created by graduate students, so, as always, you should consult the official graduate program page for official information.

Guillermo Mantilla's SEP Notes

In the summers of 2008, 2009, 2010 Guillermo Mantilla ran a well-regarded summer enchancement program in algebra preparing for the qualifying examination. Guillermo wrote up a set of notes covering the material that appears on the qualifying exam. Links appear in the order presented in class, not the order of the respective problems on the exam.

• Linear Algebra
  • Linear Algebra I
  • Linear Algebra II (inner products)
  • Linear Algebra III (Jordan Form)

• Group Theory
  • Group Theory I
  • Group Theory II (group actions)
  • Solvable & Nilpotent Groups
  • Theorems for non-simplicity
    • Non-simplicity proofs for groups of order < 1000

• Field Theory
  • Field Theory I
  • Field Theory II

• Ring Theory
  • Modules
  • Commutative Rings